(19)
(11)EP 0 168 969 B1

(12)EUROPEAN PATENT SPECIFICATION

(45)Mention of the grant of the patent:
23.08.1989 Bulletin 1989/34

(21)Application number: 85304262.0

(22)Date of filing:  14.06.1985
(51)International Patent Classification (IPC)4H03K 4/02, G06F 7/548

(54)

A method and digital circuit for generating an approximate sinusoidal waveform

Verfahren und digitale Schaltung für die Erzeugung einer angenäherten Sinuswellenform

Méthode et circuit numérique pour la génération d'une forme d'onde approximativement sinusoidale


(84)Designated Contracting States:
AT BE CH DE FR GB IT LI LU NL SE

(30)Priority: 15.06.1984 US 620993

(43)Date of publication of application:
22.01.1986 Bulletin 1986/04

(73)Proprietor: ADVANCED MICRO DEVICES, INC.
Sunnyvale, CA 94088-3453 (US)

(72)Inventor:
  • Taylor, David
    San Jose California 95148 (US)

(74)Representative: Wright, Hugh Ronald et al
Brookes & Martin 52/54 High Holborn
London WC1V 6SE
London WC1V 6SE (GB)


(56)References cited: : 
FR-A- 2 237 363
US-A- 4 328 554
  
      
    Note: Within nine months from the publication of the mention of the grant of the European patent, any person may give notice to the European Patent Office of opposition to the European patent granted. Notice of opposition shall be filed in a written reasoned statement. It shall not be deemed to have been filed until the opposition fee has been paid. (Art. 99(1) European Patent Convention).


    Description


    [0001] The present invention relates to a method and digital circuit for generating an approximate sinusoidal waveform.

    [0002] The invention will be described with reference to voltage controlled oscillators (VCOs) and to a method for approximating sinusoidal waveforms with trapezoidal waveforms in a manner which can be implemented within an arithmetic logic unit (ALU) structure.

    [0003] VCOs are used in many applications, such as frequency synthesis, modulation, demodulation, frequency multiplication and clock synchronisation. VCOs are often used as part of a phase lock loop in such applications. As the name implies, a voltage is used to control the frequency of the VCOs output signal.

    [0004] Many VCOs are analogue devices which require circuitry dedicated to the particular function involved and can generate a range of frequencies determined by the characteristics of the resistors, capacitors, transistors and other devices used.

    [0005] Other VCOs are digital devices which generate square waves or triangular waves. Square waves and triangular waves have harmonic frequencies with significant amplitudes and thus their suitability for many applications is limited.

    [0006] It is known that a trapezoidal waveform can be produced by a digital VCO, and that a trapezoidal waveform has harmonics that are smaller than those of a square wave or a triangular wave. The known method uses a digital circuit which, in a succession of equal time intervals, first generates a point on a triangular waveform having a period equal to that of the sinusoidal waveform being approximated, and then generates a corresponding point on a trapezoidal waveform. A positively sloped portion of the triangular waveform is defined by repetitiously adding an incremental value until the ALU saturates at its maximum value. A negatively sloped portion of the triangular waveform is then defined by repetitiously subtracting the incremental value until the ALU saturates at its minimum value. The trapezoidal waveform is created by truncating the peaks of the triangular waveform.

    [0007] The incremental value chosen must be small in order to minimize the phase error introduced by the amount of the incremental value in excess of the maximum amplitude at the saturation point of the ALU. Because the size of the incremental value is so limited, the range of frequencies that can be generated by this method is limited. This is because for high frequencies, a much higher sampling rate must be used to generate small incremental values relative to the period of the generated signal. The disadvantage of a large sampling rate is that a large number of calculations are required, thus reducing the availability of the ALU for other calculations. The present invention substantially mitigates or solves these problems.

    [0008] The present invention is a method and a circuit for producing a trapezoidal waveform approximating a sinusoidal waveform. The method provides for generating a triangular waveform and then truncating it to form a periodic waveform. The triangular waveform is generated by repetitiously adding an amplitude increment during a succession of equal time intervals to generate points on the positive slope of the triangular wave until a maximum value is reached. The time interval is determined by the desired sampling rate. The amplitude increment is proportional to the phase change of the desired sinusoidal frequency during the time interval. The maximum value is determined by a formula from the phase change and the amplitude increment. When the maximum value is exceeded, the slope of the triangular waveform is changed to negative and the next point is determined by subtracting the portion of the amplitude in excess of the maximum from the maximum value. Thereafter, the points on the negative slope are determined by repetitiously subtracting the amplitude increment until the minimum value is reached. At that time, the slope is changed to positive and the next point is determined by adding the portion of the amplitude increment beyond the minimum value to the minimum value. The triangular waveform produced is then truncated at a value equal to two-thirds of the maximum value to produce a trapezoidal waveform.

    [0009] Thus the present invention provides a method for generating an output time varying signal that approximates a signal having a sinusoidal waveform, comprising the steps of:

    selecting a time interval equal to a fraction of the period of the sinusoidal waveform;

    selecting a maximum value and a minimum value of the same numerical value but of opposite sign which are one and one-half times the desired maximum and minimum amplitudes of the output signal;

    determining a phase increment equal to the change in phase of the sinusoidal waveform during the time interval;

    determining an amplitude increment equal to the phase increment multiplied by twice the maximum value and divided by pi;

    forming the positively sloped portion of a triangular waveform by repetitiously adding the amplitude increment to create an amplitude value at each time interval until the maximum value is reached;

    changing the slope of the triangular waveform in the time interval in which the maximum value is exceeded by subtracting the portion of the amplitude increment in excess of the maximum value from the maximum value to create the next amplitude value;

    forming the negatively sloped portion of the triangular waveform by repetitiously subtracting the amplitude increment to create each amplitude value until the minimum value is reached;

    changing the slope of the triangular waveform in the time interval in which the minimum value is exceeded by adding the portion of the amplitude increment beyond the minimum value to the minimum value to create the next amplitude value; and

    truncating the resulting triangular waveform to form a trapezoidal waveform.



    [0010] The present invention also provides a digital circuit for generating an output time varying signal that approximates a signal having a sinusoidal waveform, comprising:

    means for providing a time interval equal to a fraction of the period of the sinusoidal waveform;

    means for providing a maximum value and a minimum value of the same numerical value but of opposite sign which are one and one-half times the desired maximum and minimum amplitudes of the output signal;

    means for providing a phase increment equal to the change in phase of the sinusoidal waveform during the time interval;

    means for providing an amplitude increment equal to the phase increment multiplied by twice the maximum value and divided by pi;

    means for forming the positively sloped portion of a triangular waveform by repetitiously adding the amplitude increment to create an amplitude value at each time interval until the maximum value is reached;

    means for changing the slope of the triangular waveform in the time interval in which the maximum value is exceeded by subtracting the portion of the amplitude increment in excess of the maximum value from the maximum value to create the next amplitude value;

    means for forming the negatively sloped portion of the triangular waveform by repetitiously subtracting the amplitude increment to create each amplitude value until the minimum value is reached;

    means for changing the slope of the triangular waveform in the time interval in which the minimum value is exceeded by adding the portion of the amplitude increment beyond the minimum value to the minimum value to create the next amplitude value; and

    means for truncating the resulting triangular waveform to form a trapezoidal waveform.



    [0011] An analog signal can be produced from this digital representation of a trapezoidal waveform by interpolating to produce closely spaced points on the trapezoidal waveform and then pro- .cessing the result through a digital-to-analog converter.

    [0012] Another aspect of the present invention is that an accurate range of frequencies around a center frequency can be produced. The phase change of the center frequency during the sampling time interval is first determined. An additional phase change corresponding to the desired change in frequency is then added or subtracted. The new value is used to determine the amplitude increment, and the waveform is then generated according to the described method.

    [0013] Thus the present invention also provides a method for utilizing an input signal to generate an output signal that approximates a sinusoidal waveform with a frequency which varies by a specified amount from the frequency of the input signal waveform, comprising the steps of:

    [0014] selecting a time interval equal to a fraction of the period of the input signal;

    [0015] selecting a maximum value and a minimum value of the same numerical value but of opposite sign which are one and one-half times the desired maximum and minimum amplitudes of the output signal;

    [0016] determining a phase increment equal to the change in phase of the input signal during the time interval plus a value equal to the additional phase change of the desired output signal during the time interval;

    [0017] determining an amplitude increment equal to the phase increment multiplied by twice the maximum value and divided by pi;

    [0018] forming the positively sloped portion of a triangular waveform by repetitiously adding the amplitude increment to create a new amplitude value at each time interval until the maximum value is reached;

    [0019] changing the slope of the triangular waveform in the time interval in which the maximum value is exceeded by subtracting the portion of the amplitude increment in excess of the maximum value from the maximum value to create the next amplitude value;

    [0020] forming the negatively sloped portion of the triangular waveform by repetitiously subtracting the amplitude increment to create each amplitude value until the minimum value is reached;

    [0021] changing the slope of the triangular waveform in the time interval in which the minimum value is exceeded by adding the portion of the amplitude increment beyond the minimum value to the minimum value to create the next amplitude value; and

    [0022] truncating the resulting triangular waveform to form a trapezoidal waveform.

    [0023] The present invention also provides a digital circuit for utilizing an input signal to. generate an output signal that approximates a sinusoidal waveform with a frequency which varies by a specified amount from the frequency of the input signal waveform, comprising:

    means for providing a time interval equal to a fraction of the period of the input signal;

    means for providing a maximum value and a minimum value of the same numerical value but of opposite sign;

    means for providing a phase increment equal to the change in phase of the input signal during the time interval plus a value equal to the additional phase change of the desired output signal during the time interval;

    means for providing an amplitude increment equal to the phase increment multiplied by twice the maximum value and divided by pi;

    means for forming the positively sloped portion of a triangular waveform by repetitiously adding the amplitude increment to create a new amplitude value at each time interval until the maximum value is reached;

    means for changing the slope of the triangular waveform in the time interval in which the maximum value is exceeded by subtracting the portion of the amplitude increment in excess of the maximum value from the maximum value to create the next amplitude value;

    means for forming the negatively sloped portion of the triangular waveform by repetitiously subtracting the amplitude increment to create each amplitude value until the minimum value is reached;

    means for changing the slope of the triangular waveform in the time interval in which the minimum value is exceeded by adding the portion of the amplitude increment beyond the minimum value to the minimum value to create the next amplitude value; and

    means for truncating the resulting triangular waveform to form a trapezoidal waveform.



    [0024] The invention can be implemented using general purpose digital circuitry including an ALU, a controller, and several memory registers. Since the circuitry can be general purpose, it has the advantage of being usable for other applications. The low sampling rate which is possible provides the additional advantage of reserving more time for such circuitry to be used for other applications.

    [0025] The invention may a low a continuous range of output frequencies to be generated since the error due to ALU saturation in the prior method is avoided by determining the next point on the next slope of the triangular waveform when the maximum or minimum value is exceeded.

    [0026] Another benefit is that an accurate range of frequencies around any center frequency can be generated because a low sampling rate is used which is not dependent on the center frequency.

    Brief description of the drawings



    [0027] 

    Figure 1 is a graphical representation of the method for forming a trapezoidal waveform.

    Figure 2 is a flow chart of the operation of the invention.

    Figure 3 is a block diagram of a circuit for forming the triangular waveform used to generate the trapezoidal waveform.

    Figure 4 is a flow chart of the operation of the triangle wave generator circuit of Figure 2.


    Description of a preferred embodiment



    [0028] The preferred embodiments of the present invention include a method for approximating sinusoidal waveforms with trapezoidal waveforms and a general purpose arithmetic processor adapted for generating digital signals according to the method. First, the method for approximating sinusoidal waveforms with trapezoidal waveforms will be described with reference to Figures 1 and 4. Next, the general implementation of the invention will be described with reference to the flow chart of Figure 2. Finally, a specific implementation with a general purpose arithmetic processor will be described with reference to Figures 3 and 4.

    [0029] In Figure 1, a signal having a sinusoidal waveform 10 is shown. Sinusoid 10 has a time varying signal strength that varies sinusoidally with time between positive and negative peak values represented by points 12 and 14. Each complete oscillation of the sinusoid defines one period represented by bidirectional arrow 16.

    [0030] A signal composed of a periodic trapezoidal waveform 18 can be utilized to approximate sinusoidal waveform 10. Trapezoidal waveform 18 has a positively sloped portion 20 that extends from negative peak value 14 up to positive peak value 12, followed by a first constant value portion 22 equal to the positive peak value, followed by a negatively sloped portion 24 that extends from the positive peak value down to the negative peak value, and followed by a second constant value portion 26 equal to the negative peak value. Since the trapezoidal waveform is periodic, the second constant value portion 26 is followed by another positively sloped portion 20, which is in turn followed by another first constant value portion 22, etc. Although Figure 1 illustrates the positively sloped portion 20 as two discontinuous segments, it does extend continuously from negative peak 14 to positive peak 12. Figure 1 shows only one of several periods of the trapezoidal and sinusoidal waveforms.

    [0031] Periodic trapezoidal waveform 18 has certain characteristics that make it a fairly good approximation of sinusoid 10. One characteristic is that the period of the trapezoidal waveform is substantially equal to the period 16 of the sinusoidal waveform 10. Another characteristic is that the maximum and minimum values of the trapezoidal waveform are substantially equal to the positive and negative peak values of the sinusoid. A further characteristic is that the magnitude of the slopes of sloped portions 20 and 24 are equal. A still further characteristic is that the time duration of each sloped portion 20 and 24 is substantially equal to one third of period 16, and the time duration of each constant value portion 22 and 26 is substantially equal to one-sixth of period 16.

    [0032] The reason why trapezoidal waveform 18 is such a close approximation to sinsoidal waveform 10 may be shown by expressing the trapezoidal waveform in terms of a Fourier series. In general, a waveform which is a bounded periodic function can be created by adding together a number of sinusoidal waveforms. Each point on the waveform can thus be represented by a series summation of cosine and sine terms called a Fourier series. Since trapezoidal waveform 18 is a bounded periodic function, a Fourier series representation can be formed. The Fourier series representation of trapezoidal waveform 18, F(t), is expressed as follows:

    when A is amplitude and equals one-half of the range from positive peak 12 to negative peak 14, B equals one-half of period 16, R equals one-half of the duration of the sloped portion 20 or 24, t equals the variable time, and pi=3.14159.

    [0033] The Fourier series representation of trapezoidal waveform 18 includes a fundamental sine term, sin(pi*t/B), having a period equal to 2B, which corresponds to sinusoidal waveform 10. The Fourier series also includes sine terms of periods 2B/3, 2B/5, 2B/7, 2B/9, 2B/11, etc., which correspond to higher frequency harmonics of sinusoid 10. If all of the higher frequency harmonic terms of F(t) were equal to zero, then trapezoidal waveform 18 would be an exact representation of sinusoid 10. Thus, the best representation is achieved when the higher frequency harmonic terms are minimized. Since the coefficients of the harmonic terms decrease as their frequencies increase, the contribution of the higher frequency harmonic terms is less than the contribution of the lower frequency harmonic terms: The largest contributor is the sin(3*pi*t/B) term, which has a period of 2B/3 and a frequency of three times that of sinsoid 10. The coefficient of this term is (1/ 3')*sin(3*pi*R/B). By selecting R to be equal to one-third of B, the coefficient of the sin(3*pi*t/B) term is equal to zero. The Fourier series representation then reduces to:

    where x=pi*t/B. Note that the 3x and 9x terms drop out, and that the 5x, 7x and 11x terms are small in comparison to the fundamental term, sin(x).

    [0034] Thus, by selecting R to be equal to one-third of B, trapezoidal waveform 18 best represents sinusoid 10. This corresponds to the characteristic described above wherein the duration of each sloped portion is equal to one-third of period 16, and the duration of each constant value portion is equal to one-sixth of period 16.

    [0035] Figure 1 also graphically illustrates a method for forming a signal having a trapezoidal waveform. A triangular waveform 28 is generated, which will later be truncated to form the trapezoidal waveform.

    [0036] First, a desired sampling frequency is chosen. The time interval represented by opposing arrows 30 is equal to the period of the sampling frequency. Next, the change in amplitude of the desired waveform 28 during time interval 30 must be determined, and is represented by an amplitude increment represented by opposing arrows 32.

    [0037] For a triangular waveform, there is a linear relationship between the amplitude (y axis) and the phase (x axis). Thus, amplitude increment 32 can be expressed as the phase change, Kp, of the desired output frequency (waveform 28) during time interval 30 multiplied by a constant. Thus,

    where amp. inc. is the amplitude increment.

    [0038] The constant can be determined as follows. If time interval 30 were equal to period 16, the amplitude increment would have to cover the entire change in amplitude of the triangular waveform during period 16, which is the maximum value of the triangular waveform, represented by point 34, multiplied by 4. For other values of time interval 30, it can be seen that the amplitude increment is the maximum value multiplied by 4 and then multiplied by a value equal to time interval 30 divided by period 16. Because time interval 30 is the period of the sampling frequency, fs, period 16 is the period of the desired output frequency, fout, and any waveform period is the inverse of the frequency, the amplitude increment can also be expressed as:



    [0039] The phase constant Kp can be expressed as follows. Because Kp is the phase change of fout during time interval 30, if time interval 30 (the period of fs) is equal to period 16 (the period of fout), Kp (in radians) would be 2*pi. It can be seen that, for other values of time interval 30, Kp can be expressed in radians as follows:

    By combining equations 2 and 3, the amplitude increment can be determined as follows:

    The peak value is chosen to give the desired amplitude for the output frequency.

    [0040] An understanding of the generation of waveform 28 in Figure 1 is aided by reference to the flow chart of Figure 4, which shows the operation of the circuit of Figure 3, discussed later, where the accumulator stores the amplitude value. To generate waveform 28, amplitude increment 32 is added to the amplitude value during each time interval 30. When the amplitude value generated is greater than the maximum value, the next point is on the negatively sloped portion of waveform 28. The portion of the amplitude increment in excess of the maximum must be subtracted from the maximum to give this next point. This subtraction result can also be achieved by subtracting the new amplitude value which is in excess of the maximum from twice the maximum.

    [0041] To produce the negatively sloped portion of waveform 28, the amplitude increment is subtracted during each time interval until the minimum value represented by point 36 is reached or exceeded. The next point should be on the positively sloped portion of waveform 28, and is determined by subtracting the new amplitude value from twice the minimum value.

    [0042] A numerical example may be helpful. Assume that the maximum value is 1.0, the minimum value is -1.0, the current amplitude value is 0.1, the amplitude increment is 0.6, and the slope of the waveform is negative. The next amplitude is generated by adding -0.6 to 0.1 to give -0.5. The value of -0.5 is compared to the minimum value, and since it does not exceed the minimum value, it becomes the output amplitude. In addition, the slope is still negative, so the amplitude increment is still negative. The next amplitude is generated by adding -0.6 to -0.5 to give -1.1. This is compared to the minimum value of -1.0 and found to exceed it, so the output amplitude is calculated as 2*(minimum value=-1.0)-(-1.1 )=-0.9. Thus, the output amplitude is -0.9 and the amplitude increment is changed from -0.6 to 0.6. The positive slope of the triangular waveform is then generated in the succeeding time intervals until the maximum value is exceeded, after which the sign of the amplitude increment is again changed to negative and the process is repeated.

    [0043] After the triangular waveform is generated, it is truncated to give trapezoidal waveform 18. As discussed before, each flat portion 22 and 26 of the trapezoidal waveform is 1/6 of period 16, while the positively sloped portion 20 and the negatively sloped portion 24 are each 1/3 of period 16. The positive portion of the positive slope thus has a duration of 1/6 of the period and would reach the maximum value in half of the time covered by the flat portion 22, or 1/12 of the period. Because the amplitude and phase are proportional, the amplitude of the flat portion 22 is the maximum value multiplied by 1/6 period and divided by 1/6 period plus 1/12 period, thus giving the amplitude of the flat portion as 2/3 the maximum value as follows:



    [0044] Figure 2 is a flow chart of the operation of the method. In addition, Figure 2 illustrates an additional feature of the method allowing the generation of an output frequency which varies by a small amount from a given center frequency. This is accomplished by altering the amplitude increment used to generate the triangular waveform. Referring to Figure 2, the phase change, Kfc, of the center frequency during one period of the sampling frequency is first determined. An incremental phase change, which may be positive or negative, is added to Kfc to give the phase change Kp of the desired output frequency. This phase increment can be represented by a voltage V. which is multiplied by a scaling factor Kc. Adding this phase increment to Kfc gives a new phase constant Kp which is used to determine the amplitude increment used to generate the triangle wave. Thus, Kp is determined as follows:

    Combining equations 3 and 5 yields equation 6:

    where Kfc and K. are expressed in radians.

    [0045] Equation 6 shows that any frequency for an output signal can be generated by choosing the appropriate values for Kfc, V. and Kc.

    [0046] After the triangle wave is generated, it is limited to 2/3 of its maximum and minimum values. By interpolation, a large number of points on the waveform are created, and the signal is then converted from digital to an analog signal. The limiting and interpolating functions are easily performed by a microprocessor or a similar device by known methods.

    [0047] Figure 3 illustrates a digital circuit for performing a method of generating a triangular wave of the present invention. The circuit includes an arithmetic logic unit (ALU) and accumulator 40, a controller 42 and several registers 44, 46, 48, 50, and52. The ALU is capable of addition, subtraction and comparison. The accumulator is a storage register that holds the results of the latest arithmetic operation performed by the ALU, and can also serve as an input register to the ALU. Controller 42 monitors the ALU to detect a com- parision showing an amplitude value in excess of the maximum value or less than the minimum value, and generally controls the operation of the circuit. The accumulator holds the current amplitude value, register 44 holds the amplitude increment, and registers 46, 48, 50, and 52 hold the maximum value, minimum value, twice the maximum value, and twice the minimum value, respectively. The output terminals of the registers are connected to input terminals of the ALU. An output terminal of the ALU issues the output signal.

    [0048] To generate a triangular waveform, the circuit operates according to the flowchart of Figure 4. First, the accumulator is cleared. Then, the input amplitude increment is added to the value of the accumulator and the result is stored in the accumulator. Next, the ALU compares the value in the accumulator with the maximum and minimum values. If neither value is exceeded, the accumulator value is the current value of the triangular waveform and controller 42 sends an enable signal to the next stage (not shown).

    [0049] If the comparison shows that either the maximum or minimum value is exceeded, the controller instructs the ALU to subtract the accumulator value from twice the exceeded value. The resulting value becomes the accumulator value and is the current value of the triangular waveform. Controller 42 then sends an enable signal to the next stage and changes the sign of the amplitude increment in register 44. The process is repeated to produce subsequent points on the digital waveform.

    [0050] The triangular wave output is then limited to form a trapezoidal wave and may have additional points added by interpolation and be processed through a digital to analog converter to produce the output oscillating signal. The limiting, interpolating and digital to analog conversion methods are well known to those skilled in the art.

    [0051] From the above description, it will be apparent that the invention disclosed herein provides a novel and advantageous method for approximating sinusoidal waveforms with trapezoidal waveforms, and a circuit for generating such signals.


    Claims

    1. A method for generating an output time varying signal that approximates a signal having a sinusoidal waveform, comprising the steps of:

    selecting a time interval equal to a fraction of the period of the sinusoidal waveform;

    selecting a maximum value and a minimum value of the same numerical value but of opposite sign which are one and one-half times the desired maximum and minimum amplitudes of the output signal;

    determining a phase increment equal to the change in phase of the sinusoidal waveform during the time interval;

    determining an amplitude increment equal to the phase increment multiplied by twice the maximum value and divided by pi;

    forming the positively sloped portion of a triangular waveform by repetitiously adding the amplitude increment to create an amplitude value at each time interval until the maximum value is reached;

    changing the slope of the triangular waveform in the time interval in which the maximum value is exceeded by subtracting the portion of the amplitude increment in excess of the maximum value from the maximum value to create the next amplitude value;

    forming the negatively sloped portion of the triangular waveform by repetitiously subtracting the amplitude increment to create each amplitude value until the minimum value is reached;

    changing the slope of the triangular waveform in the time interval in which the minimum value is exceeded by adding the portion of the amplitude increment beyond the minimum value to the minimum value to create the next amplitude value; and

    truncating the resulting triangular waveform to form a trapezoidal waveform.


     
    2. A method as recited in claim 1 wherein the step of truncating the triangular waveform comprises the steps of:

    making each amplitude value in excess of two-thirds of the maximum value equal to two-thirds of the maximum value; and

    making each amplitude value less than two-thirds of the minimum value equal to two-thirds of the minimum value.


     
    3. A method for utilizing an input signal to generate an output signal that approximates a sinusoidal waveform with a frequency which varies by a specified amount from the frequency of the input signal waveform, comprising the steps of:

    selecting a time interval equal to a fraction of the period of the input signal;

    selecting a maximum value and a minimum value of the same numerical value but of opposite sign which are one and one-half times the desired maximum and minimum amplitudes of the output signal;

    determining a phase increment equal to the change in phase of the input signal during the time interval plus a value equal to the additional phase change of the desired output signal during the time interval;

    determining an amplitude increment equal to the phase increment multiplied by twice the maximum value and divided by pi;

    forming the positively sloped portion of a triangular waveform by repetitiously adding the amplitude increment to create a new amplitude value at each time interval until the maximum value is reached;

    changing the slope of the triangular waveform in the time interval in which the maximum value is exceeded by subtracting the portion of the amplitude increment in excess of the maximum value from the maximum value to create the next amplitude value;

    forming the negatively sloped portion of the triangular waveform by repetitiously subtracting the amplitude increment to create each amplitude value until the minimum value is reached;

    changing the slope of the triangular waveform in the time interval in which the minimum value is exceeded by adding the portion of the amplitude increment beyond the minimum value to the minimum value to create the next amplitude value; and

    truncating the resulting triangular waveform to form a trapezoidal waveform.


     
    4. A method as recited in claim 3, wherein the step of truncating the triangular waveform comprises the steps of:

    making each amplitude value in ecess of two-thirds of the maximum value equal to two-thirds of the maximum value; and

    making each amplitude value less than two thirds of the minimum value equal to two-thirds of the minimum value.


     
    5. A digital circuit for generating an output time varying signal that approximates a signal having a sinusoidal waveform, comprising:

    means for providing a time interval equal to a fraction of the period of the sinusoidal waveform;

    means for providing a maximum value and a minimum value of the same numerical value but of opposite sign which are one and one-half times the desired maximum and minimum amplitudes of the output signal;

    means for providing a phase increment equal to the change in phase of the sinusoidal waveform during the time interval;

    means for providing an amplitude increment equal to the phase increment multiplied by twice the maximum value and divided by pi;

    means for forming the positively sloped portion of a triangular waveform by repetitiously adding the amplitude increment to create an amplitude value at each time interval until the maximum value is reached;

    means for changing the slope of the triangular waveform in the time interval in which the maximum value is exceeded by subtracting the portion of the amplitude increment in excess of the maximum value from the maximum value to create the next amplitude value;

    means for forming the negatively sloped portion of the triangular waveform by repetitiously subtracting the amplitude increment to create each amplitude value until the minimum value is reached;

    means for changing the slope of the triangular waveform in the time interval in which the minimum value is exceeded by adding the portion of the amplitude increment beyond the minimum value to the minimum value to create the next amplitude value; and

    means for truncating the resulting triangular waveform to form a trapezoidal waveform.


     
    6. A digital circuit as recited in claim 5 wherein the means for truncating the triangular waveform comprises:

    means for making each amplitude value in excess of two-thirds of the maximum value equal to two-thirds of the maximum value; and means for making each amplitude value less than two-thirds of the minimum value equal to two-thirds of the minimum value.


     
    . 7. A circuit as recited in claim 5 wherein the means for forming the positively sloped portion of the triangular waveform and the means for forming the negatively sloped portion of the triangular waveform jointly comprise:

    arithmetic means for performing arithmetic operations;

    a memory register coupled to the arithmetic means for temporarily storing the amplitude value of the triangular waveform;

    comparator means for comparing the value of the triangular waveform to a maximum and minimum value; and

    control means for periodically directing said arithmetic means to increment the value of the triangular waveform by an amplitude increment, and for directing the arithmetic means to change the slope of the triangular waveform in the time interval in which the maximum value is exceeded by subtracting the portion of the amplitude increment in excess of the maximum value from the maximum value to create the next amplitude value and to change the slope of the triangular waveform in the time interval in which the minimum value is exceeded by adding the portion of the amplitude increment in excess of the minimum value to the minimum value to create the next amplitude value.


     
    8. A circuit as recited in claim 7 wherein the arithmetic means comprises an arithmetic logic unit and an accumulator.
     
    9. A circuit as recited in claim 5 wherein the means for changing the slope of the triangular waveform comprises:

    arithmetic means for performing arithmetic operations; and

    control means for enabling the arithmetic means.


     
    10. A circuit as recited in claim 9 wherein the arithmetic means comprises an arithmetic logic unit and an accumulator.
     
    11. A digital circuit for utilizing an input signal to generate an output signal that approximates a sinusoidal waveform with a frequency which varies by a specified amount from the frequency of the input signal waveform, comprising: means for providing a time interval equal to a fraction of the period of the input signal;

    means for providing a maximum value and a minimum value of the same numerical value but of opposite sign;

    means for providing a phase increment equal to the change in phase of the input signal during the time interval plus a value equal to the additional phase change of the desired output signal during the time interval;

    means for providing an amplitude increment equal to the phase increment multiplied by twice the maximum value and divided by pi;

    means for forming the positively sloped portion of a triangular waveform by repetitiously adding the amplitude increment to create a new amplitude value at each time interval until the maximum value is reached;

    means for changing the slope of the triangular waveform in the time interval in which the maximum value is exceeded by subtracting the portion of the amplitude increment in excess of the maximum value from the maximum value to create the next amplitude value;

    means for forming the negatively sloped portion of the triangular waveform by repetitiously subtracting the amplitude increment to create each amplitude value until the minimum value is reached;

    means for changing the slope of the triangular waveform in the time interval in which the minimum value is exceeded by adding the portion of the amplitude increment beyond the minimum value to the minimum value to create the next amplitude value; and

    means for truncating the resulting triangular waveform to form a trapezoidal waveform.


     
    12. A digital circuit as recited in claim 11 wherein the step of truncating the triangular waveform comprises:

    means for making each amplitude value in excess of two-thirds of the maximum value equal to two-thirds of the maximum value; and means for making each amplitude value less than two-thirds of the minimum value equal to two-thirds of the minimum value.


     
    13. A circuit as recited in claim 11 wherein the means for forming the positively sloped portion of the triangular waveform and the means for forming the negatively sloped portion of the triangular waveform jointly comprise:

    arithmetic means for performing arithmetic operations;

    a memory register coupled to the arithmetic means for temporarily storing the amplitude value of the triangular waveform;

    comparator means for comparing the value of the triangular waveform to the maximum and minimum values; and

    control means for periodically directing said arithmetic means to increment the value of the triangular waveform by an amplitude increment,' and for directing the arithmetic means to change the slope of the triangular waveform in the time interval in which the maximum value is exceeded by subtracting the portion of the amplitude increment in excess of the maximum value from the maximum value to create the next amplitude value and to change the slope of the triangular waveform in the time interval in which the minimum value is exceeded by adding the portion of the amplitude increment in excess of the minimum value to the minimum value to create the next amplitude value.


     
    14. A circuit as recited in claim 13 wherein the arithmetic means comprises an arithmetic logic unit and an accumulator.
     
    15. A circuit as recited in claim 11 wherein the means for changing the slope of the triangular waveform comprises:

    arithmetic means for performing arithmetic operations; and

    control means for enabling the arithmetic means.

    16. A circuit as recited in claim 15 wherein the arithmetic means comprises an arithmetic logic unit and an accumulator.


     


    Ansprüche

    1. Verfahren zur Erzeugung eines zeitlich variierenden Ausgangssignals, das einem Signal mit Sinuswellenform angenähert ist, mit den folgenden Schritten:

    Wählen eines Zeitintervalls, das gleich einem Bruchteil der Periode der Sinuswellenform ist;

    Wählen eines Maximalwertes und eines Minimalwertes mit gleichem Zahlenwert, aber mit entgegengesetzten Vorzeichen, die das Anderthalbfache der gewünschten Maximal- und Minimalamplituden des Ausgangssignals betragen;

    Bestimmen eines Phaseninkrements, das gleich der Veränderung der Phase der Sinuswellenform während des Zeitintervalls ist;

    Bestimmen eines Amplitudeninkrements, das dem mit dem doppelten Maximalwert multipli-

    zierten und durch Pi geteilten Phaseninkrement gleich ist;

    Bilden des positiv ansteigenden Bereiches einer dreieckigen Wellenform durch wiederholtes Addieren des Amplitudeninkrements zur Erzeugung eines Amplitudenwertes bei jedem Zeitintervall, bis der Maximalwert erreicht ist;

    Verändern der Steigung der dreieckigen Wellenform in dem Zeitintervall, in dem der Maximalwert überstiegen wird durch Subtrahieren des über den Maximalwert hinausgehenden Bereiches des Amplitudeninkrements von dem Maximalwert zur Erzeugung des nächsten Amplitudenwertes;

    Bilden des negativ abfallenden Bereichs der dreieckigen Wellenform durch wiederholtes Subtrahieren des Amplitudeninkrements zur Erzeugung eines jeden Amplitudenwertes, bis der Minimalwert erreicht ist;

    Verändern der Steigung der dreieckigen Wellenform in dem Zeitintervall, in dem der Minimalwert übertroffen wird durch Addieren des über den Minimalwert hinausgehenden Bereiches des Amplitudeninkrements zum Minimalwert zur Erzeugung des nächsten Amplitudenwertes; und

    Runden der sich ergebenden dreiegkigen Wellenform zur Bildung einer trapezförmigen Wellenform.


     
    2. Verfahren nach Anspruch 1, bei dem der Schritt des Rundens der dreieckigen Wellenform die folgenden Schritte umfaßt:

    Gleichmachen eines jeden Amplitudenwertes, der zwei Dritten des Maximalwertes übersteigt, mit zwei Dritteln des Maximalwertes;

    Gleichmachen eines jeden Amplitudenwertes, der zwei Drittel des Minimalwertes unterschreitet, mit zwei Dritteln des Minimalwertes.


     
    3. Verfahren yur Verwendung eines Eingangssignals zur Erzeugung eines Ausgangssignals, das einer Sinuswellenform mit einer Frequenz angenähert ist, die um einen bestimmten Betrag von der Frequenz der Eingangssignalwellenform abweicht, mit den folgenden Schritten:

    Wählen eines Zeitintervalls, das gleich einem Bruchteil der Periode des Eingangssignals ist;

    Wählen eines Maximalwertes und eines Minimalwertes mit gleichem Zahlenwert, aber mit entgegengesetzten Vorzeichen, die das Anderthalbfache der gewünschten Maximal- und Minimalamplituden des Ausgangssignals betragen;

    Bestimmen eines Phaseninkrements, das gleich der Veränderung der Phase des Eingangssignals während des Zeitintervalls ist, plus einem Wert, der gleich der zusätzlichen Veränderung der Phase der gewünschten Ausgangssignals während des Zeitintervalls ist;

    Bestimmen eines Amplitudeninkrements, das der mit dem doppelten Maximalwert multiplizierten und durch Pi geteilten Phaseninkrement gleich ist;

    Bilden des positiv ansteigenden Bereiches einer dreieckigen Wellenform durch wiederholtes Addieren des Amplitudeninkrements zur Erzeugung eines neuen Amplitudenwertes bei jedem Zeitintervall, bis der Maximalwert erreicht ist;

    verändern der Steigung der dreieckigen Wellenform in dem Zeitintervall in dem der Maximalwert übersteigen wird durch Subtrahieren des über den Maximalwert hinausgehenden Bereiches des Amplitudeninkrements von dem Maximalwert zur Erzeugung des nächsten Amplitudenwertes;

    Bilden des negativ abfallenden Bereichs der dreieckigen Wellenform durch wiederholtes Subtrahieren des Amplitudeninkrements zur Erzeugung eines jeden Amplitudenwertes, bis der Minimalwert erreicht ist;

    Verändern der Steigung der dreieckigen Wellenform in dem Zeitintervall in dem der Minimalwert übertroffen wird durch Addieren des über den Minimalwert hinausgehenden Bereiches des Amplitudeninkrements zum Minimalwert zur Erzeugung des nächsten Amplitudenwertes; und

    Runden der sich ergebenden dreickigen Wellenform zur Bildung einer trapezförmigen Wellenform.


     
    4. Verfahren nach Anspruch 3, bei dem der Schritt des Rundens der dreieckigen Wellenform die folgenden Schritte umfaßt:

    Gleichmachen eines jeden Amplitudenwertes, der zwei Drittel des Maximalwertes übersteigt, mit zwei Dritteln des Maximalwertes;

    Gleichmachen eines jeden Amplitudenwertes, der zwei Drittel des Minimalwertes unterschreitet, mit zwei Dritteln des Minimalwertes.


     
    5. Digitalschaltung zur Erzeugung eines zeitlich variierenden Ausgangssignals, das einem Signal mit Sinuswellenform angenähert ist, mit:

    einem Mittel zum Erstellen eines Zeitintervalls, das gleich einem Bruchteil der Periode der Sinuswellenform ist;

    einem Mittel zum Erstellen eines Maximalwertes und eines Minimalwertes mit gleichem Zahlenwert, aber mit entgegengesetzten Vorzeichen, die das Anderthalbfache der gewünschten Maximal- und Minimalamplituden des Ausgangssignals betragen;

    einem Mittel zum Erstellen eines Phaseninkrements, das gleich der Veränderung der Phase der Sinuswellenform während des Zeitintervalls ist;

    einem Mittel zum Erstellen eines Amplitudeninkrements, das dem mit dem doppelten Maximalwert multiplizierten und durch Pi geteilten Phaseninkrement gleich ist;

    einem Mittel zum Bilden des positiv ansteigenden Bereiches einer dreieckigen Wellenform durch wiederholtes Addieren des Amplitudeninkrements zur Erzeugung eines Amplitudenwertes bei jedem Zeitintervall, bis der Maximalwert erreicht ist;

    einem Mittel zum Verändern der Steigung der dreieckigen Wellenform in dem Zeitintervall in dem der Maximalwert überstiegen wird durch Subtrahieren des über den Maximalwert hinausgehnden Bereiches des Amplitudeninkrements von dem Maximalwert zur Erzeugung des nächsten Amplitudenwertes;

    einem Mittel zum Bilden des negativ abfallenden Bereichs der dreieckigen Wellenform durch wiederholtes Subtrahieren des Amplitudeninkrements zur Erzeugung eines jeden Amplitudenwertes, bis der Minimalwert erreicht ist;

    einem Mittel zum Verändern der Steigung der dreieckigen Wellenform in dem Zeitintervall in dem der Minimalwert übertroffen wird, durch Addieren des über den Minimalwert hinausgehenden Bereiches des Amplitudeninkrements zum Minimalwert zur Erzeugung des nächsten Amplitudenwertes; und

    einem Mittel zum Runden der sich ergebenden dreieckigen Wellenform zur Bildung einer trapezförmigen Wellenform.


     
    6. Digitalschaltung nach Anspruch 5, bei der das Mittel zum Runden der dreieckigen Wellenform umfaßt:

    ein Mittel zum Gleichmachen eines jeden Amplitudenwertes, drei zwei Drittel des Maximalwertes übersteigt, mit zwei Dritteln des Maximalwertes;

    ein Mittel zum Gleichmachen eines jeden Amplitudenwertes, der zwei Drittel des Minimalwertes unterschreitet, mit zwei Dritteln des Minimalwertes.


     
    7. Schaltung nach Anspruch 5, bei der das Mittel zum Bilden des positiv ansteigenden Bereiches der dreieckigen Wellenform und das Mittel zum Bilden des negativ abfallenden Bereiches der dreieckigen Wellenform gemeinsam umfassen:

    ein arithmetisches Mittel zum Durchführen arithmetischer Operationen;

    ein Speicherregister, das mit dem arithmetischen Mittel gekoppelt ist, um die Amplitudenwerte der dreieckigen Wellenform zeitweise zu speichern;

    ein Komparatormittel zum Vergleichen des Wertes der dreieckigen Wellenform mit einem Maximal- und einem Minimalwert; und

    ein Steuermittel zum periodischen Veranlassen des arithmetischen Mittels den Wert der dreieckigen Wellenform um ein Amplitudeninkrement zu erhöhen, und zum Veranlassen des arithmetischen Mittels die Steigung der dreieckigen Wellenform in dem Zeitintervall in dem der Maximalwert überstiegen wird, durch Subtrahieren des über den Maximalwert hinausgehenden Bereiches des Amplitudeninkrements von dem Maximalwert zu Erzeugung des nächsten Amplitudenwertes zu verändern und die Steigung der dreiekkigen Wellenform in dem Zeitintervall in dem der Minimalwert übertroffen wird, durch Addieren des über den Minimalwert hinausgehenden Bereiches des Amplitudeninkrements zum Minimalwert zur Erzeugung des nächsten Amplitudenwertes zu verändern.


     
    8. Schaltung nach Anspruch 7, bei der das arithmetische Mittel eine arithmetische LogikEinheit und einen Akkumulator aufweist.
     
    9. Schaltung nach Anspruch 5, bei der das Mittel zur Veränderung der Steigung der dreieckigen Wellenform umfaßt:

    ein arithmetisches Mittel zum Durchführen arithmetischer Operationen; und

    ein Steuermittel zum Aktivieren des arithmetischen Mittels.


     
    10. Schaltung nach Anspruch 9, bei der das arithmetische Mittel eine arithmetische LogikEinheit und einen Akkumulator aufweist.
     
    11. Digitalschaltung zur Verwendung eines Eingangssignals zur Erzeugung eines Ausgangssignals, das einer Sinuswellenform mit einer Frequenz angenähert ist, die um einen bestimmten Betrag von der Frequenz der Eingangssignalwellenform abweicht, mit:

    einem Mittel zum Erstellen eines Zeitintervalls, das gleich einem Druchteil der Periode des Eingangssignals ist;

    einem Mittel zum Erstellen eines Maximalwertes und eines Minimalwertes mit gleichem Zahlenwert, aber mit entgegengesetzten Vorzeichen;

    einem Mittel zum Erstellen eines Phaseninkrements, das gleich der Veränderung der Phase des Eingangssignals während des Zeitintervalls ist, plus einem Wert, der gleich der zusätzlichen Veränderung der Phase des gewünschten Ausgangssignals während des Zeitintervalls ist;

    einem Mittel zum Erstellen eines Amplitudeninkrements, das dem mit dem doppelten Maximalwert multiplizierten und durch Pi geteilten Phaseninkrement gleich ist;

    einem Mittel zum Bilden des positiv ansteigenden Bereiches einer dreieckigen Wellenform durch wiederholtes Addieren des Amplitudeninkrements zur Erzeugung eines Amplitudenwertes bei jedem Zeitintervall, bis der Maximalwert erreicht ist;

    einem Mittel zum Verändern der Steigung der dreickigen Wellenform in dem Zeitintervall in dem der Maximalwert übersteigen wird, durch Subtrahieren des über den Maximalwert hinausgehenden Bereiches des Amplitudeninkrements von dem Maximalwert zur Erzeugung des nächsten Amplitudenwertes;

    einem Mittel zum Bilden des negativ abfallenden Bereichs der dreieckigen Wellenform durch wiederholtes Subtrahieren des Amplitudeninkrements zur Erzeugung eines jeden Amplitudenwertes, bis der Minimalwert erreicht ist;

    einem Mittel zum Verändern der Steigung der dreieckigen Wellenform in dem Zeitintervall in dem der Minimalwert übertroffen wird, durch Addieren des über den Minimalwert hinausgehenden Bereiches des Amplitudeninkrements zum Minimalwert zur Erzeugung des nächsten Amplitudenwertes; und

    einem Mittel zum Runden der sich ergebenden dreieckigen Wellenform zur Bildung einer trapezförmigen Wellenform.


     
    12. Digitalschaltung nach Anspruch 11, bei der der Schritte des Rundens der dreieckigen Wellenform umfaßt:

    ein Mittel zum Gleichmachen eines jeden Amplituden wertes, der zwei Drittel des Maximalwertes übersteigt, mit zwei Dritteln des Maximalwertes;

    ein Mittel zum Gleichmachen eines jeden Amplitudenwertes, der zwei Drittel des Minimalwertes unterschreitet, mit zwei Dritteln des Minimalwertes.


     
    13. Schaltung nach Anspruch 11, bei der das Mittel zur Bildung des positiv ansteigenden Bereiches der dreieckigen Wellenform und das Mittel zur Bildung des negativ abfallenden Bereichs der dreieckigen Wellenform gemeinsam umfassen:

    ein arithmetisches Mittel zum Durchführen arithmetischer Operationen;

    ein Speicherregister, das mit dem arithmetischen Mittel gekoppelt ist, um die Amplitudenwerte der dreieckigen Wellenform zeitweise zu speichern;

    ein Komparatormittel zum Vergleichen des Wertes der dreieckigen Wellenform mit dem Maximal- und dem Minimalwert; und

    ein Steuermittel zum periodischen Veranlassen des arithmetischen Mittels den Wert der dreieckigen Wellenform um ein Amplitudeninkrement zu erhöhen, und zum Veranlassen des arithmetischen Mittels die Steigung der dreieckigen Wellenform in dem Zeitintervall in dem der Maximalwert überstiegen wird durch Subtrahieren des über den Maximalwert hinausgehenden Bereiches des Amplitudeninkrements von dem Maximalwert zur Erzeugung des nächsten Amplitudenwertes zu verändern und die Steigung der dreiekkigen Wellenform in dem Zeitintervall in dem der Minimalwert übertroffen wird, durch Addieren des über den Minimalwert hinausgehenden Bereiches des Amplitudeninkrements zum Minimalwert zur Erzeugung des nächsten Amplitudenwertes zu verändern.


     
    14. Schaltung nach Anspruch 13, bei der das arithmetische Mittel eine arithmetische LogikEinheit und einen Akkumulator aufweist.
     
    15. Schaltung nach Anspruch 11, bei der das Mittel zur Veränderung der Steigung der dreieckigen Wellenform umfaßt:

    ein arithmetisches Mittel zum Durchführen arithmetischer Operationen; und

    ein Steuermittel zum Aktivieren des arithmetischen Mittels.


     
    16. Schaltung nach Anspruch 15, bei der das arithmetische Mittel eine arithmetische LogikEinheit und einen Akkumulator aufweist.
     


    Revendications

    1. Un procédé pour engendrer un signal de sortie variant dans le temps et constituant une approximation d'un signal de forme d'onde sinusoïdale, comprenant les étapes suivantes:

    sélection d'un intervalle de temps égal à une fraction de la période de la forme d'onde sinusoïdale;

    sélection d'une valeur maximum et d'une valeur minimum d'une même valeur numérique, mais de signes opposés, qui sont égales à une fois et demie les amplitudes maximum et minimum désirées du signal de sortie;

    détermination d'un incrément de phase égal à la variation de phase de la forme d'onde sinusoïdale pendant l'intervalle de temps;

    détermination d'un incrément d'amplitude égal à l'incrément de pahse multiplié par le double de la valeur maximum et divisé par n;

    formation de la partie de pente positive d'une forme d'onde triangulaire par addition répétée de l'incrément d'amplitude pour créer une valeur d'amplitude à chaque intervalle de temps jusqu'à atteindre la valeur maximum;

    modification de la pente de la forme d'onde triangulaire dans l'intervalle de temps pour lequel la valeur maximum est dépassée, par soustraction, de cette valeur maximum, de la partie de l'incrément d'amplitude qui excède la valeur maximum pour créer la valeur d'amplitude suivante;

    formation de la partie de pente négative de la forme d'onde triangulaire par soustraction répétée de l'incrément d'amplitude pour créer chaque valeur d'amplitude jusqu'à ce que la valeur minimum soit atteinte;

    modification de la pente de la forme d'onde triangulaire pendant l'intervalle de temps où la valeur minimum est dépassée, par addition de la partie de l'incrément d'amplitude qui se trouve au-delà de la valeur minimum, à cette valeur minimum, de manière à créer la valeur d'amplitude suivante; et

    écrêtage de la forme d'onde triangulaire résultante pour former une forme d'onde trapézoïdale.


     
    2. Un procédé conforme à la revendication 1, dans lequel l'écrêtage de la forme d'onde triangulaire comprend les étapes suivantes:

    on ramène chaque valeur d'amplitude dépassant les deux tiers de la valeur maximum à une valeur égale aux deux tiers de la valeur maximum; et

    on ramène chaque valeur d'amplitude inférieure aux deux tiers de la valeur minimum à une valeur égale aux deux tiers de la valeur minimum.


     
    3. Un procédé pour utiliser un signal d'entrée à la génération d'un signal de sortie constituant une approximation d'une forme d'onde sinusoïdale présentant une fréquence qui varie d'une quantité spécifiée à partir de la fréquence de la forme d'onde du signal d'entrée, comprenant les étapes suivantes:

    sélection d'un intervalle de temps égal à une fraction de la période du signal d'entrée;

    sélection d'une valeur maximum et d'une valeur minimum de la même valeur numérique, mais de signes opposées, qui sont égales à une fois et demie les amplitudes maximum et minimum désirées du signal de sortie;

    détermination d'un incrément de phase égal à la variation de phase du signal d'entrée pendant l'intervalle de temps additionnée à une valeur égale à la variation de phase additionnelle du signal de sortie désiré pendant l'intervalle de temps;

    détermination d'un incrément d'amplitude égal à l'incrément de phase multiplié par le double de la valeur maximum et divisé par n;

    formation de la partie de pente positive d'une forme d'onde triangulaire par addition répétée de l'incrément d'amplitude pour créer une nouvelle valeur d'amplitude à chaque intervalle de temps, jusqu'à atteindre la valeur maximum;

    modification de la pente de la forme d'onde triangulaire dans l'intervalle de temps pour lequel la valeur maximum est dépassée, par soustraction de la partie de l'incrément d'amplitude qui dépasse la valeur maximum, de la valeur maximum, pour créer la valeur d'amplitude suivante;

    formation de la partie de pente négative de la forme d'onde triangulaire par soustraction répétée de l'incrément d'amplitude pour créer chaque valeur d'amplitude jusqu'à atteindre la valeur minimum;

    modification de la pente de la forme d'onde triangulaire dans l'intervalle de temps pour lequel la valeur minimum est dépassée par addition de la partie de l'incrément d'amplitude qui dépasse la valeur minimum, à la valeur minimum, pour créer la valeur d'amplitude suivante; et

    écrêtage de la forme d'onde triangulaire résultante pour former une forme d'onde trapézoïdale.


     
    4. Un procédé conforme à la revendication 3, dans lequel la troncature de la forme d'onde triangulaire comprend les étapes suivantes:

    on ramène la valeur d'amplitude qui dépasse pes deux tiers de la valeur maximum à une valeur égale aux deux tiers de la valeur maximum; et

    on ramène chaque valeur d'amplitude inférieure aux deux tiers de la valeur minimum à une valeur égale aux deux tiers de la valeur minimum.


     
    5. Un circuit numérique pour engendrer un signal de sortie variant dans le temps qui constitue une approximation d'un signal présentant une forme d'onde sinusoïdale, comprenant:

    des moyens pour définir un intervalle de temps égal à une fraction de la période de la forme d'onde sinusoïdale;

    des moyens pour définir une valeur maximum et une valeur minimum de la même valuer numérique mais de signe opposé, qui sont égales à une fois et demie les amplitudes maximum et minimum désirées du signal de sortie;

    des moyens pour définir un incrément de phase égal au changement de phase de la forme d'onde sinusoïdale pendant l'intervalle de temps;

    des moyens pour définir un incrément d'amplitude égal à l'incrément de phase multiplié par deux fois la valeur maximum et divisé par n;

    des moyens pour former la partie de pente positive d'une forme d'onde triangulaire par addition répétée de l'incrément d'amplitude pour créer une valeur d'amplitude à chaque intervalle de temps jusqu'à atteindre la valeur maximum;

    des moyens pour modifier la pente de la forme d'onde triangulaire dans l'intervalle de temps pour lequel la valeur maximum est dépassée, par soustraction de la partie de l'incrément d'amplitude qui dépasse la valeur maximum, de la valeur maximum, pour créer la valeur d'amplitude suivante;

    des moyens pour former la partie de pente négative de la forme d'onde triangulaire par soustraction répétée de l'incrément d'amplitude pour créer chaque valeur d'amplitude jusqu'à atteindre la valeur minimum;

    des moyens pour modifier la pente de la forme d'onde triangulaire dans l'intervalle de temps pour lequel la valeur minimum est dépassée, par addition de la partie de l'incrément d'amplitude qui se situe au-delà de la valeur minimum, à la valeur minimum, pour créer la valeur d'amplitude suivante; et

    des moyens pour écrêter la forme d'onde triangulaire résultante, pour former une forme d'onde trapézoïdale.


     
    6. Un circuit numérique conforme à la revendication 5, dans lequel les moyens pour écrêter la forme d'onde triangulaire comprennent:

    des moyens pour ramener chaque valeur d'amplitude en excès des deux tiers de la valeur maximum à une valeur égale aux deux tiers de la valeur maximum; et

    des moyens pour ramener chaque valeur d'amplitude inférieure aux deux tiers de la valeur minimum à une valeur égale aux deux tiers de la valeur minimum.


     
    7. Un circuit conforme à la revendication 5, dans lequel les moyens pour former la partie de pente positive de la forme d'onde triangulaire et les moyens pour former la partie de pente négative de la forme d'onde triangulaire comprennent conjointement:

    des moyens arithmétiques pour réaliser des opérations arithmétiques;

    un registre de mémoire couplé aux moyens arithmétiques pour conserver temporairement la valeur d'amplitude de la forme d'onde triangulaire;

    des moyens de comparaison pour comparer la valeur de la forme d'onde triangulaire à une valeur minimum et à une valeur maximum; et

    des moyens de commande pour conditionner périodiquement lesdits moyens arithmétiques pour que ceux-ci incrémentent la valeur de la forme d'onde triangulaire d'un incrément d'amplitude, et pour conditionner les moyens arithmétiques pour modifier la pente de la forme d'onde triangulaire dans l'intervalle de temps pour lequel la valeur maximum est dépassée, par soustraction de la partie de l'incrément d'amplitude qui dépasse la valeur maximum, de la valeur maximum, pour créer la valeur d'amplitude suivante et pour modifier la pente de la forme d'onde triangulaire dans l'intervalle de temps pour lequel la valeur minimum est dépassée, par addition de la partie de l'incrément d'amplitude qui dépasse la valeur minimum, à la valeur minimum, pour créer la valeur d'amplitude suivante.


     
    8. Un circuit conforme à la revendication 7, dans lequel les moyens arithmétiques comprennent une unité arithmétique et logique et un accumulateur.
     
    9. Un circuit conforme à la revendication 5, dans lequel les moyens pour modifier la pente de la forme d'onde triangulaire comprennent:

    des moyens arithmétiques pour réaliser des opérations arithmétiques; et

    des moyens de commande pour valider les moyens arithmétiques.


     
    10. Un circuit conforme à la revendication 9, dans lequel les moyens arithmétiques comprennent une unité arithmétique et logique et un accumulateur.
     
    11. Un circuit numérique pour utiliser un signal d'entrée à la génération d'un signal de sortie qui constitue une approximation d'une forme d'onde sinusoïdale présentant une fréquence qui varie d'une quantité spécifiée à partir de la fréquence du signal d'entrée, comprenant:

    des moyens pour définir un intervalle de temps égal a une fraction de la période du signal d'entrée;

    des moyens pour définir une valeur maximum et une valeur minimum d'une même valeur numérique, mais de signes opposés;

    des moyens pour définir un incrément de phase égal à la variation de phase du signal d'entrée pendant l'intervalle de temps, additionné à une valeur égale à la variation de phase additionnelle du signal de sortie désiré pendant l'intervalle de temps;

    des moyens pour définir un incrément d'amplitude égal à l'incrément de phase multiplié par deux fois la valeur maximum et divisé par n;

    des moyens pour former la partie de pente positive d'une forme d'onde triangulaire par addition répétée de l'incrément d'amplitude pour créer une nouvelle valeur d'amplitude à chaque intervalle de temps, jusqu'à atteindre la valeur maximum;

    des moyens pour changer la pente de la forme d'onde triangulaire dans l'intervalle de temps pour lequel la valeur maximum est dépassée, par soustraction de la partie de l'incrément d'amplitude qui dépasse la valeur maximum, de la valeur maximum, pour créer la valeur d'amplitude suivante;

    des moyens pour former la partie de pente négative de la forme d'onde triangulaire par soustraction répétée de l'incrément d'amplitude pour créer chaque valeur d'amplitude jusqu'à atteindre la valeur minimum;

    des moyens pour modifier la pente de la forme d'onde triangulaire dans l'intervalle de temps pendant lequel on dépasse la valeur minimum, par addition de la partie de l'incrément d'amplitude qui se situe au-delà de la valeur minimum, à la valeur minimum, pour créer la valeur d'amplitude suivante; et

    des moyens pour écrêter la forme d'onde triangulaire résultante pour former une forme d'onde trapézoïdale.


     
    12. Un circuit numérique conforme à la revendication 11, dans lequel l'écrêtage de la forme d'onde triangulaire s'obtient par:

    des moyens pour ramener chaque valeur d'amplitude qui dépasse les deux tiers de la valeur maximum à une valeur égale aux deux tiers de la valeur maximum; et

    des moyens pour ramener chaque valeur d'amplitude inférieure aux deux tiers de la valeur minimum, à une valeur égale aux deux tiers de la valeur minimum.


     
    13. Un circuit conforme à la revendication 11, dans lequel les moyens pour former la partie de pente positive de la forme d'onde triangulaire et les moyens pour former la partie de pente négative de la forme d'onde triangulaire comprennent conjointement:

    des moyens arithmétiques pour réaliser des opérations arithmétiques;

    un registre de mémoire couplé aux moyens arithmétiques pour conserver temporairement la valeur d'amplitude de la forme d'onde triangulaire;

    des moyens de comparaison pour comparer la valeur de la forme d'onde triangulaire à la valeur maximum et à la valeur minimum; et

    des moyens de commande pour conditionner périodiquement ces moyens arithmétiques de manière à incrémenter la valeur de la forme d'onde triangulaire d'un incrément d'amplitude, et pour conditionner les moyens arithmétiques pour modifier la pente de la forme d'onde triangulaire pendant l'intervalle de temps où la valeur maximum est dépassée, par soustraction de la partie de l'incrément d'amplitude qui dépasse la valeur maximum, de la valeur maximum, pour créer la valeur d'amplitude suivante et pour modifier la pente de la forme d'onde triangulaire dans l'intervalle de temps pendant lequel la valeur minimum est dépassée, par addition de la partie de l'incrément d'amplitude qui dépasse la valeur minimum à cette valeur minimum, pour créer la valeur d'amplitude suivante.


     
    14. Un circuit conforme à la revendication 13, dans lequel les moyens arithmétiques comprennent une unité arithmétique et logique et un accumulateur.
     
    15. Un circuit conforme à la revendication 11, dans lequel les moyens pour modifier la pente de la forme d'onde triangulaire comprennent:

    des moyens arithmétiques pour réaliser des opérations arithmétiques; et

    des moyens de commande pour valider les moyens arithmétiques.


     
    16. Un circuit conforme à la revendication 15, dans lequel les moyens arithmétiques comprennent une unité arithmétique et logique et un accumulateur.
     




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