JPH11133966A - Waveform generator - Google Patents

Abstract

PROBLEM TO BE SOLVED: To generate waeform data limiting the band area, by a digital processing. SOLUTION: By integrating a frequency number f to specify the pitch of a generating waveform by a digital integrator which consists of an adder 2 and a delay circuit 3, a serrate waveform data A is produced. This waveform data A is multiplied with a correcting data output from a window function table 10, in a multiplier 11, so as to output a serrate waveform data E receiving a specific band area limitation. The window function table 10 stores a data corresponding to the error between the serrate waveform and the serrate waveform having the band area limitation, and by reading the window function table 10 through an adder 5 to shift the phase 180 deg. in order to make the discontinuous point of the serrate waveform data A to a cross point; a multiplier to multiply the output of the adder 5 with the output of an inverse table 4; a shifter 7; a limiter 8; and an absolute valve circuit 9; a specific number of sample values before and after the discontinuous point of the serrate waeform can be read out.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a waveform generator for generating pulse waveform data such as a sawtooth wave, a rectangular wave or a triangular wave by digital processing.

[0002]

2. Description of the Related Art In an analog synthesizer, a voltage corresponding to a pressed keyboard is generated, and a VCO (Voltage Controlled) constituted by an integrator or the like is generated based on the voltage.
Oscillator) generates a simple waveform such as a sawtooth wave or a square wave and converts it into a VCF (Voltage Controlled Filte).
r) and a VCA (Voltage Controlled Amplifier) to adjust the tone and volume. The operation of such an analog synthesizer is likely to be unstable because it is an analog operation, and at present, most of the synthesizers have been replaced with digital synthesizers. However, an analog synthesizer has a unique sound quality, and in recent years, it has been desired to generate a musical tone generated by the analog synthesizer by digital processing.

[0003]

SUMMARY OF THE INVENTION By digital processing, V
As a method of generating a CO waveform, a feedback FM system and a waveform memory system are known. Feedback F
In the M method, the obtained sawtooth wave (SAW: Saw-Tooth Wa
ve) The waveform is distorted, is vertically asymmetric, and has a DC component. Therefore, when this SAW waveform is used for frequency modulation of a RING modulator or another VCO, an output different from that of the above-described analog operation is obtained. When the waveform memory method is used,
It is difficult to smoothly connect a plurality of band-limited waveforms according to the frequency, and LFO (Low Frequency Oscillat
When the frequency is changed drastically in (or), there is a problem that the discontinuity of the joint of the waveform is heard as noise. Furthermore, VC such as sawtooth wave and triangle wave
When generating an O waveform by digital processing, it is an important issue how to suppress aliasing (aliasing) of the waveform. That is, when a VCO waveform is generated by digital processing, a sample value that changes sharply at a discontinuous point of the waveform is output, resulting in waveform data containing a very large amount of high frequency components, and aliasing distortion occurs here. Becomes

SUMMARY OF THE INVENTION It is an object of the present invention to provide a waveform generator which solves the above-mentioned problems, has no aliasing, has good similarity to a waveform in an analog synthesizer, and does not cause waveform discontinuity. . That is,
It is an object of the present invention to provide a novel algorithm for digitally synthesizing waveforms such as sawtooth waves and pulse waveforms, which are indispensable for the tone of a classic analog synthesizer.

[0005]

In order to achieve the above object, a waveform generator according to the present invention comprises: a pulse waveform generating means for generating predetermined pulse waveform data by digital processing; Correction data generating means for generating correction data for the pulse waveform when the band is limited; and generating the pulse waveform based on the output of the correction data generation means at a sampling point near a discontinuous point in the pulse waveform. Correction means for correcting the output of the means. Further, the predetermined pulse waveform data is sawtooth waveform data, the correction data generating means is a window function table for generating band-limited window function data, and the correction means includes the pulse waveform and the window function. This is a multiplier that multiplies the output data of the table. Further, the predetermined pulse waveform data is sawtooth waveform data, and the correction data generating means generates correction data corresponding to a difference between a step waveform and a band-limited step response. Is a subtractor for subtracting the correction data from the sawtooth waveform data.

Further, the predetermined pulse waveform data is rectangular waveform data, and the correction data generating means generates correction data corresponding to a difference between a step waveform and a band-limited step response. The correction means is a subtractor for subtracting the correction data from the rectangular waveform data. Still further, still another waveform generator of the present invention has an odd number of means for generating data corresponding to a band-limited step response, and generates a band-limited rectangular wave by sequentially activating them. It is something that has been done. Still further, another waveform generator of the present invention is a means for generating triangular waveform data by digital operation, a means for generating sine waveform data, and a means for generating an interpolation coefficient corresponding to a frequency of a generated waveform. And a means for synthesizing the triangular wave waveform data and the sine wave waveform data in accordance with a mixing ratio determined by the interpolation coefficient.

[0007]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, embodiments of the waveform generator of the present invention will be described. However, the waveform generator of the present invention can be realized not only by hardware but also by
It can be realized by software or firmware using a DSP (Digital Signal Processor) or the like. First, a configuration example of a saw-tooth waveform generator for generating a band-limited saw-tooth waveform according to an embodiment of the waveform generator of the present invention will be described with reference to FIG. In FIG. 1, (a) is a block diagram showing a functional configuration of an embodiment of the saw-tooth wave (SAW) waveform generator,
(B) and (c) are diagrams showing an example of a waveform in a main part thereof. Here, (b) shows the waveforms of the respective parts indicated by A to E in FIG. 1A when a low-frequency SAW waveform is generated, and (c) generates the same high-frequency SAW waveform. The waveform of each part in the case is shown. Here, the amplitude of the output sawtooth wave is -1.
The description will be made assuming that the range is normalized to the range of +1.

In FIG. 1A, reference numeral 1 denotes an input terminal to which a frequency number (f number) for determining a repetition frequency (pitch) of a generated sawtooth wave is input. A value of f ≦ 1 is input. Here, the frequency number f is specified by, for example, a 14-bit binary number, whereby the repetition frequency of the sawtooth wave generated in 0.1-cent units can be set. 2 is a frequency number f input from the input terminal 1.
And an output of the delay circuit 3. In addition,
In the present invention, two types of adders are used. The first type of adder ignores even if the addition result overflows the number of digits, executes the addition, and outputs the remainder to the maximum value as the addition result (modulo adder, mo in the figure). The second is an overflow-detection type adder (ov in the figure) in which, when the addition result overflows, the subsequent addition result is fixed to the maximum value.
Described). Here, the adder 2 is the modulo adder. Reference numeral 3 denotes a delay circuit for delaying the output signal of the adder 2 by one sampling period. The adder 2 and the delay circuit 3 constitute a digital integration circuit. The output A of the adder 2 increases by f every sampling period, and when the adder overflows, the addition is started again from the beginning. Thus, the output A of the adder 2 becomes sawtooth waveform data having a repetition frequency determined by the frequency number f.

Here, the saw-tooth waveform A output from the adder 2 is not subjected to band limitation, and has waveform data having discontinuous points as shown in FIGS. 1B and 1C. And includes aliasing. In this embodiment of the present invention, the sawtooth waveform data A including the aliasing is input to a multiplier 11 and is multiplied by correction data D read from a window function table 10 before and after the discontinuity point. Thus, the ideal saw-tooth waveform data E without aliasing is output. The details of this modified data (window function) will be described later, but this window function has a SAW waveform having a predetermined passband characteristic and a S
It is data corresponding to the quotient with the AW waveform.

Hereinafter, a configuration for outputting such correction data D will be described. Reference numeral 4 denotes a reciprocal table for receiving a frequency number f from the input terminal 1 and outputting a number (R / f) proportional to the reciprocal thereof.
Modulo adder for adding the output of and a constant “−1”, 6
Is a multiplier for multiplying the output B of the adder 5 by the output (R / f) of the reciprocal table 4, 7 is a shifter for multiplying the output of the multiplier 6 by a constant s, and 8 is a shifter for the shifter 7. A limiter 9 for limiting the amplitude of the output to -1 to +1 is an absolute value circuit to which the output of the limiter 8 is input and which outputs the absolute value. The output C of the absolute value circuit 9 is input to the window function table 10 as an address, and the corresponding correction data D is output from the window function table 10.

In such a configuration, the output B of the adder 5 has a waveform obtained by shifting the phase of the output A of the adder 2 by 180 ° as shown in FIGS.
The position of the discontinuous point in the sawtooth waveform data A output from the adder 2 without band limitation is converted into the position of the zero cross point in the output B of the adder 5. Note that the slope of the sawtooth wave is the sampling period Fs
F / Fs because the frequency number f increases by each time. On the other hand, R / f is output from the reciprocal table 4, the output of the multiplier 6 is obtained by multiplying the waveform data B by R / f, and is further multiplied by a constant s in the shifter 7, thereby obtaining the limiter 8 The waveform data B
A waveform multiplied by s / f is input. Here, since the slope of the waveform B is f / Fs, the slope of the output of the shifter 7 is (f / Fs) × (R · s / f) = R · s / Fs, and is independent of the frequency number f. Constant value. This output is limited by ± 1 in the limiter 8, and the output C is used as the address of the window function table 10 via the absolute value circuit 9. Therefore, the slope portion of the output C is a portion where the discontinuous portion of the SAW waveform in the multiplier 11 is corrected.

The width of the portion where this correction is performed is 2Fs /
(R · s), and the number of samples N read from the window function table 10 in this portion is N = 2 / (R
S). Here, the coefficient R is the lowest frequency at which the window function table can be read at a constant speed, and the number N of read samples of the window function can be set to an arbitrary value depending on the magnitude of the constant s. It should be noted that as the number N of samples increases, the cutoff slope for band limitation can be made steeper, but conversely, at high frequencies, the window function can only be read halfway. Therefore, at frequencies where the entire window function can be read,
The number of aliases can be considerably small or almost zero, but increases sharply above a certain frequency. On the other hand, when N is reduced, some alias occurs, but does not increase suddenly even at higher frequencies. In general, in the case of a VCO, it is necessary to output a signal having a frequency up to near the Nyquist frequency.

In this manner, before and after the discontinuity point of the SAW waveform A, the corresponding correction data D is read from the window function table 10, and is multiplied by the multiplier 11 with the SAW waveform from the adder 2. And modified SA
The W waveform E is output. As shown in (b) and (c) of the figure, the output E is a straight line in the slope portion, and has an ideal SAW waveform with a limited pass frequency band in the discontinuous portion.

FIG. 2 is a diagram for explaining an example of a configuration for generating a window function (correction data) stored in the window function table 10. As shown in FIG. In this figure, reference numeral 21 denotes a frequency response setting unit for setting a frequency band. The frequency band characteristic set in the frequency response setting unit 21 may be a normal low-pass frequency characteristic having a flat pass band, or a predetermined pass band characteristic for adding a predetermined tone color characteristic. May be provided.

Reference numeral 22 denotes an inverse FFT (Fast Fourier Transform) for performing an inverse Fourier transform on the frequency characteristic set by the frequency response setting unit 21 to convert the frequency characteristic into a time-domain signal.
Reference numeral 23 denotes a window serving as a window for limiting the time response of the output signal of the inverse FFT unit 22. Also, 2
Reference numeral 4 denotes an FFT unit that converts the time response signal limited by the window unit 23 into a signal in the frequency domain again.
Reference numeral 25 denotes a SAW waveform output unit that outputs a normal SAW waveform that is not band-limited, and reference numeral 26 denotes an FFT unit that converts the SAW waveform output from the SAW waveform output unit 25 into a signal in the frequency domain.

Reference numeral 27 denotes a frequency response characteristic output from the FFT unit 24 and an SA output from the FFT unit 26.
This is a complex multiplier that performs complex multiplication with a signal in the frequency domain of the W waveform. Reference numeral 28 denotes an inverse FFT unit for converting the output of the complex multiplier 27 into the time domain.
A SAW waveform in which the passband characteristic set by the frequency response setting unit 21 is added to the AW waveform is output. 29 is a SAW waveform (x) to which a predetermined pass band characteristic output from the inverse FFT unit 28 is added,
A divider that divides the SAW waveform (y) from the SAW waveform output unit 25 that has not been band-limited and outputs a quotient (x / y). The output of the divider 29 is stored in the window function table 10. At this time, since the window function has a waveform that overshoots, when storing the window function in the window function table 10, it is necessary to set the maximum value to "1".

As described above, the window function is a band-limited S
Since the ratio (x / y) between the AW waveform (x) and the SAW waveform (y) that is not band-limited is output from the adder 2 in the multiplier 11 in FIG. By multiplying the SAW waveform of the frequency by this window function, it becomes possible to output SAW waveform sample data to which a desired pass band characteristic is added at a discontinuous portion.

When calculating the window function, the window function is calculated using a sampling frequency higher than the sampling frequency. As the oversampling is performed in this manner, the readout accuracy can be improved.
As an example, N = 16, the size of the window function (the size of the FFT) is 4096 (the actual size is half that of 2048)
Then, the oversampling ratio Or becomes Or = 409.
6/16 = 256, so the pass frequency band is 1
/ 256 or less to generate a window function. Also, N =
4. When the size is 4096, Or = 1024, so the band is set to 1/1024 or less. At this time, R = 1
If / 512, then s = 256.

As described above, according to the SAW waveform generator of this embodiment, the ideal SW in which the frequency band is limited at the discontinuous portion regardless of the frequency of the generated SAW waveform.
An AW waveform can be obtained.

In the embodiment shown in FIG. 1A, the frequency number f is set to 0 ≦ f ≦ 1, but the present invention is not limited to this, and positive and negative frequency numbers f are used. You can also. That is, FIG. 3 is a diagram showing a main configuration of the SAW waveform generator according to the present embodiment. In this case, since the frequency number f is set to −1 ≦ f ≦ 1, an absolute value circuit 14 may be provided on the input side of the reciprocal table 4 as illustrated. Other configurations may be the same as those in the case of FIG. Further, instead of the reciprocal table 4, a divider for dividing the coefficient R by the frequency number may be used.

Further, the window function (correction data) can be generated by a method other than the method shown in FIG. FIG. 4 is a diagram illustrating another example of a method for generating the window function. This method obtains a band-limited step response and uses it as a window function. In FIG. 4, reference numeral 31 denotes a SINC function (SINC
(X) = (sin πx) / πx) generation unit,
The INC function generator 31 outputs a signal corresponding to an impulse response when the spectrum amplitude function in a certain frequency range is constant. Reference numeral 32 denotes a window unit for limiting the output of the SINC function generation unit 31 to a necessary and sufficient time range. The window unit 32 outputs an impulse response waveform whose time range is limited. 33 is a step waveform generator for generating a step waveform. The time-limited SINC function output from the window unit 32 and the step waveform output from the step waveform generation unit 33 are convolution-integrated in a convolution operation unit 34, and the convolution integration operation results A predetermined part is cut out and stored in the window function table. Thus, from the step waveform limited to the predetermined frequency band,
The window function may be generated.

Next, a SAW waveform generator according to another embodiment of the waveform generator of the present invention will be described. In the embodiment shown in FIG. 1A, the SAW waveform is multiplied by the correction data, and the SA is subjected to a desired band limitation.
While this embodiment generates a W waveform,
By adding predetermined correction data to the AW waveform, a SAW waveform subjected to a desired band limitation is generated.

Before describing the configuration of the SAW waveform generator according to this embodiment, first, the operation principle of this embodiment will be described with reference to FIG. (A) of FIG.
FIG. 4 is a diagram for explaining the formation of the AW waveform. As shown in this diagram, it can be said that the SAW waveform a is composed of a ramp waveform and a plurality of step waveforms whose timings are shifted. Therefore, as shown in FIG. 5B, the band-limited SAW waveform x can be obtained from the sum of the ramp waveform and a plurality of band-limited step response waveforms whose timings are shifted. From the above, FIG.
As shown in (c), in order to obtain a band-limited SAW waveform, the difference d (= bc) between the step waveform b and the band-limited step response waveform c is subtracted from the SAW waveform a. I just need. Therefore, as shown in FIG. 5D, the SAW waveform x whose band is limited can be obtained by calculating a-d for all the falling edges of a.

FIG. 6 is a block diagram showing an example of the configuration of a SAW waveform generator constructed based on such a principle, and FIG. 7 is a waveform diagram showing an example of waveforms at portions indicated by A to H. is there. In FIG. 6, 51 is the S to be generated.
An input terminal to which a frequency number f for determining the frequency of the AW waveform is input.
A frequency number f ≦ 1 is input. This frequency number f is applied to one input of an adder 52 that performs modulo addition, and the other input of the adder 52 is a delay circuit 53 that delays the output of the adder 52 by one sampling period (Fs). Output is input. The adder 52 and the delay circuit 53 constitute a digital integration circuit, and f is accumulated for each sampling period, and when the adder 52 overflows, returns to the initial value and the accumulation is repeated. As a result, as in the case of the above-described embodiment, the band-limited sawtooth waveform data A
Is output.

The SAW waveform A that is not band-limited and output from the adder 52 is input to a delay circuit 54. In the example shown in this figure, since the correction data of four samples is read from the difference table 66 described later, the delay circuit 54 delays the SAW waveform A by two sampling periods. The SAW waveform A, which is not band-limited and passed through the delay circuit 54, is multiplied by a constant “0.5” in a multiplier 73, and is then input to an adder 74 for correcting the waveform. A predetermined band-limited SAW is added to the correction data H read from the difference table 66 and
The waveform I is output from the output terminal 75. In the difference table 66, a waveform d (= difference) between the step waveform shown in FIG.
Data corresponding to bc) is stored.

The unlimited-band SAW waveform A output from the adder 52 is added to a constant "-1" in an adder 56 for performing modulo addition, so that the phase becomes 1.
The waveform is shifted by 80 ° and the waveform indicated by B in FIG.
6 is output. As can be seen by comparing waveform A and waveform B in FIG. 7, the discontinuous portion of waveform A is the zero cross point of waveform B. The frequency number f input from the input terminal 51 is input to a reciprocal table 55, and a number 1 / (fs) corresponding to the reciprocal is output from the reciprocal table 55 using the frequency number f as an argument. Is done. Note that an arithmetic unit that performs division may be used instead of the reciprocal table 55. The waveform data B output from the adder 56 and the output 1 /
(F · s) is multiplied by a multiplier 57 and further multiplied by a constant s by a shifter 58. The output of the shifter 58 is multiplied by a constant “0.5” in an adder 59,
Further, a constant “−1” is added in the adder 60.
The output of the adder 60 is applied to the S terminal of the changeover switch 62.

The changeover switch 62 is controlled by an output v of an overflow detector 61 for detecting an overflow in the modulo adder 52. When an overflow is detected, the S (set) terminal is selected. Is controlled to select the C (clear) terminal. The C terminal is connected to the output of a delay circuit 64 that delays the output of an overflow type adder 63 that adds a constant “0.5” to the output of the changeover switch 62 by one sampling period. The output of the changeover switch 62 is input to an absolute value circuit 65, and the output of the absolute value circuit 62 is input to a difference table 66 as an address. The output of the difference table 66 is input to the adder 74 via a buffer amplifier 67. The buffer amplifier 67 outputs the input signal with the same polarity or inverted polarity based on the control signal.

The output v of the overflow detector 61 is input to a second switch 68 as a switching control signal, and a constant “0.75” is applied to the S terminal of the second switch 68. The output of a delay circuit 70 that delays the output of an adder 69 that adds a constant “0.5” to the output of the changeover switch 68 by one sampling period is connected to the C terminal. The output of the second changeover switch 68 changes the amplitude of the input signal from -1 to +1.
The output of the limiter 72 is applied to the buffer amplifier 67 as a control signal.

In the SAW waveform generator thus constructed, as shown in FIG. 7A, the output of the adder 52 is added by f every sampling period (Fs), and the SAW waveform has a slope f / It rises at Fs. Then, it is assumed that an overflow has occurred in the adder 52 at the timing 5. At this time, the generated S
The discontinuous point of the AW waveform is at the position indicated by a in the figure. Assuming that the value of the output of the adder 56 at the timing 5 at which the overflow occurs is P, the slope of the slope portion of the SAW waveform is f / Fs. P / f) · Fs, that is, the phase of the discontinuous portion is P / f =
It can be seen that it is shifted forward by T (0 ≦ T <1). In this manner, the phase shift of the discontinuous portion of the SAW waveform A can be detected from the output value P of the adder 56 at the overflow occurrence timing.

As described above, when the overflow occurs in the adder 52 and the overflow detection signal v is output from the overflow detector 61, the output of the shifter 58 becomes P / f = T, and the adder 60
To 0.5T-1 are applied to the S terminal of the changeover switch 62. The S terminal is selected by the changeover switch 62, and this value 0.5T-1 becomes the initial value of the read address of the difference table 66 for outputting the correction data H corresponding to the discontinuous portion.

Referring to FIG. 8, reading of data from the difference table 66 will be described. Actually, the difference data has the form shown in FIG. 9, but since this data is point-symmetric with respect to the origin, the difference table 6
No. 6 stores only the data of 0 to +1. In this embodiment, the difference table 66
= 4 samples of data are read, and it is necessary to advance the reading phase of the difference table 66 by T with respect to the sampling period. In order to change the address of the difference table from 1 to −1 in four samples, the increment of the address per sample is (1−1).
(-1)) / 4 = 0.5. Therefore, in order to read the difference table by the phase T, the initial value of the read address of the table is set to 0.5T-1.

The switch 62 selects the terminal C at a timing other than the timing at which the overflow occurs in the adder 52. Therefore, as shown in FIG. 7D, an output whose initial value is 0.5T-1 and which is increased by 0.5 every sample period is obtained from the changeover switch 62. The output of the changeover switch 62 is input to an absolute value circuit 65, and the output of the absolute value circuit 65 is input to a difference table 66 as an address.
The difference data for the sample is read.

As described above, the difference table 6
6 stores only a part (0 ≦ x ≦ 1) of the difference data d. Therefore, at the time of correction, the output of the difference table 66 is changed to the non-band-limited SA.
It is necessary to determine whether to subtract or add from the W waveform. For this purpose, the changeover switch 68 and the adder 6
9. A counter comprising a delay circuit 70, a shifter 71 and a limiter 72 are provided. After overflow, two samples are subtracted, and thereafter control is performed so as to be added.

That is, a constant "-0.75" is applied to the S terminal of the changeover switch 68, and the output of the changeover switch 68 is -0.75, -0.25, 0.2
Are counted as 5, 0.75..., Multiplied by a constant “4” in the shifter 71, and −1 to 1 in the limiter 72.
Limited to values in the range of 1. Therefore, the output of the limiter 72 is -1, -1,1,1,. This signal is applied to the buffer amplifier 67 and the signal is -1
In this case, the polarity of the output of the buffer amplifier 67 is inverted, and when the signal is 1, the output is output with the same polarity. The output of the buffer amplifier 67 is applied to an adder 74 as one input, and is added to the output of the multiplier 73 applied as the other input. Therefore, after overflow, the two samples are stored in the difference table 66.
Is subtracted with respect to the SAW waveform that is not band-limited, and the output of the difference table 66 is added to the subsequent samples. In this way, the correction process for the SAW waveform that is not band-limited is performed.

The reason why the difference data is stored in the difference table 66 in the above-described manner is as follows. That is, when the difference data is stored in a discontinuous form as shown in FIG. 9, the value that should become positive near 0 becomes negative due to an error in obtaining the initial value, or vice versa. May be positive,
This causes noise. Therefore, in the present embodiment, the difference data is stored as described above, and the correction operation is executed with the correct polarity using the counter as described above.

In the above embodiment, since four samples are read from the difference table 66, aliasing is performed at a frequency at which an overflow occurs at least once in four samples, that is, at a frequency of Fs / 4 = F _N / 2 or more. There is a problem that increases. Therefore, an embodiment that avoids such a problem will be described. FIG. 10 is a block diagram showing a configuration example of this embodiment. This embodiment provides the above-described problem by providing a plurality of means (portions surrounded by broken lines in FIG. 6) for reading the difference table in the embodiment of FIG. 6 and sequentially using them. Have been around. Generally, when reading N samples from the difference table, N
/ When the two difference table reading means is provided which can reproduce frequencies up to F _N.
In the embodiment shown in FIG. 10, two difference table reading means are used, and reading of the difference table is performed alternately.

In FIG. 10, the same components as those in FIG. 6 are denoted by the same reference numerals to avoid duplication of description. In this figure, reference numerals 100 and 101 denote difference table reading means, which correspond to the difference table reading means enclosed by broken lines in FIG. Also,
Reference numeral 81 denotes a changeover switch that switches between the input terminals S and C according to the output v of the overflow detection unit 61 and outputs the result. A delay circuit that outputs to the adder 83 is a modulo adder that adds the output of the delay circuit 82 and a constant “−1” and outputs the result to the input terminal S. Reference numeral 84 denotes a sign detection unit that detects the sign of the sign output from the changeover switch 81. The output n of the code detection unit 84 is supplied to the changeover switches 85, 86, 90, and 97 provided in the difference table reading means 100 and 101, respectively, as a changeover control signal.

The changeover switch 81 selects the input terminal S when the overflow detection signal v is output from the overflow detection section 61, and selects the input terminal C at other timings. Now, it is assumed that the modulo adder 52 overflows and the overflow detection unit 61 outputs an overflow signal v. At this time, the changeover switch 81 is connected to the s input terminal by the overflow signal v. The modulo adder 83 outputs a value between -1 and +1. Here, before the overflow is detected, the delay circuit 82
Is positive (0 to +1), the output of the adder 83 has a negative value, the output of the changeover switch 81 has a negative value via the input terminal S, and the negative output Is input to the delay circuit 82, and the negative value is held until the next overflow is detected. At this time, the sign detection unit 84 outputs an output signal n indicating negative. That is, a negative output signal is output instead of the output signal indicating positive before the overflow is detected.

On the other hand, if the output of the delay circuit 82 is a negative value (a value between -1 and 0) before the overflow is detected, the modulo of the negative value and "-1" is calculated. Due to the addition, the modulo adder 83 overflows, and its output becomes a positive value. Therefore, a positive signal is selected via the input terminal S, and the code detection unit 84
Is a signal indicating positive, and this positive signal is held through the delay circuit 82 until the next overflow is detected. As described above, the changeover switch 8
1. The output of the circuit by the delay circuit 82 and the modulo adder 83 is switched from positive to negative or from negative to positive every time the overflow occurs in the modulo adder 52.

Therefore, the output n of the code detection circuit 84 is switched between positive and negative each time an overflow occurs. As described above, this output n is supplied to the changeover switches 85 and 8 in the difference table reading means 100.
6. Applied as a control signal to the changeover switches 90 and 97 in the difference table reading means 101, each changeover switch is connected to the "+" side when the output n is a signal corresponding to a positive value, and corresponds to a negative value. If it is a signal, it is connected to the "-" side. FIG. 10 shows that the output n is positive and the changeover switches 85, 86, 90 and 9
7 is connected to the “+” side. In this case, the changeover switches 85 and 86 are set to “+”
Table, the difference table reading means 100
Has the same connection as the difference table reading means in FIG. 6, and, as described with reference to FIG. 6, reading of four samples of difference data is performed from the time of detection of the overflow.

On the other hand, in the difference table reading means 101, the output of the changeover switch 87 is connected to the “−” side of the changeover switch 90, and the output of the changeover switch 94 is connected to the “−” side of the changeover switch 97. It is connected to the. Therefore, as shown in FIG.
4 is the signal corresponding to the positive, and the changeover switch 90
And 97 are connected to the “+” side, the output v of the overflow detection unit 61 allows the outputs of the changeover switches 87 and 94 to be output even if the changeover switches 87 and 94 are connected to the s side. The input is not selected by the changeover switches 90 and 97 and the input of the absolute value circuit 91 and the input of the shifter 98 have no influence. That is, when the output of the code detection unit 84 is a signal corresponding to a positive value, the difference table reading means 100 operates in response to the overflow detection signal.

Next, when an overflow occurs again in the modulo adder 52 and the overflow signal v is output from the overflow detector 61, the output of the changeover switch 81 becomes a negative signal as described above, The sign detector 84 outputs a signal corresponding to a negative value. Thereby, the changeover switches 85, 86, 90
And 97 are switched to the "-" side. Thereby, in the difference table reading means 100, the outputs of the changeover switches 62 and 68 are not connected to the outputs of the changeover switches 85 and 86, while in the difference table reading means 101, the changeover switches 87 and 94 Are output from the changeover switches 90 and 97, respectively.
Will be connected. As a result, the difference data is read from the difference table 92 in response to the detection of the overflow, and the adder 7
In step 4, a correction process for the overflow is executed.

As described above, a plurality of difference table reading means 100 and 101 are provided, and these are alternately switched and used for each overflow of the modulo adder 52, thereby reading the difference table corresponding to one overflow. It is possible to eliminate the influence of the sample number N on the alias. Therefore, by setting N to be sufficiently large and providing the corresponding number of difference table reading means, aliases can be reduced to the ideal.

Further, this method can be applied to the generation of a rectangular wave. FIG. 11 is a conceptual diagram when this method is applied to generation of a rectangular wave. As shown in FIG. 11, a desired band-limited rectangular wave is corrected by sequentially using difference data corresponding to the rising and falling edges as shown in the drawing to the original non-band-limited rectangular wave. Can generate waves. However, in the case of a rectangular wave, it is necessary to correct both the rising and the falling, so it is necessary to read the table twice as frequently as in the case of the SAW waveform described above.
Alternatively, when the same number of tables are to be read, the upper limit frequency is １ ／ that of the SAW waveform.

Further, in the SAW waveform generator shown in FIG. 10, the difference table reading part is changed to the step response waveform reading, and the odd number table reading means is used. It is also possible to use a rectangular wave generator that generates a variable rectangular wave. When generating a rectangular wave with a variable duty, when the duty is changed, the pulse width may be shorter than the sampling period. Even in such a case, it is possible to generate a rectangular wave whose band is limited.

FIG. 12 is a diagram for explaining the outline of this embodiment. In this figure, (a) shows an example of a generated rectangular wave. When a pulse narrower than the sampling period is generated as shown in this figure, the output of the pulse indicated by A in the figure is output. It will not be generated. In order to prevent this, (b) of the figure
As described above, the SAW waveform C having a discontinuous portion corresponding to the rising position of the rectangular wave and the SAW waveform D delayed from the pulse waveform by the pulse width of the pulse waveform are generated as described above, and the discontinuous Is detected by the overflow detection unit 111. An odd number (three in the illustrated example) of step readout units 112 to 114 are provided, and by using these step readout units 112 to 114, in response to an overflow detection signal from the overflow detection unit 111, The band-limited step response waveforms corresponding to the falling or the rising are sequentially read, and the outputs from these are added by the adder 115 to output a band-limited narrow pulse waveform.

For example, the overflow detector 1 corresponding to the discontinuous portion (1) of the SAW waveform C shown in FIG.
11, the falling step waveform is read from the first step reading unit 112, and the SAW waveform D
The step waveform corresponding to the rising edge is read from the second step reading unit 113 in correspondence with the discontinuous portion (2). Next, a step waveform corresponding to the falling edge is read from the third step reading unit 114 corresponding to the discontinuous portion (3) of the SAW waveform C, and the step waveform corresponding to the discontinuous portion (4) of the SAW waveform D is read out. A step waveform corresponding to the rising edge is read from the first step reading unit. That is, each of the step readout units 111 to 113 alternately reads the falling and rising waveforms. In this manner, by providing an odd number of step reading units and sequentially reading the falling and rising step waveforms, a predetermined pulse waveform having a narrow width in which rising and falling occur within one sample period can be obtained. It is possible to generate a band-limited waveform.

FIG. 13 is a diagram showing a flowchart of the processing executed in this embodiment. Where f
Is a flag for indicating whether the next step waveform to be read is a rising waveform or a falling waveform. When f = 0, it indicates that the next waveform to be read next is a falling waveform. A value of 1 indicates that a rising waveform is read next.

When this process is started, first, in step S11, it is determined whether or not the flag f is 0. If the result is YES, proceed to step S12,
It is determined whether or not an overflow of the SAW waveform C (FIG. 12B) has occurred. Here, when an overflow occurs, the reading of the falling waveform designated by the flag f is started for one of the step reading units 112 to 114 (these are sequentially started) (S13). ), And sets the flag f to 1 (S
14). Then, the process proceeds to step S18. On the other hand, the S
When the overflow of the SAW waveform is not detected in step 12, the process proceeds to the next step S18. If the flag f is not 0 in step S11,
Proceeding to 15, it is determined whether an overflow of the delayed SAW waveform D has occurred. Here, when an overflow occurs, one of the step reading units 112 to 114 starts reading the rising waveform indicated by the flag f (S16), and clears the flag f to 0 (S17). If the overflow has not occurred in step S15, the process proceeds to step S18.

Step S18 and subsequent steps are performed in steps S11 to S1.
The same processing as in step 7 is performed. This is within one sample
This is because rising and falling (or vice versa) may be present simultaneously. In this manner, by sequentially reading the falling or rising step waveform from the odd number of step reading sections, the pulse waveform having the narrow pulse width can be generated.

Next, still another embodiment of the present invention will be described. In this embodiment, a band-limited triangular wave is generated. FIGS. 14A and 14B are diagrams for explaining this embodiment. FIG. 14A is a block diagram schematically showing the functional configuration, and FIG. 14B is a block diagram.
FIG. 6 is a diagram showing output waveforms at various parts in the block diagram shown in FIG. In this figure, reference numeral 121 denotes an input terminal for inputting a frequency number f, and a frequency number f between -1 and +1 is input from this terminal 121. Reference numeral 122 denotes a modulo adder for adding the frequency number f and the output from the delay circuit 123, and reference numeral 123 denotes a delay circuit for delaying the output of the modulo adder 122 by one sampling period.
A digital integration circuit is constituted by the modulo adder 122 and the delay circuit 123, and the output A thereof has a SAW waveform that is not band-limited.

Reference numeral 124 denotes a sine wave output y (y = −) corresponding to the output A of the modulo adder 122 as an address x.
(sin πx). The sine table 124 outputs a sine wave output B as shown in FIG. A multiplier 125 multiplies the sine wave output B by a constant “2 / π”. Such multiplication by 2 / π makes the maximum value of the slope of the output triangular wave and that of the sine wave the same. To do that. Note that the multiplier 125 does not necessarily have to be provided. An adder 126 modulo-adds the output A of the modulo adder 122 and a constant "-0.25". The output of the adder 126 is an output C obtained by phase-shifting the output A by 90 [deg.]. .

Reference numeral 127 denotes an absolute value circuit which receives the output C of the modulo adder 126 and outputs its absolute value.
28 indicates “−” with respect to the absolute value output from the absolute value circuit 127.
An adder 129 for adding 0.5 ”is a shift circuit for multiplying the output of the adder 128 by a constant“ 2 ”. The output D of the shift circuit 129 is an output as shown in FIG. D. From the absolute value circuit 127, the output C
Is returned at the 0 level, and a triangular wave having an amplitude of 0 to +1 is output.
The level is shifted to a triangular wave having an amplitude of 0.5 to +0.5, and is further multiplied by a constant 2 in the shift circuit 129 to convert the amplitude of the triangular wave to -1 to +1 to obtain a triangular wave indicated by D. And

An interpolation coefficient generator 130 outputs an interpolation coefficient k corresponding to the frequency number f.
An interpolation coefficient k is output based on an expression such as k = a · f + b (a and b are constants). As will be described later, the interpolation coefficient k is a coefficient for determining a correction amount when a band corresponding to a vertex of a generated triangular wave is interpolated by a sine wave to apply a band limitation. For example, the frequency number f is small, When the frequency of the triangular wave to be generated is low, the value of the interpolation coefficient k is reduced to output a triangular wave with a small amount of interpolation, and the frequency number f
When a large triangular wave of high frequency is generated, a large interpolation coefficient is generated to increase the correction amount by the sine wave.

A multiplier 131 multiplies the triangular wave whose band is not limited by the shift circuit 129 and the interpolation coefficient k output from the interpolation coefficient generator 130.
32 is a multiplier for multiplying the sine wave output from the multiplier 125 by the interpolation coefficient k from the interpolation coefficient generator 130. 133 denotes the sinusoidal waveform B × k output from the multiplier 132, and the shift circuit 12
9 and the multiplier 131
Is an adder for adding the inverted waveform of the output D × k. Thus, the output of the adder 133 is k · B
+ D−k · D = k · B + (1−k) · D. As a result, a triangular waveform output E interpolated with a sine wave is obtained according to the mixture ratio determined by the interpolation coefficient k.

As described above, according to the present embodiment, it is possible to generate a triangular wave whose band is limited according to the frequency to be generated, and to prevent aliasing. In addition, as the interpolation coefficient generating unit 130,
The present invention is not limited to the one that calculates and outputs the interpolation coefficient k corresponding to the frequency number f using the above-described arithmetic expression. For example, a type that refers to a table may be used.

[0057]

As described above, according to the waveform generator of the present invention, it is possible to generate pulse waveform data such as a sawtooth wave, a rectangular wave, and a triangular wave whose band is limited by the waveform level. Also, at that time, regardless of the pitch of the generated waveform, it is possible to output an ideal waveform in which the band of the discontinuous point is limited, and it is possible to generate a tone color similar to an analog synthesizer.

[Brief description of the drawings]

FIG. 1 is a block diagram showing a configuration example of a sawtooth wave generator which is an embodiment of a waveform generator of the present invention, and a diagram showing an example of a waveform of each part thereof.

FIG. 2 is a diagram for describing a means for generating a window function in the sawtooth wave generator shown in FIG.

FIG. 3 is a diagram showing a modified example of the sawtooth wave generator shown in FIG.

FIG. 4 is a diagram for explaining another means for generating a window function in the sawtooth wave generator shown in FIG. 1;

FIG. 5 is a diagram for explaining the principle of another configuration example of the sawtooth wave generator which is another embodiment of the waveform generator of the present invention.

FIG. 6 is a diagram illustrating a configuration example of a sawtooth wave generator configured based on the principle illustrated in FIG. 5;

FIG. 7 is a diagram showing an example of a waveform of each part of the sawtooth wave generator shown in FIG.

FIG. 8 is a diagram for explaining reading of a difference table in the sawtooth wave generator shown in FIG. 6;

FIG. 9 is a diagram for describing correction data in the sawtooth wave generator shown in FIG.

FIG. 10 is a block diagram showing a configuration example of a saw-tooth wave generator configured to generate sawtooth waveform data having a high pitch.

FIG. 11 is a diagram for explaining the principle of a rectangular wave generator which is another embodiment of the waveform generator according to the present invention.

FIG. 12 is a diagram for explaining an operation principle of a rectangular wave generator having a pulse width shorter than a sampling period, which is still another embodiment of the waveform generator of the present invention.

FIG. 13 is a flowchart for explaining the operation of the rectangular wave generator shown in FIG.

FIG. 14 is a block diagram illustrating a configuration example of a triangular wave generator as still another embodiment of the waveform generator according to the present invention;
It is a figure showing an example of a waveform of each part.

[Explanation of symbols]

1, 51, 121 input terminals, 2, 5, 52, 56, 6
0, 63, 69, 74, 83, 88, 95, 115, 1
22, 126, 128, 133 Adders, 3, 53, 5
4, 64, 70, 82, 89, 96, 123 delay circuit, 4, 55 reciprocal table, 6, 11, 57, 59,
73, 125, 131, 132 Multiplier, 7, 58, 7
1, 98, 129 shifter, 8, 72, 99 limiter, 9, 13, 65, 91, 127 absolute value circuit, 10
Window function table, 12, 75, 134 output terminal, 2
1 frequency response setting unit, 22, 28 inverse FFT unit, 2
3, 32 window section, 24, 26 FFT section, 25
SAW waveform generator, 27 complex multiplier, 29 divider,
31 SINC function generator, 33 step waveform generator, 34 convolution calculator, 61, 111 overflow detector, 62, 68, 81, 85, 86, 87,
90, 94, 97 selector switch, 66, 92 difference table, 67, 93 buffer amplifier, 84 code detector, 112 to 114 step readout unit, 124 sine table, 120 interpolation coefficient generator

Claims (6)

[Claims] 1. A pulse waveform generating means for generating predetermined pulse waveform data by digital processing, and a correction data generating means for generating correction data for the pulse waveform when a predetermined band limitation is applied to the pulse waveform. And a correction means for correcting the output of the pulse waveform generation means based on the output of the correction data generation means at a sampling point near a discontinuous point in the pulse waveform. 2. The method according to claim 1, wherein the predetermined pulse waveform data is sawtooth waveform data, the correction data generating means is a window function table for generating band-limited window function data, and wherein the correction means 2. The waveform generator according to claim 1, wherein the multiplier is a multiplier that multiplies output data of the window function table. 3. The predetermined pulse waveform data is sawtooth waveform data, and the correction data generating means generates correction data corresponding to a difference between a step waveform and a band-limited step response. 2. The waveform generator according to claim 1, wherein said correction means is a subtractor for subtracting said correction data from said sawtooth waveform data. 4. The method according to claim 1, wherein the predetermined pulse waveform data is rectangular waveform data, and the correction data generating means generates correction data corresponding to a difference between a step waveform and a band-limited step response. 2. The waveform generator according to claim 1, wherein said correction means is a subtracter for subtracting said correction data from said rectangular waveform data. 5. The method according to claim 1, further comprising the step of generating an odd number of means for generating data corresponding to the band-limited step response, and generating a band-limited rectangular wave by sequentially activating them. Waveform generator. 6. A means for generating triangular wave waveform data by digital operation, a means for generating sine wave waveform data, a means for generating an interpolation coefficient corresponding to the frequency of the generated waveform, and the means for determining the interpolation coefficient. A waveform generator for generating a band-limited triangular wave, comprising: means for synthesizing the triangular wave waveform data and the sine wave waveform data according to a mixing ratio.