JPH07281668A - Waveform generating device - Google Patents

Abstract

PURPOSE:To obtain a sinusoidal waveform with a desired frequency and precision by performing a simple sum of products operation using a system in which the multiplying means and the subtracting means are respectively constituted of a multiplier and an adder. CONSTITUTION:Sawtooth waves generated by a sawtooth wave generator 10 are divided into two sections: one is to be inputted into a sawtooth-wave-to- triangular-wave converter 14a and the other to be inputted into sawtooth-wave- to-triangular-wave converters, 14b, 14c, 14d...14z via first multipliers, 12b, 12c, 12d...12z. Triangular waves outputted from the sawtooth-wave-to-triangular-wave converter 14a are inputted into an adder 18 and triangular waves outputted from the sawtooth-wave-to-triangular-wave converters, 14b, 14c, 14d...14z are inputted into the adder 18 via second multipliers, 16b, 16c, 16d...16z. The adder 18 outputs the difference obtained by subtracting the triangular waves outputted from the second multipliers, 16b, 16c, 16d...16z from the triangular waves outputted from the sawtooth-wave-to-triangular-wave converter 14a to output sinusoidal waves.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION The present invention relates to a waveform generator,
More specifically, it relates to a waveform generator that generates a waveform by calculation.

[0002]

2. Description of the Related Art Generally, as a modulator for modulating a tone signal as a modulated wave, a tone signal is delayed to produce a chorus,
Effect adding devices that add effects such as vibrato, flanger, or phaser are widely known.

FIG. 11 shows the overall structure of such an effect adding device.
Processing for adding effects such as vibrato, flanger, or phaser is executed. That is, in this effect adding device, a musical tone signal (analog signal) generated by a sound source (not shown) is converted into a digital signal by the analog-digital converter (AD) 102 and input to the DSP 100. Digital-to-analog converter (DA) 10 after the addition of
4 is converted into an analog signal, is further output to a sound system (not shown) composed of an amplifier, a speaker and the like, and is emitted as a musical sound in space.

The DSP 100 is controlled by the CPU 106.
ROM 108 storing a program of processing executed by
And a RAM 110 storing coefficients and offset data required for effect addition processing by the DSP 100. In addition, the DSP 100 has a RAM 112 (delay
(Corresponding to line 130) is connected.

The coefficient and offset data stored in the RAM 110 can be rewritten by operating the operator group 114, and the current setting state of the coefficient and offset data is displayed on the display unit 116. It

FIG. 12 shows a functional block diagram for realizing the chorus effect added by the effect adding device shown in FIG. 11 described above.
The digital signal output from 2 is branched into a direct signal directly input to the adder 132 and an input signal input to the delay line 130, and the delay line 1
Input signal data is sequentially written into 30. Then, the pitch conversion is performed by changing the read address of the data written in the delay line 130.

That is, address modulation is performed by addressing the read pointer (RP) 134 of the delay line 130 based on the modulated wave output from the waveform generator 136. As a result, pitch conversion that periodically causes pitch fluctuation is performed, and the pitch-converted signal (effect signal) and the direct signal are added by the adder 132, whereby the chorus effect is realized. Become. Then, the digital signal output from the adder 132 is the DA 104
Is input to.

Further, there is known a panning device which imparts a panning effect in which a sound image periodically moves to the left and right, and its configuration is shown in FIG.

That is, this panning apparatus is provided with an amplifier 200 for the left side output (L) and an amplifier 202 for the right side output (R), and the volume of the musical sound is generated by the modulated wave output from the waveform generator 204. By modulating the amplifier 200 in the positive phase and the amplifier 204 in the opposite phase,
This is a panning effect in which the sound image periodically moves left and right.

[0010]

The modulated wave generated by the waveform generator in the effect adding device or the panning device described above is a triangular wave or a sine wave (si).
n) Waves have been used.

On the other hand, in order to generate a waveform by digital calculation, a method based on sum of products calculation has been conventionally used.
For waveforms such as sine waves that are difficult to generate by simple product-sum calculation, table reading, approximate calculation,
Methods such as filtering have been taken.

However, in order to generate an accurate sine wave at a low frequency, the above method is
There are problems that the scale of the table becomes large, the calculation becomes complicated, and the filter design becomes difficult.

The present invention has been made in view of the above-mentioned various problems of the prior art, and its object is to provide a sine wave waveform having an arbitrary frequency by a simple product-sum operation. It is an object of the present invention to provide a waveform generator capable of generating a sine wave waveform having a desired accuracy even at a low frequency.

[0014]

In order to achieve the above-mentioned object, a waveform generator according to the present invention is a waveform generator which generates a sine wave waveform, and has the same frequency as a desired sine wave frequency. A first triangular wave generating means for generating a first triangular wave and a second triangular wave having a frequency of 2n + 1 times (n is a positive integer) the frequency of the first triangular wave generated by the first triangular wave generating means. , A second triangular wave generating means for respectively generating a number corresponding to a predetermined value of n, and an amplitude coefficient for supplying a desired amplitude coefficient respectively corresponding to the n triangular waves generated by the second triangular wave generating means. Supplying means, and multiplying means for multiplying each of the n triangular waves generated by the second triangular wave generating means by the amplitude coefficient supplied by the amplitude coefficient supplying means,
And a subtracting means for subtracting the n triangular waves obtained by the multiplying means from the output of the first triangular wave generating means.

Further, the waveform generator according to the present invention is a waveform generator for generating a sine wave waveform, wherein the first square wave generating means generates a square wave having the same frequency as the frequency of the desired sine wave waveform. And 2n + 1 times the frequency of the square wave generated by the first square wave generating means (n
Is a positive integer), and second square wave generating means for respectively generating a square wave having a frequency of a predetermined value of n,
The amplitude coefficient supplying means for supplying desired amplitude coefficients respectively corresponding to the n square waves generated by the second square wave generating means, and the amplitude coefficient supplied by the amplitude coefficient supplying means are Multiplication means for multiplying each of the n square waves generated by the square wave generation means, and subtraction means for subtracting the n square waves obtained by the multiplication means from the output of the first square wave generation means. And have.

[0016]

Since the multiplication means can be constituted by the multiplier and the subtraction means can be constituted by the adder, it is possible to obtain a sine wave waveform having a desired frequency and a desired accuracy by a simple product-sum operation.

[0017]

Embodiments of the waveform generator according to the present invention will now be described in detail with reference to the accompanying drawings.

FIG. 1 is a block diagram of a waveform generator according to the first embodiment of the present invention.

In FIG. 1, reference numeral 10 indicates a sawtooth wave generator. The sawtooth wave generated by the sawtooth wave generator 10 is directly input to the sawtooth wave-triangle wave converter 14a and a first multiplier. 12z via 12b, 12c, 12d ... 12z and are branched into those input to the saw-to-triangle converters 14b, 14c, 14d.

The triangular wave output from the sawtooth-triangular wave converter 14a is directly input to the adder 18, and the triangular waves output from the sawtooth-triangular wave converters 14b, 14c, 14d ... Second multipliers 16b, 16c, 1
It is input to the adder 18 via 6d ... 16z.

In the adder 18, the second multiplier 16 is converted from the triangular wave output from the sawtooth-wave converter 14a.
The triangular waves output from b, 16c, 16d, ..., 16z are subtracted and output, and a sine wave waveform is generated here.

The sine wave waveform output from the adder 18 is amplified to a desired value by the third multiplier 20 and then input to the LPF (low pass filter) 22. It will be used as a modulated wave after cutting the second harmonic component.

Next, each component of the first embodiment shown in FIG. 1 will be described in detail. First, the sawtooth wave generator 10 has a finite bit length and adds constants based on a constant clock. , A sawtooth wave having an arbitrary frequency with an amplitude of "+1 to -1" is obtained. For example, when the bit length of the counter is "16", as shown in FIG. 2, the amplitude is in the range of the maximum value "7FFF (H)" and the minimum value "8000 (H)". Yes, overflows that occur during addition are ignored.

Here, "H" is used as a symbol representing a hexadecimal number and is written as "7FFF (H)". In the following description, this notation will be used. In addition,
“7FFF (H)” and “8000 (H)” are decimal numbers “32767” and 2 ’s complement display, respectively.
It represents "-32768".

In the sawtooth generator 10, the frequency of the sine wave waveform finally generated can be changed by changing the constant to be added.

The first multipliers 12b, 12c, 12d ...
12z triples the frequency of the sawtooth wave generated by the sawtooth wave generator 10, triples 5 times, 7 times ... 2n + 1 times (n is a positive integer), thereby multiplying 3 times, 5 times, 7 times. Double ...
A sawtooth wave having a uniform phase and level is obtained at a frequency of 2n + 1 times. The resulting overflow shall be ignored.

For example, when the above 16-bit counter is tripled by the first multiplier 12b, it becomes as shown in FIG. That is, when a sawtooth wave (FIG. 3A) that oscillates from the maximum value to the minimum value is tripled, a waveform shown by a broken line in FIG. For more information, see “7FFF
(H) (maximum value) to 8000 (H) (minimum value) ". First multiplier 12c, 12
At d ... 12z, sawtooth waves having frequencies of 5 times, 7 times ... 2n + 1 times are also generated in the same manner as above.

Saw-to-triangle converters 14a, 14b, 14
c, 14d ... 14z are the 1 × (sawtooth wave directly input by the sawtooth wave generator 10) generated above, the 3 × sawtooth wave, the 5 × sawtooth wave, the 7 × sawtooth wave ... The processing shown in the flowchart of FIG. 4A is performed for each of the 2n + 1 times sawtooth waves. Further, FIG. 4B shows the waveform generated in the processing of each step of the flowchart of FIG.

That is, first, from a sawtooth wave (SAW) having an amplitude of "-1 to +1" (START: start), its absolute value is obtained to generate a triangular wave (TRI) (step S40).
2). In other words, the waveform on the minus (-) side is plus (+)
As a result, a triangular wave having an amplitude of "0 to +1" is obtained.

Next, the value of the triangular wave generated in step S402 is subtracted by "0.5" to generate a triangular wave oscillating around "0" (step S404). That is, the value of the triangular wave generated in step S402 is "-0.5".
By shifting, the center of the amplitude is adjusted to "0". It should be noted that subtracting the value of the triangular wave by "0.5" means that if it is a 16-bit counter, it is "4000".
(H) ”will be drawn.

Furthermore, the value of the triangular wave generated in step S404 is doubled (step S406). That is, the amplitude of the triangular wave generated in step S404 is doubled, and "-
A triangular wave having an amplitude of "1 to +1" is generated.

Then, the triangle wave generated in step S406 is added to the adder 18 (in the case of the sawtooth-wave converter 14a).
Alternatively, the second multipliers 16b, 16c, 16d ... 16
z (sawtooth wave-triangle wave converters 14b, 14c, 14d ...
14z) (step S40)
8).

Sawtooth-to-triangle converters 14b, 14c, 14
d ... The second multiplier 16 to which the triangular wave is output from 14z
b, 16c, 16d, ... 16z are coefficients (amplitude coefficients) for the triangular waves oscillated by "-1 to +1" output from the sawtooth-triangular wave converters 14b, 14c, 14d, ... 14z.
As (1/9), (1/25), (1/4)
9) ... is multiplied, and the amplitudes of the triangular waves having amplitudes of “−1 to +1” are multiplied by (1/9), (1/25), and (1
/ 49) times ...

Then, in the adder 18, the second multipliers 16b, 16c, 16 are converted from the triangular wave having the frequency of the desired sine wave output from the sawtooth-wave converter 14a.
d ... 3 times, 5 times, 7 respectively output from 16z
The frequency is doubled, and the amplitude is (1 / n).
By subtracting the triangular wave multiplied by 9), (1/25), (1/49), etc., a sine wave waveform can be obtained.

At this time, for example, as the first multipliers, up to the first multiplier 12d for multiplying the frequency of the sawtooth wave by 7 are used,
As a result, the saw-to-triangle converter and the second multiplier are also saw-to-triangle converter 14d and second multiplier 1.
If up to 6d is used, the first multipliers 12b, 12c, 12d for inputting the sawtooth wave output from the sawtooth wave generator 10
The 3rd, 5th, and 7th harmonic components corresponding to the coefficient of can be removed, and a waveform extremely approximate to a sine wave having slightly higher harmonic components than the 11th harmonic can be obtained.

Then, if a waveform extremely close to the sine wave output from the adder 18 is amplified through the third multiplier 20 and the LPF 22 cuts overtones of 11th order or higher from the waveform output from the adder 18. An accurate sine wave can be obtained.

Since the LPF 22 only needs to cut the slightly remaining overtones of the 11th order or higher, it is extremely easy to design as compared with the LPF used in the conventional waveform generator.

As described above, the waveform output from the adder 18 may be used as it is as a modulated wave without passing the waveform output from the adder 18 to the LPF 22, or the third multiplier may be used. It may be used after being amplified via 20.

That is, in the above embodiment, by setting the value of "n: positive integer" to an arbitrary value, the (2n + 1) th harmonic component can be removed.
A sine wave with a desired accuracy can be easily obtained by only the product-sum calculation.

That is, when the triangular wave (Tri) of the angular frequency ω is Fourier expanded, Tri (ω) = A [cosω + (1/9) cos3ω + (1/25) cos5ω + ... + {(1 / (2n + 1) ² } cos (2n + 1) ω + ...], and Tri (3ω) = A {cos3ω + (1/9) cos9ω + ...} Tri (5ω) = A {cos5ω + (1/9) cos15ω + ...} , And so on, cos (ω) = A {Tri (ω)-(1/9) Tri (3ω)-(1/25) Tri (5ω) ...}.

Therefore, when a sine wave is generated up to a triangular wave of 7ω according to the above example, f (ω) = Tri (ω)-(1/9) Tri (3ω)-(1/25) Tri (5ω) − (1/49) Tri (7ω) = A {cosω + (1/121) cos (11ω) + ...} Equation 1 is obtained.

Therefore, the LPF 22 for cutting the higher harmonics
For this, it is sufficient to cut off 11ω or more.

FIG. 5 shows the relationship between the order N (coefficient of the first multiplier) and the coefficient (amplitude coefficient) P of the second multiplier to be removed, which is obtained from the equation 1. N in the table shown in
By selecting the higher harmonics that you want to remove sequentially from the smallest value of, you can obtain the accurate sine wave at a low frequency only by a simple multiply-accumulate operation without reading the table or performing a highly accurate operation. it can.

Here, the coefficient P of the second multiplier shown in FIG. 5 corresponds to the "amplitude coefficient" in the claims, and this coefficient P is the sawtooth-triangle wave converter 1.
4a does not match the amplitude of the overtone component of the triangular wave, because the sawtooth-triangle wave converters 14b, 14c, 14d, ... This is because the amplitude coefficient is set to cancel the component.

As a method of obtaining such an amplitude coefficient, for example, there is a method described below.

[First Method] The table shown in FIG. 5 is used as the amplitude coefficient table in advance in the ROM 108 or R shown in FIG.
How to store in AM110.

[Second Method] 1 / (2n + 1) ² when it is not necessary to remove even higher harmonics
A method of using as an amplitude coefficient by calculating.

For example, when removing 3ω to 9ω, n may be calculated from 1 to 3. Specifically, the amplitude coefficient of the 3ω triangular wave 1 / (2 × 1 + 1) ² = 1/9 5ω of the triangular wave amplitude coefficient 1 / (2 × 2 + 1) ² = 1/25 7ω of the triangular wave amplitude coefficient 1 / ( A triangular wave of 2 × 3 + 1) ² = 1/49 9ω has an amplitude coefficient of 0 and therefore cannot be calculated.

If 3ω to 13ω is removed, 1 to 6 may be calculated except when n is 4. Specifically, the amplitude coefficient of the 3ω triangular wave 1 / (2 × 1 + 1) ² = 1/9 5ω of the triangular wave amplitude coefficient 1 / (2 × 2 + 1) ² = 1/25 7ω of the triangular wave amplitude coefficient 1 / ( 2 × 3 + 1) ² = 1/49 9ω triangular wave has amplitude coefficient 0, so it is not calculated 11ω triangular wave amplitude coefficient 1 / (2 × 5 + 1) ² = 1/121 13ω triangular wave amplitude coefficient 1 / (2 × 6 + 1) ² = 1/169.

[Other Method] A method of obtaining the amplitude coefficient by assembling an equation for obtaining the amplitude coefficient of each overtone from the Fourier expansion equation.

FIG. 6 shows a triangular wave (the output waveform of the sawtooth-triangular wave converter 14a in FIG. 1) and a waveform obtained by removing the third harmonic from the triangular wave (the first multiplier 12b, the sawtooth wave in FIG. 1).
The output waveform of the adder 18 when the triangular wave converter 14b and the second multiplier 16b are used) and the waveform obtained by removing the fifth harmonic from the triangular wave (the first multiplier 12c, the sawtooth-triangular wave converter in FIG. 1). 14c, the output waveform of the adder 18 when using up to the second multiplier 16c) and the waveform from the triangular wave to the 7th harmonic (first multiplier 12d, sawtooth-triangular wave converter 14d, The output waveform of the adder 18 when using up to 2 multipliers 16d) and the waveform of the sine wave are shown in comparison. The waveform obtained by removing the 7th higher harmonics is extremely sine wave. It turns out that they can be approximated.

FIG. 7 shows a block diagram of a waveform generator according to a second embodiment of the present invention. The same components as those of the first embodiment shown in FIG. 1 are designated by the same reference numerals, and detailed description thereof will be omitted.

In FIG. 7, reference numeral 10 denotes a sawtooth wave generator. The sawtooth wave generated by the sawtooth wave generator 10 is directly input to the sawtooth wave to square wave converter 30a and is subjected to the first multiplication. 12z through the converters 12b, 12c, 12d, ... 12z to those input to the saw-to-square wave converters 30b, 30c, 30d, ... 30z.

The square wave output from the sawtooth-square wave converter 30a is directly input to the adder 18 and output from the sawtooth-square wave converters 30b, 30c, 30d ... 30z. The square wave is generated by the fourth multipliers 32b, 32c, 3
It is input to the adder 18 via 2d ... 32z.

In the adder 18, the fourth wave from the square wave output from the sawtooth-square wave converter 30a to the fourth multiplier 32.
The square waves output from b, 32c, 32d, ..., 32z are subtracted and output, and a sine wave waveform is generated here.

The sine wave-shaped waveform output from the adder 18 is amplified to a desired value by the third multiplier 20 and then input to the LPF (low pass filter) 22. It will be used as a modulated wave after cutting the second harmonic component.

Next, each constituent element of the second embodiment shown in FIG. 7 will be described in detail. The sawtooth-square wave converters 30a, 3 will be described.
0b, 30c, 30d ... 30z are sawtooth wave generators 10
1 × sawtooth wave directly input by the first multiplier 12
3 input by b, 12c, 12d ... 12z
Double sawtooth wave, 5 times sawtooth wave, 7 times sawtooth wave ... 2n + 1 times sawtooth wave, (i) Corresponds "+1" (maximum value) to the plus (+) side Let (Ii) "-1" (minimum value) is associated with the minus (-) side portion of the waveform. Is performed. For example, when the 16-bit counter described in detail in the first embodiment is used, it is assumed that it is a two's complement display, and the processing shown in the flowchart of FIG. 8A is performed. In addition, in FIG.
Waveforms generated in the processing of each step of the flowchart of FIG. 8A are shown.

That is, first, SA having an amplitude of "-1 to +1"
From W (sawtooth) (START: start), mask all but the most significant bit of SAW to zero (step S9).
02). In other words, the binary number "1000 0000 000"
"0000" and the SAW are ANDed. As a result, SQR (square wave) becomes "0000 (H)" (binary number "0
"000 0000 0000 0000") or "8000 (H)" (binary number "1000 0000 0
000000 ").

Next, the SQR generated in step S902
The value of is rotated left by 1 bit (step S904). In other words, the binary number "0000 0
000 0000 0000 "(= 0000 (H))
Rotates 1 bit to the left and performs a rotate shift to "000
0 0000 00000000 "(= 0000
(H)) and the binary number "1000 0000 000"
"0000" (= 8000 (H)) is 1 bit to the left, and when rotated, it becomes "0000 0000".
00000001 ”(= 0001 (H)).

Further, "7FFF (H) (binary number" 0111 1111 11111111 ") is added to SQR (step S906). In other words, "0000
If you add "7FFF (H)" to "(H)", you get "7FFF
(H) ”, but“ 7FFF ”is added to“ 0001 (H) ”
(H) ”is added, the binary number becomes“ 1000 0000
0000 0000 ". This is "800
0 (H) ".

Then, the square wave generated in step S906 is added to the adder 18 (in the case of the sawtooth-square wave converter 30a).
Alternatively, the fourth multipliers 32b, 32c, 32d ... 32
z (sawtooth-square wave converter 30b, 30c, 30d ...
In the case of 30z), it is output (step S90).
8).

Sawtooth-to-square wave converters 30b, 30c, 30
d ... The fourth multiplier 32 that outputs a square wave from 30z
b, 32c, 32d ... 32z are coefficients (amplitude coefficients) for the square waves oscillating at "-1 to +1" output from the saw-to-square wave converters 30b, 30c, 30d ... 30z.
As (1/3), (1/5), (1/7).
.. is multiplied, and the amplitudes of the square waves having amplitudes of "-1 to +1" are multiplied by (1/3), (1/5), (1/7), ...

Then, in the adder 18, from the square wave having the frequency of the desired sine wave output from the sawtooth-square wave converter 30a, the fourth multipliers 32b, 32c, 32 are obtained.
d ... 3 times, 5 times, 7 respectively output from 32z
The frequency is doubled, and the amplitude is (1 / n).
3) times, (1/5) times, (1/7) times ... Subtracting the square wave, a sine wave waveform can be obtained.

At this time, for example, as the first multipliers, up to the first multiplier 12d for multiplying the frequency of the sawtooth wave by 7 are used,
Accordingly, the saw-to-square wave converter 30d and the fourth multiplier 3 are also used for the saw-to-square wave converter and the fourth multiplier.
If up to 2d is used, the first multipliers 12b, 12c, 12d that input the sawtooth wave output from the sawtooth wave generator 10 are input.
The 3rd, 5th, and 7th harmonic components corresponding to the coefficient of can be removed, and a waveform extremely approximate to a sine wave having slightly higher harmonic components than the 11th harmonic can be obtained.

Then, when a waveform extremely approximate to the sine wave output from the adder 18 is amplified through the third multiplier 20 and the LPF 22 cuts the overtones of the 11th order or higher from the waveform output from the adder 18. An accurate sine wave can be obtained.

Since the LPF 22 only needs to cut the slightly remaining overtones of the 11th order or higher, it is extremely easy to design as compared with the LPF used in the conventional waveform generator. The same as the above-mentioned first embodiment.

Further, similarly to the first embodiment, the waveform output from the adder 18 may be used as it is as a modulated wave without passing the waveform output from the adder 18 to the LPF 22. However, it may be used after being amplified through the third multiplier 20.

That is, also in the second embodiment,
By setting the value of “n: positive integer” to an arbitrary value,
Since the (2n + 1) th harmonic component can be removed, a sine wave with desired accuracy can be easily obtained only by the sum of products operation.

That is, when the square wave (Sqr) of the angular frequency ω is subjected to Fourier expansion, Sqr (ω) = A [sinω + (1/3) sin3ω + (1/5) sin5ω + ... + {(1 / (2n + 1 )} Sin (2n + 1) ω + ...], and Sqr (3ω) = A {sin3ω + (1/3) sin9ω + ...} Sqr (5ω) = A {sin5ω + (1/3) sin15ω + ...} , And so on, sin (ω) = A {Sqr (ω)-(1/3) Sqr (3ω)-(1/5) Sqr (5ω) ...}.

Therefore, when a sine wave is generated up to a square wave of 7ω according to the above example, f (ω) = Sqr (ω)-(1/3) Sqr (3ω)-(1/5 ) Sqr (5ω) − (1/7) Sqr (7ω) = A {sinω + (1/11) sin (11ω) + ...} Equation 2 is obtained.

Therefore, the LPF 22 for cutting the higher harmonics
For this, it is sufficient to cut off 11ω or more.

FIG. 9 shows the relationship between the order N (coefficient of the first multiplier) and the coefficient (amplitude coefficient) Q of the fourth multiplier of the overtone to be removed, which is obtained from the equation 2. N in the table shown in
By selecting the higher harmonics to be sequentially removed from the smaller value of, the sine wave with high accuracy at low frequency can be obtained by a simple product-sum operation without performing table reading or complicated operation.

Here, the coefficient Q of the fourth multiplier shown in FIG. 9 also corresponds to the "amplitude coefficient" in the claims as in the first embodiment, but this coefficient Q is a saw. What does not match the amplitude of the overtone component of the square wave obtained by the wave-square wave converter 30a is the sawtooth-triangle wave converters 30b, 30c, 30d ... 3 which are the second square wave generating means.
This is because each of 0z also includes a harmonic component, and the amplitude coefficient is set so as to cancel the component.

As with the first embodiment, there is a method for obtaining such an amplitude coefficient, for example, as described below.

[First Method] The table shown in FIG. 9 is used as the amplitude coefficient table in advance in the ROM 108 or R shown in FIG.
How to store in AM110.

[Second Method] A method of using 1 / (2n + 1) as the amplitude coefficient by calculating 1 / (2n + 1) when it is not necessary to remove even higher harmonics.

For example, if 3ω to 9ω is to be removed, n can be calculated from 1 to 3. Specifically, the amplitude coefficient of the square wave of 3ω 1 / (2 × 1 + 1) = 1/3 the amplitude coefficient of the square wave of 5ω 1 / (2 × 2 + 1) = 1/5 The amplitude coefficient of the square wave of 7ω 1 / A square wave of (2 × 3 + 1) = 1/7 9 ω has an amplitude coefficient of 0 and therefore cannot be calculated.

If 3ω to 13ω is removed, 1 to 6 may be calculated except when n is 4. Specifically, the amplitude coefficient of the square wave of 3ω 1 / (2 × 1 + 1) = 1/3 the amplitude coefficient of the square wave of 5ω 1 / (2 × 2 + 1) = 1/5 The amplitude coefficient of the square wave of 7ω 1 / A square wave of (2 × 3 + 1) = 1/7 9 ω has an amplitude coefficient of 0 and therefore is not calculated. Amplitude coefficient of 11 ω square wave 1 / (2 × 5 + 1) = 1/11 11 A coefficient of 13 ω square wave 1 / ( 2 × 6 + 1) = 1/13.

[Other Method] A method of obtaining the amplitude coefficient by assembling an equation for obtaining the amplitude coefficient of each overtone from the Fourier expansion equation.

FIG. 10 shows a square wave (the output waveform of the sawtooth-square wave converter 30a in FIG. 7) and a waveform obtained by removing the third harmonic from the square wave (first multiplier 12b, sawtooth wave in FIG. 7). The output waveform of the adder 18 when the square wave converter 30b and the fourth multiplier 32b are used) and the waveform obtained by removing the fifth harmonic from the square wave (first multiplier 12c, sawtooth-square in FIG. 7). The output waveform of the adder 18 when using the wave converter 30c and the fourth multiplier 32c) and the waveform obtained by removing the seventh harmonic from the square wave (the first multiplier 12d in FIG. 7,
The output waveform of the adder 18 in the case of using the sawtooth-square wave converter 30d and the fourth multiplier 32d) and the waveform of the sine wave are shown in comparison, and the seventh harmonic It can be seen that the waveform removed up to is extremely close to a sine wave.

[0081]

Since the present invention is constructed as described above, it has the following effects.

It is possible to generate a sine wave waveform having an arbitrary frequency by a simple product-sum operation and also to generate a sine wave waveform having a desired accuracy even at a low frequency.

Even when a filter is provided in order to obtain a more accurate sine wave waveform, a sine wave waveform from which harmonics of a desired order have been removed can be obtained by a simple product-sum operation. The design becomes easy.

[Brief description of drawings]

FIG. 1 is a block diagram showing a waveform generator according to a first embodiment of the present invention.

FIG. 2 is a waveform diagram of a sawtooth wave generated by a sawtooth wave generator.

3A and 3B are waveform diagrams showing waveform processing of a first multiplier.

FIG. 4A is a flowchart showing waveform processing of a sawtooth-wave converter, and FIG. 4B is a waveform diagram at each step of the flowchart shown in FIG.

FIG. 5 is a comparison table showing the harmonic order N (coefficient of the first multiplier) and the coefficient (amplitude coefficient) P of the second multiplier in the first embodiment.

[Sixth] FIG. 6 is a waveform diagram showing a waveform and a sine wave obtained in the first embodiment.

FIG. 7 is a block diagram showing a waveform generator according to a second embodiment of the present invention.

8A is a flowchart showing waveform processing of a sawtooth-square wave converter, and FIG. 8B is a waveform diagram at each step of the flowchart shown in FIG. 8A.

FIG. 9 is a comparison table showing the harmonic order N (coefficient of the first multiplier) and the coefficient (amplitude coefficient) Q of the fourth multiplier in the second embodiment.

FIG. 10 is a waveform diagram showing a waveform and a sine wave obtained in the second embodiment.

FIG. 11 is a block configuration diagram showing an overall configuration of an effect adding device.

12 is a functional block diagram for realizing a chorus effect added by the effect adding device shown in FIG.

FIG. 13 is a functional block diagram of a panning device.

[Explanation of symbols]

10 sawtooth wave generators 12b, 12c, 12d ... 12z first multipliers 14a, 14b, 14c, 14d ... 14z sawtooth-triangular wave converters 16b, 16c, 16d ... 16z second multipliers 18 addition 20th third multiplier 22 LPF (low-pass filter) 30a, 30b, 30c, 30d ... 30z saw-to-square wave converter 32b, 32c, 32d ... 32z fourth multiplier

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[Procedure amendment]

[Submission date] July 20, 1994

[Procedure Amendment 1]

[Document name to be amended] Statement

[Name of item to be corrected] Brief description of the drawing

[Correction method] Change

[Correction content]

[Brief description of drawings]

FIG. 1 is a block diagram showing a waveform generator according to a first embodiment of the present invention.

FIG. 2 is a waveform diagram of a sawtooth wave generated by a sawtooth wave generator.

3A and 3B are waveform diagrams showing waveform processing of a first multiplier.

FIG. 4A is a flowchart showing waveform processing of a sawtooth-wave converter, and FIG. 4B is a waveform diagram at each step of the flowchart shown in FIG.

FIG. 5 is a comparison table showing the harmonic order N (coefficient of the first multiplier) and the coefficient (amplitude coefficient) P of the second multiplier in the first embodiment.

FIG. 6 is a waveform diagram showing a waveform and a sine wave obtained in the first embodiment.

FIG. 7 is a block diagram showing a waveform generator according to a second embodiment of the present invention.

8A is a flowchart showing waveform processing of a sawtooth-square wave converter, and FIG. 8B is a waveform diagram at each step of the flowchart shown in FIG. 8A.

FIG. 9 is a comparison table showing the harmonic order N (coefficient of the first multiplier) and the coefficient (amplitude coefficient) Q of the fourth multiplier in the second embodiment.

FIG. 10 is a waveform diagram showing a waveform and a sine wave obtained in the second embodiment.

FIG. 11 is a block configuration diagram showing an overall configuration of an effect adding device.

12 is a functional block diagram for realizing a chorus effect added by the effect adding device shown in FIG.

FIG. 13 is a functional block diagram of a panning device.

[Explanation of Codes] 10 sawtooth wave generators 12b, 12c, 12d ... 12z first multipliers 14a, 14b, 14c, 14d ... 14z sawtooth-triangle wave converters 16b, 16c, 16d. 2 multiplier 18 adder 20 third multiplier 22 LPF (low pass filter) 30a, 30b, 30c, 30d ... 30z saw-to-square wave converter 32b, 32c, 32d ... 32z fourth multiplication vessel

Claims (8)

[Claims] 1. A waveform generator for generating a sine wave waveform, comprising: first triangle wave generating means for generating a first triangle wave having the same frequency as that of a desired sine wave waveform; and the first triangle wave. Second triangular wave generating means for respectively generating a second triangular wave having a frequency of 2n + 1 times (n is a positive integer) the frequency of the first triangular wave generated by the generating means, in a number corresponding to a predetermined value of n. The amplitude coefficient supply means for supplying desired amplitude coefficients respectively corresponding to the n triangular waves generated by the second triangular wave generation means, and the amplitude coefficient supplied by the amplitude coefficient supply means Multiplying means for multiplying n triangular waves generated by the triangular wave generating means, and subtracting n triangular waves obtained by the multiplying means from the output of the first triangular wave generating means. Waveform generator, characterized in that it comprises a subtraction means. 2. The waveform generator according to claim 1, further comprising a filter means for cutting frequency components higher than 2n + 1 times after the subtraction means. 3. The amplitude coefficient supply means comprises a storage means for storing a desired amplitude coefficient, and supplies the amplitude coefficient read from the storage means.
The waveform generator according to the item. 4. The amplitude coefficient supply means is 1 / (2n +).
1) The waveform generator according to claim 1 or 2, further comprising arithmetic means for performing the arithmetic operation ² and supplying the amplitude coefficient determined by the arithmetic operation by the arithmetic means. 5. A waveform generator for generating a sine wave waveform, comprising: first square wave generating means for generating a square wave having the same frequency as that of a desired sine wave waveform; and the first square wave. Second square wave generating means for respectively generating a square wave having a frequency of 2n + 1 times (n is a positive integer) the frequency of the square wave generated by the generating means, each of which corresponds to a predetermined value of n; The amplitude coefficient supply means for supplying desired amplitude coefficients respectively corresponding to the n square waves generated by the second square wave generation means, and the amplitude coefficient supplied by the amplitude coefficient supply means Multiplication means for multiplying n square waves generated by the square wave generation means, respectively, and subtraction means for subtracting n square waves obtained by the multiplication means from the output of the first square wave generation means. Have Waveform generator, characterized in that. 6. The waveform generator according to claim 5, further comprising a filter unit that cuts a frequency component higher than 2n + 1 times after the subtraction unit. 7. The amplitude coefficient supply means comprises a storage means for storing a desired amplitude coefficient, and supplies the amplitude coefficient read out from the storage means.
The waveform generator according to the item. 8. The amplitude coefficient supply means is 1 / (2n +
7. The waveform generator according to claim 5, further comprising a calculation means for performing the calculation of 1), and supplying the amplitude coefficient determined by the calculation by the calculation means.