JPH0486792A - Waveform generator - Google Patents

Abstract

PURPOSE:To regenerate a high-grade waveform data array regardless of the kinds of waveforms by providing a multiplying means which multiplies the waveform data regenerated by a waveform regenerating means and a scale factor in a digital filter means. CONSTITUTION:The multiplying means for multiplying the scale factor K obtd. by multiplying the expansion rate for standardizing the range of the waveform data by the grain factor relating to filtering processing and the waveform data WO is included in the digital filter means 33 which digitally filters the waveform data from the waveform regenerating means 29. The waveform information is expressed by the compressed difference data array compressed by the compression rate dependent upon the magnitude of the fluctuation in the waveform data array expressing audio signals and, therefore, the storage capacity of a waveform information memory decreases. Then, the regeneration of the original waveform data array is executed simply by accumulating the compressed difference data and multiplying the accumulated output by the expansion rate associated with the compression rate. The high-grade waveform output array is regenerated regardless of the kinds of the waveforms in this way.

Description

DETAILED DESCRIPTION OF THE INVENTION [Technical Field of the Invention] The present invention relates to a waveform generation device used in electronic musical instruments and the like, and particularly to a waveform generation device that generates a waveform using a memory of compressed waveform information.

F Background of the Invention] A PCM sound source converts musical tones into waveform data (PCM data).
It has a built-in waveform memory that stores it as a sequence of . In operation, the PCM sound source generates a musical tone signal of a desired pitch by reading waveform data from a waveform memory at a speed corresponding to the required pitch.

A disadvantage of the PCM sound source is that it requires a memory with a large storage capacity as a waveform memory.

To avoid this drawback, there is a differential PCM method. The differential PCM method is based on the expectation that the number of bits required to express the difference value between adjacent waveform data will be smaller than the number of bits necessary to express the waveform data, and instead of the waveform data string. A data string of difference values (difference data string) is recorded in . During reproduction, the differential PCM sound source reproduces waveform data by accumulating the differential data read from the differential data string memory.

Unfortunately, the conventional differential PCM method has a problem in that the reproduction accuracy varies depending on the timbre of the original sound.

In the conventional differential PCM recording method, a sequence of waveform data (X(n)) with a certain number of bits (for example, 16 bits) is converted into a sequence of differential data (d(n)) with a smaller number of bits (for example, 8 bits). Convert to The basic principle of the conversion is as follows. First, adjacent waveform data x (k), x
Calculate the difference in (k-1).

x (k) 7X (k -1) = Dx (Formula 1) Here, the difference Dx is difference data expressed in 16 bits. If the size of this difference data Dx is a size that can be expressed with 8 bits (128 to 127), the lower 8 bits of the 16-bit difference data Dx are converted to the next 8-bit difference data d (
k).

For example, Dk is When d (k) is oiooooooo.

(Here, we assume two's complement).

However, if the size of Dx indicates a value in a range that cannot be expressed in 8 bits, d(k) can be expressed in 8 bits, rJ
Clip to the maximum value possible.

For example, Dx oooootoooooooooo.

(2048 in decimal), d (k) is the maximum positive value of 8 bits (1 in decimal)
27) Clipped to .

In addition, in order to reduce the accumulation of errors due to this clipping,
Actually, instead of (formula l), is calculated, and the difference data dx expressed in 16 bits is converted into the difference data d(k) in 8 bits as described above.

Due to the clip described above, a sequence of differential data (d(n))
Distortion occurs in the waveform played back.

Even more inconveniently, the frequency of occurrence of clipping, which is a cause of deterioration of the SN ratio, depends on the waveform data sequence (X(n)), and therefore on the spectrum or timbre of the original sound to be recorded. As a result, in the conventional differential PCM method, the SN ratio varies depending on the type of original sound, and desired reproduction accuracy cannot be guaranteed.

Therefore, there is a need for a waveform reproduction technique that can realize desired waveform reproduction from a memory with a relatively small storage capacity, regardless of the type of original sound.

Furthermore, with sound sources that use waveform information memory such as waveform data strings and differential data strings, rather than outputting the played waveform data string as is, it is further digitally processed after playback processing for tone processing etc. Filtering processing is often performed on a waveform data string to generate a processed waveform data string. This type of sound source (waveform generation device) generally requires high-speed processing. Therefore, when applying waveform reproduction technology that can ensure the desired reproducibility accuracy to this type of waveform generation device, the configuration of the waveform generation device will not become complicated or the processing speed will not decrease due to the application. It is desirable to do so.

[Object of the Invention] Therefore, an object of the present invention is to have a simple configuration, to be able to reproduce a high-quality waveform data string regardless of the type of waveform from a data string with a relatively small number of beats, and to perform desired processing on the waveform. It is an object of the present invention to provide a waveform generation device that can be applied to a data string.

[Structure and operation of the invention] According to the present invention, there is provided a compressed difference data string storage means for storing a compressed difference data string compressed at a compression rate that depends on the magnitude of variation in a waveform data string representing an audio signal; waveform reproduction means for reading compressed difference data from a compression difference data string storage means and reproducing waveform data; digital filter means for digitally filtering the waveform data from the waveform reproduction means; and expansion related to the compression ratio. scale factor storage means for storing a scale factor obtained by multiplying an expansion rate for normalizing the range of waveform data reproduced from the waveform reproduction means by a gain coefficient related to the filtering process of the digital filter means; There is provided a waveform generation device, wherein the digital filter means includes a multiplication means for multiplying the waveform data reproduced by the waveform reproduction means by the scale factor from the scale factor storage means.

The first feature of the present invention is that the waveform information stored in the storage means as a waveform information memory is compressed by a compressed difference data string compressed at a compression ratio that is consistent with the magnitude of fluctuations in the waveform data string representing the audio signal. It is what is being expressed. This reduces the storage capacity of the waveform information memory (compressed differential data string storage means). In order to reproduce the original waveform data string from such a compressed difference data string, the compressed difference data is accumulated, and the accumulated output (compressed reproduced waveform data) is given an expansion rate (of the compression rate) that is related to the compression rate. The reciprocal number or a value close to it) can be used to reproduce a high-quality waveform data sequence regardless of the type of waveform.

Such a concept of compression rate and expansion rate is not present in conventional differential PCM technology. Conventional differential PCM technology basically calculates the difference between adjacent waveform data during recording, records the lower N bits of the difference as differential data, and accumulates the differential data across the width during playback. This method reproduces waveform data using For this reason, fatal distortion and noise occur in portions where adjacent waveform data have a large difference (that is, portions where the difference is not reflected in the difference data).

In contrast, in the present invention, if the variation in the original waveform data string is large, the compressed difference data string compressed at a compression ratio corresponding to the variation is recorded in the compressed difference data string storage means, so that the variation in the waveform data string is This will be reflected in the compressed differential data string as faithfully as possible, making it possible to reproduce high-quality waveforms regardless of the type of waveform.

On the other hand, in the present invention, with the introduction of an expansion rate that did not exist in the past, it is necessary to multiply the data by the expansion rate in order to reproduce the original waveform data. Therefore, if such waveform reproduction technology is applied as is to a waveform generation device that has a digital filter function such as processing timbre, the expansion rate for waveform reproduction (normalization) will be reduced in order to generate one waveform data. and the filter gain coefficient multiplication for digital filtering must be performed separately.

The processing load on the waveform generation device increases.

Therefore, according to the second feature of the present invention, a scale factor corresponding to a value obtained by multiplying an expansion rate and a filter gain coefficient is stored in the scale factor storage means, and the scale factor is stored in the digital filter means instead of the filter gain coefficient. By providing a multiplication means for multiplying the waveform data.

Reduces the number of multiplications required to generate a waveform.

Further, according to the present invention, there is provided compressed difference data string storage means for storing a compressed difference data string compressed at a compression rate that depends on the magnitude of variation in a waveform data string representing an audio signal; The expansion rate is used to standardize the range of the waveform data string when playing the waveform data string, and the filter gain coefficient is related to the digital filtering process that should be performed to process the timbre of the waveform data string. scale factor storage means for storing a scale factor having a value multiplied by waveform generating means for signal-processing the compressed difference data string from the compressed difference data string storage means to generate a timbre-processed waveform data string, so that digital filtering processing can be achieved; The generation means relates to the multiplication by the expansion rate and the digital filtering process for normalizing the range of the waveform data string by one multiplication using the scale factor from the scale factor storage means as a multiplier. A waveform generation device is provided that includes a multiplication means that simultaneously performs multiplication of a filter gain coefficient.

Here, the multiplication means may perform multiplication at an appropriate processing stage of the signal processing of the waveform generation means, and is not limited to a specific processing stage. Any suitable processing order may be used as long as the functions of waveform data reproduction and processing (digital filtering) are achieved.

[Example] The present invention will be described in detail below with reference to the drawings. First, a waveform recording device will be described, followed by a description of a waveform generation device that uses recording results to generate waveforms in accordance with the present invention.

FIG. 1 shows the overall configuration of a waveform recording device. A digital audio tape l is a master tape on which natural musical instrument sounds, etc. are recorded, and the recorded information is played back as a waveform data string by a DATil 12, and then sent to a computer via a digital audio interface 3. Transferred to 4. The computer 4 performs processing to be described later on the transferred waveform data string to generate a compressed difference data string and various parameters. The compressed differential data string is written to the FROM 6 by the FROM writer 5. The written FROM6 is a waveform generator (
This becomes the differential waveform memory 11 shown in FIG. 4). Further, various parameters (expansion rate, envelope parameters) are used as control information for the waveform generation device.

FIG. 2 is a flowchart of compressed differential data string generation in the computer 4. First, parameter a is set in Sl, and a waveform data string is loaded into the array (X(n)).

Here, the parameter a is a coefficient used to generate the compression ratio (compression scale factor), which will be described later, and a≧1.0.
takes the value of

In the next step S2, the waveform data string (x (n)l, i.e., x
(0), x (1)...x (n)・
The envelope (e (n)
-264206, Patent Application No. 62-264207)
.

For example, information indicating the size of the waveform data for each predetermined section of the waveform data string, for example, the absolute value of the waveform data 1x (
n) Find the maximum value of l, the magnitude of the peak of the waveform data, or the power of the waveform data (for example, the square root of the sum of the squares of the waveform data) as an envelope. For example, the fundamental period of the waveform data sequence is selected as the predetermined interval. In FIG. 3, for each predetermined section X of the waveform data string,
Extract the maximum value of (n)1, find it as the envelope level ELk, find the envelope plate ERk in a predetermined section X by ERk = (ELb - ELb-+) / An envelope value e(n) corresponding to waveform data d(n) is obtained. The extracted envelope (e (n)) is used to normalize the waveform 7'-data sequence (x (n)) in the next step S3.

In other words, each waveform data x (n) is converted into an envelope value e (n)
Divide by. This removes the envelope (
A normalized) waveform data sequence (XO(n)) is obtained. By removing the envelope, the reproducibility of low volume parts is improved.

Next, at 54, x+(n)4- (A/xo max) m
The waveform data string (x+ (n)) is normalized according to xo(n). Here, XOmaX is a waveform data string (x.

For example, if A=32767.0 is selected as A, which is the absolute value of the largest waveform data in (n)), the waveform data string tx+(n)> is normalized to ±15 bits.

In other words, the maximum value in the waveform data string (x+(n)) is +
It is expressed as a binary number indicating 32787 or -32787. The reason for standardization is to equalize the reproduction level when a waveform data string (x+(n)) is reproduced for various waveforms in a reproduction device.

Next, in step 35, the difference between adjacent waveform data of the waveform data string (x+(n)) is calculated to form a difference data string (d+(n)), and in step S6, the difference data string (d+(n)) is calculated. Nakano (
The maximum value dmaX of d+(n)) is extracted. Here, the number of bits of differential data d+(n) is equal to the number of bits of waveform data x+(n), or x+(n) and XI (
The number of beats that can accurately represent the maximum value of the difference in n-1) (i.e., d.

The number of bits of (n) is 37, and the compression rate ae (B 7 a max
) using
+(n), and assuming that the number of bits of the compressed difference data d2(n) generated in step 58 is 8 bits, B = 127.0. Here a21.0
Then, the absolute value of the maximum f- of the compressed difference value data calculated from the waveform data X2(n) is 127.0, and all compressed difference data can be expressed in 8 bits without clipping. That is, B/dmax represents the compression ratio without clipping. In this case, waveform reproducibility is good in parts where the waveform fluctuation is steep, and poor in parts where the waveform fluctuation is small. The parameter a is a variable to compensate for this point, and according to experience, a = 1.0 to 2.
Within the range of about 0, reproduced sound with the best audible quality can be obtained. What should be noted is that the compression ratio a·(B/dmax) depends on the magnitude of fluctuation in the waveform data string. Note that bit a of the data of the compressed waveform data string (x2(n))
is the same as the number of bits of waveform data
The top 13 bits of +(n)! Ii is the fractional part, and the lower 3 bits are regarded as the decimal part, which is data x 2(n)).

Next, in S8, the compressed waveform data string (x2(n)
) to form a compressed differential data string (d2(n)).

Here, d2(n) is -B-1≦d2 (n)≦B, and if the value on the right side of the above equation is smaller than -B-1, then c12(
n) = -B-1, and if the value on the right side is larger than B, it is clipped to d2(n) = H. d2(n)
is expressed by the number of bits defined by the value B, where B = 12
If it is 7.0, it is 8 bits.

In addition, 37. Instead of S8, directly write the difference data string (d+
(n) Using the compression ratio (a*B/dmax) from 't,
A compressed differential data string (d2(n)) may also be obtained.

= a-B/dmax(d+ (n)+ 1!(II-
1))=e(n-2)+(dzn-n
(dmax/a-8)・d? (n-+) ) (As mentioned above, d2(n) is clipped to d2(n) = B-1 if the value on the right side is smaller than -B-1, and d2(n) = B if the value on the right side is larger than B. ).

Also, when a = 1 (no clip), the following formula is used. In such a case, instead of S7 and S8, d2(n) = a・ (
B/dmax) · The compressed difference data string (d2(n)) can be obtained by d+(n).

Next, in S9, the compression ratio is inverse @dmax/a-B
As can be imagined from the explanation of the recording system where 0 or more is stored as the expansion rate norm in the waveform data reproduction system, the waveform data obtained by accumulating the compressed difference data in the reproduction system has n
By multiplying by the value of orm, the waveform data will fall within a certain numerical range (for example - -) regardless of the type of waveform data.
32767-32767). An example of the value of norm is a value of 5 to 15 for piano waveform data sampled at a sampling frequency of 32KH2.

In the final step 510, the calculated compressed difference data string (d2(n
)) Save to the file.

Through the above processing, the compressed difference data string (d2(n)),
Expansion rate norm, envelope data string (e (n)
)was gotten.

The above process (second
), perform playback, save the data with the best reproducibility (expansion ratio, compressed difference data string, envelope data string) from the auditory experiment, and save the compressed difference data string as FR.
The differential waveform memory 11 is created by writing to OM6.

Next, the waveform generation device will be explained. FIG. 4 is a block diagram of an electronic musical instrument incorporating a waveform generating device.

The microcomputer 8 scans the switch 9 in a well-known manner to transfer data corresponding to the selected tone to the tone generator 10, and also scans the keyboard 7 to transfer information about the pressed key to the tone generator IO. . According to the present invention, the tone generator 10 calculates the compressed difference data in the difference waveform memory 11 to generate a musical tone waveform W,
Sound is generated via the DAC 12, amplifier 13, and speaker 14.

FIG. 5 shows the configuration of the tone generator 10. The interface 24 writes data from the microcomputer 8 shown in FIG. 4 to the tone generator 10.
Envelope level data ELk and envelope plate data ERk are stored in the envelope data memory 25, and 63 B is stored in the scale factor memory 27 as a scale factor used by the waveform generator 29. The scale factor B has a value obtained by multiplying norm by the filter gain coefficient, and the scale factor B represents one or more filter coefficients other than the filter gain coefficient used for digital filtering processing in the waveform generator 29. When using a first-order IIR type digital filter as shown in FIG. 7, which will be described later, the scale factor B is one parameter and represents a feedback coefficient.
The envelope generator 26 writes frequency data corresponding to the pitch into the address generator 28 via the ace 24, and receives envelope level data ELk and envelope plate data ERk from the envelope data memory 25 and generates an envelope E. Address generator 28 generates address A that changes at a rate corresponding to the frequency data, and sends an increment signal i to waveform generator 29 each time address A changes. The waveform generator 29 is a waveform generating means that generates a waveform according to the present invention,
In response to the increment signal i from the address generation circuit 28, the compressed difference data D from the difference waveform memory 11 and the scale factor from the scale factor memory 27 are
B. A musical sound waveform W is generated using the envelope E from the envelope generator 26.

The function of the waveform generator 29 is shown in FIG.
When the compressed difference data from the difference waveform memory 11 is updated due to a change in the data, the data is passed through and input to an accumulator composed of an adder 31 and an FF 32. The accumulator accumulates the compressed difference data D to generate 8 to 16 bit waveform data (accumulated output). This cumulative output WO is the cumulative value of compressed difference data,
That is, it represents compressed reproduced waveform data.

Therefore, by multiplying this cumulative output by the expansion rate norm, reproduced waveform data whose range is normalized to ±15 bits can be obtained. Furthermore, if the standardized reproduced waveform data is digitally filtered using a filter coefficient such as a filter gain coefficient, waveform data with processed tones and the like will be generated. However, with this method, the multiplication by the expansion rate for standardization and the multiplication by the filter gain coefficient for filtering processing are performed separately, which increases the processing load on the waveform generator 29. If the polyphonic number of the generator 29 is N, this type of multiplication must be performed 2N times per sampling period.

Therefore, in the embodiment, a digital filter 33 is used in the waveform generator 29 to perform both normalization and digital filtering processing.

FIG. 7 illustrates the function of the digital filter 33. Here, a first-order IIR filter is used as a digital filter, but the number of orders and filter characteristics are not limited in the present invention. The configuration is shown, and (b) shows the logical configuration of the HPF.

Both include an input multiplier 35, an adder 36, a delay device 37,
It consists of a feedback multiplier 38 and an adder 40.

The fifth point to note is that the input multiplier 35 applies a scale factor K to the input data WO, that is, expands it in.

rm is multiplied by a scale factor K, which corresponds to a value obtained by multiplying rm by a filter gain coefficient (referred to as K'). This involves two multiplications: WQXnorm and
This indicates that K'X (WoXnorm) is realized by one multiplication KXWo by individual or shared hardware multiplication circuits.

Here, for convenience of explanation, if we separate the standardization process and the digital filtering process, the standardization process is W@Xn
The digital filtering process is a process that uses '' and a feedback coefficient B as a filter gain coefficient. The transfer function of the digital filtering process is for the LPF. Also, if we choose the /<Towers characteristic, B=(α−
1)/(α+1) K ′= (1+g) /2 ct= L an (wf c/f s) (here fc
is the cutoff frequency and fs is the sampling frequency).

In electronic musical instruments, it is often desired to modulate the cutoff frequency fc by operating input from performance operators. In such an environment, the microcomputer 8 in FIG. 4 obtains cutoff frequency information from the operation input,
Based on this, '' is determined for the feedback coefficient B and the filter gain coefficient using a conversion table or the like. The microcomputer 8 stores data on the expansion rate norm, and the microcomputer 8 calculates the scale filter K by multiplying the filter gain coefficient ' by the expansion rate norm. K and B thus obtained are set in the scale factor memory 27HPF of the tone generator IO and used by the standardization digital filter 33 of the waveform generator 29.

Therefore, by executing the process shown in FIG. 7, the normalization of the reproduced waveform data using the expansion rate norm and the digital filtering process using the filter gain coefficient ' and the feedback coefficient B can be achieved at the same time. . In particular, the multiplication of the expansion rate norm and the multiplication of the filter gain coefficient by ' can be achieved simultaneously by one multiplication shown in 35, and the number of required multiplications can be reduced.

Returning to FIG. 6, the timbre-processed waveform data W output from the digital filter 33 is multiplied by the F-helope E from the envelope generator 26 in a multiplier 34, and becomes the final musical waveform output W.

Note that the envelope level and rate data set in the envelope data memory 25 can be determined based on the envelope extracted by the waveform recording device 32 (FIG. 2). Generally, the number of envelope segments (attack segments, etc.) generated by the envelope generator 26 is limited, so the extracted envelope can be approximated by the envelope of a limited number of segments (envelope level and rate for each segment). become.

For such envelope approximation, for example,
1-264205 can be used. Basically, set an appropriate number of segments, and evaluate the error between the polygonal envelope (for example, the characteristic switching point, or break point, is selected as a point on the extraction envelope) and the extraction envelope at that number of segments. , optimal approximation is possible by selecting the polygonal envelope that minimizes the error. This result (information on the envelope level and rate for each segment defining the selected polygonal envelope) is stored as a reference envelope parameter in the microcomputer 8 of the electronic musical instrument. During operation, the microcomputer 8 changes the reference envelope parameters depending on key touches and the like, and writes the results into the envelope data memory 25.

However, if desired, the envelope may be generated independently of the extracted envelope.

f Modification] This concludes the description of the embodiment, but various modifications and changes are possible within the scope of the present invention.

For example, the processing order in the waveform generator 29 is shown in FIG.
The order shown in FIG. 7 is not necessarily limited; therefore, the process of multiplying by the scale factor K can also be performed at any appropriate stage. If desired, the envelope multiplication by 34 and the scale factor multiplication by 36 can be performed by generating an envelope corresponding to (E It is possible to achieve this simultaneously with a single multiplication operation.

In addition, in the above embodiment, the envelope is removed from the waveform in the recording system in order to improve reproducibility at low volume levels, and the envelope is added to the waveform in the playback system. This process can be omitted. Further, the envelope may not be removed in the recording system, but the envelope may be added in the reproduction system.

Furthermore, the expansion rate norm does not necessarily have to be the reciprocal of the compression rate, and may take a value close to the reciprocal.

[Effects of the Invention] As explained in detail above, in the present invention, a compressed difference data string compressed at a compression rate that depends on the magnitude of variation in the waveform data string is stored in the waveform information memory, and this compressed difference data string is stored in the waveform information memory. When reproducing a waveform data string and generating a processed waveform data string, the waveform data is multiplied by an expansion rate (having a value related to the compression rate) to standardize the range of the waveform data. Since the multiplication of the filter gain coefficient in the digital filtering process for processing the waveform is simultaneously achieved in a single multiplication operation, it is possible to reduce the burden on the waveform generation process regardless of the type of waveform. At the same time, high-quality waveforms can be generated.

[Brief explanation of drawings]

Figure 1 is an overall configuration diagram of the waveform recording device, Figure 2 is a flowchart of the compressed difference data string generation process executed by the computer in Figure 1, and Figure 3 is the envelope extraction process performed in the process of Figure 2. FIG. 4 is an overall configuration diagram of an electronic musical instrument incorporating the waveform generation device according to the present invention; FIG. 5 is a block diagram showing an example of the configuration of the tone generator shown in FIG. 4; FIG. FIG. 7 is a block diagram illustrating the digital filter that also serves as data standardization in FIG. 6. 27...Scale factor memory 29...
... Waveform generator 33 ... Standardization digital filter 35 ...
・・・Multiplier D・・・Compression difference data norm・・・Expansion rate K・・・Scale factor Patent applicant Casio Keita Co., Ltd.

Claims (2)

[Claims] (1) compressed difference data string storage means for storing a compressed difference data string compressed at a compression rate that depends on the magnitude of fluctuation in a waveform data string representing an audio signal; and compressed difference data from the compressed difference data string storage means. waveform reproduction means for reading and reproducing waveform data; digital filter means for digitally filtering the waveform data from the waveform reproduction means; and an expansion rate related to the compression rate that is reproduced from the waveform reproduction means. scale factor storage means for storing a scale factor obtained by multiplying an expansion rate for normalizing a range of waveform data by a gain coefficient related to the filtering process of the digital filter means; A waveform generation device comprising: a multiplier for multiplying the waveform data reproduced by the waveform reproduction means by the scale factor from the scale factor storage means. (2) compressed difference data string storage means for storing a compressed difference data string compressed at a compression rate that depends on the magnitude of variation in a waveform data string representing an audio signal; and an expansion rate that is related to the compression rate. A value obtained by multiplying the expansion rate for normalizing the range of a waveform data string when reproducing the waveform data string by a filter gain coefficient related to digital filtering processing that should be performed for timbre processing of the waveform data string. scale factor storage means for storing a scale factor having a scale factor; and digital filtering that achieves reproduction of a waveform data sequence based on the compressed difference data sequence and the expansion rate, and that has the filter gain coefficient for the waveform data sequence. waveform generation means for signal-processing the compressed difference data string from the compressed difference data string storage means to generate a timbre-processed waveform data string so that the processing is achieved; , the multiplication of the expansion rate for normalizing the range of the waveform data sequence by one multiplication using the scale factor from the scale factor storage means as a multiplier, and the filter gain coefficient related to digital filtering processing. A waveform generation device characterized in that it has a multiplication means that simultaneously accomplishes the multiplication of .