JPH0442607A - Digital filter - Google Patents

Abstract

PURPOSE:To realize a calculation for apporximating the amplitude characteristic with high accuracy at high speed by converting a cut-off frequency and a maximum frequency in a digital region into a correction frequency subject to correction of distortion by bilinear s-z conversion, a correction transfer function whose amplitude characteristic is coincident with an analog region transfer function, and applying the bilinear s-z conversion to the function so as to obtain a digital region transfer function. CONSTITUTION:A cut-off frequency and a maximum frequency in a digital region are converted into a correction frequency subject to correction of distortion by bilinear s-z conversion respectively, and a correction transfer function whose amplitude characteristic is coincident with an analog region transfer function at the correction frequency is obtained. The correction transfer function is converted into a digital region transfer function by the bilinear s-z conversion. A digital filter having the said transfer function is easily realized by adjusting coefficients of multipliers 2 - 5,8,9. Thus, the amplitude characteristic of the transfer function in the analog region is approximated with high accuracy from a low frequency region to a high frequency region and the transfer function in the digital region is calculated at high speed.

Description

[Detailed Description of the Invention] [Industrial Application Field] The present invention is applied to, for example, a graphic equalizer, which is a type of equalizing amplifier that adjusts sound quality by amplifying or attenuating an audio signal for each frequency band. Concerning suitable digital filters.

[Summary of the invention]

The present invention is based on a bilinear S
- In a digital filter having a transfer function in the digital domain obtained by Z transformation, the cutoff frequency and the maximum frequency in the digital domain are respectively expressed as bilinear s
- Convert the distortion due to Z conversion to a corrected frequency, find a corrected transfer function in the analog domain whose amplitude characteristics match the transfer function of the analog domain at this corrected frequency, and convert this corrected transfer function into a bilinear S-Z By converting it into a transfer function in the digital domain, the amplitude characteristics of the transfer function in the analog domain can be approximated with high precision from the low frequency domain to the high frequency domain, and the transfer function in the digital domain can be calculated at high speed. This is what I did.

[Conventional technology]

Conventionally, analog graphic equalizers have been used as a type of equalizing amplifier for adjusting sound quality by amplifying or attenuating audio signals for each frequency band. However, with the advancement of digital technology, such analog graphic equalizers are also
digital signal processor) etc. (for example, see Japanese Unexamined Patent Publication No. 80913/1983). It is required that the amplitude characteristics of the function approximate as much as possible the transfer function of the conventional analog domain.

Generally, in the analog domain, inputs and outputs are Fourier transformed (
Strictly speaking, the ratio of the output component to the input component at the angular frequency ω is expressed as ``ω, that is, S (strictly speaking, S=
The function H(s) expressed as a function of σ+ω) is called a transfer function. On the other hand, in the digital domain, the input x (nT) and output y (nT) (n is an integer), which are discrete time signals, are converted by 2 with the sampling period T
(z) and Y(2), and find the open number H(
z) is called the transfer function. In this case, z=exp (jωT) (1)
, the 2 transform for discrete-time signals is equivalent to the discrete Fourier transform.

A method using bilinear s-2 transformation is known as a method for finding a digital domain transfer function that approximates an analog domain transfer function. For example, to explain the case where the peaking transfer function in the analog domain is HP (s) and the bilinear sz transformation is applied to this transfer function, the peaking transfer function HP (s> in the analog domain is expressed as expressed.

ωo2 +! i! ωo / Q + s 2...
(2) In this equation (2), ω0 is the central angular frequency of the peak,
0 is the Q value, and B is the magnitude of the peak amplitude. (dB)
Then, 20βog (k+1) = Bo
...There is the relationship (3). Further, by converting the angular frequency ω into a frequency f (ω=2πf), the square of the amplitude characteristic of the transfer function HP (s) in equation (2) is expressed as follows.

...(4) Differentiating this equation (4) with f2 and setting it as 0 gives -(f,/
Q) 2(f” −f,”) (k2+2k) (f
2+f0'') = Q...(5), and this formula (5) holds true when f=f, so formula 61 (
4) becomes maximum when f=f0. Its maximum value is HP
(f,) ” = (1+k)” ・・
...(6). Also, f, -f2= f, /Q...
(7) f, f2=f, ・
...(8) and (and, fl and f can be expressed as follows.

The square of the amplitude characteristic when f=f and f=f2 is as follows.

HP(f,) l 2= l HP(f2) l 2(
1+(1+k)") / 2...Equation (11) (
To convert the analog domain transfer function HP (s) in 2) into the digital domain transfer function H(z), the following bilinear S-Z transformation, which is an approximation of equation (1), is applied. be done.

s = (2/T) (1-z-')/(1+ z-'
)...(12) When formula (2) is transformed by formula (12), the transfer function H(z) of the following form is obtained, apart from constant multiplication.
is obtained.

In this equation (13), the coefficients a - e are respectively B0. ω
.

When a digital filter having a transfer function of equation (13) with a sampling period T of 1 is constructed as a so-called direct type I, it becomes as shown in FIG.

In this Figure 11, human power x (n) (n is an integer)
The delay time is one sampling period (same for other delay elements)
The output of the delay element (1) is supplied to the delay element (3) and the multiplier (4) that multiplies the coefficient d, and the delay The output of the child (3) is fed to the multiplier (5) which multiplies the coefficient e, and the multiplier (2)
, (4) and (5) are added by adders (6) and (7). Also, the final output y (n)
is supplied to the delay element (8), the output of the delay element [8] is supplied to the delay element (9) and the multiplier (10) which multiplies the coefficient -a, and the output of the delay element (9) is supplied to the coefficient -a. Multiplier (
11), and the outputs of multipliers (10) and (11) are sent to adders (12) and (13) to add multipliers (2) and (4).
) and (5), and the sum output of all the multipliers, which is the output of the adder (13), becomes the output y (n>.The transfer function H( Z
) approximates the analog domain transfer function of equation (2).

[Problem to be solved by the invention]

However, simply performing bilinear SZ transformation has the disadvantage that distortion occurs in high frequency regions.

That is, in the bilinear S-Z transformation of equation (12), the frequency in the analog domain is ωS, and the frequency in the digital domain is ω2.
Then, from the relationship such as equation (1), s= j ωs,
z-'=exp (-ko ωzT) -(
14) holds true. By substituting this equation (14) into equation (12), the following relational expression is obtained.

=(2/T) j tan(ω, T/2) By simplifying this relational expression, the following expression is obtained.

(tls = (2/T) tan(a+, T/2)
= ... (15) In this equation (15), the angular frequency ωS and ω when the sampling period T is set to 1
2 is shown by curve (14) in FIG. This song!
(14) is approximately equal to the straight line (15) with ω, = ω2 near the origin, but as you move away from the origin, the curve <15)
It begins to deviate significantly from the Furthermore, according to the Nyquist condition, the maximum value of the angular frequency ω2 in the digital domain is equal to π (=π/T), which is 1/2 of the sampling angular frequency, but when ω2=π, ω=beautiful.

As is clear from Fig. 12, on the curve (14), ω
S=ω. When , ω2=ω2o, but ωZO<ω
. holds true. Therefore, for example, let ω be the central angular frequency of the transfer function HP (s) in the analog domain.

Then, the corresponding transfer function H(2
) is the angular frequency ω2o at the center of the peaking.

, and the larger the angular frequency ω5 in the analog domain, the greater the angular frequencies ωZ and ωS in the digital domain.
It can be seen that the difference between the two values increases and the distortion of the amplitude characteristics increases.

A method is also known in which a digital domain transfer function is obtained by directly approximating the analog domain transfer function by the method of least squares, but this method has the disadvantages of being time consuming and having poor accuracy in low frequency domains. The reason for this poor accuracy is that the numerical aperture COS ω used in the approximation is poor in the region where ω is small.

In view of these points, the present invention provides a digital filter that can approximate the amplitude characteristics of the original analog domain transfer function with high precision from the low frequency region to the high frequency region, and has a digital domain transfer function that can be calculated at high speed. The purpose is to

[Means to solve the problem]

The digital filter according to the present invention has a digital domain transfer function obtained by bilinear S-2 transformation from an analog domain transfer function that has a cutoff frequency and converges to a predetermined level at an infinite frequency. - In the filter, its cutoff frequency (for example, the angular frequency ω in Figure 1) and the maximum frequency in the digital domain (for example, if the sampling period T is 1, the angular frequency π in Figure 1)
are converted to corrected frequencies (for example, ω, . and oo in the example in Figure 1) that correct distortion by bilinear S-Z conversion, and the amplitude characteristics match the transfer function of the analog domain at these corrected frequencies. A corrected transfer function of the domain is obtained, and this corrected transfer function is subjected to bilinear S-2 transformation to obtain the transfer function of the digital domain.

[Effect]

According to the present invention, since the bilinear SZ transform is used, the approximation accuracy in the low frequency region is good. Furthermore, convert the cutoff frequency and the maximum frequency in the digital domain to a correction frequency, find a correction transfer function in the analog domain whose amplitude characteristics match the original analog domain transfer function at these correction frequencies, and calculate this correction transfer function. is bilinear s-
Since z-transformation is performed, the approximation accuracy in the high frequency region is also good.

Furthermore, since it is not necessary to perform repeated calculations such as the method of least squares, the transfer function in the digital domain can be calculated at high speed.

〔Example〕

Hereinafter, embodiments of the present invention will be described with reference to FIGS. 1 to 10. This embodiment uses digital filters such as low-pass filters, bypass filters, and shelping filters that have a cutoff frequency and have a transfer function in the digital domain that is approximated to a transfer function in the analog domain that converges to a predetermined level at an infinite frequency. The present invention is applied to.

G. First embodiment (first-order low-pass filter) The cutoff frequency is f. The transfer function HL(s) of a first-order low-pass filter in the analog domain (angular frequency is ω) can be expressed as follows. 2 of the absolute value of the amplitude of this transfer function
The frequency characteristics (amplitude characteristics) of the power can be expressed by the following equation.

■ HL(f)l”= ・・・(17
)1+f2/f,2 In this example, first, in order to correct frequency distortion due to bilinear sz transformation, the corrected transfer function H in the analog domain is calculated from the transfer function HL(S) of equation (16) as described later. (S) is derived, and the amplitude characteristic of this corrected transfer function H(s) with respect to the angular frequency ω is defined as follows using coefficients α and β.

In the bilinear S-Z transformation defined by equation (12),
The difference between the angular frequency 5 in the analog domain and the angular frequency ω2 in the digital domain is as shown in equation (15), assuming the sampling period T is 1, ωz=2tan(ω2/2) (1)
9), and this relationship is shown by the curve (14) in FIG. Furthermore, the frequency f in the digital domain cannot exceed 0.5 (=0.5/T) according to the Nyquist condition, so the maximum value of the frequency f in the digital domain is 0.5.
(The maximum value of angular frequency ω2 is π). Therefore, in this example, as shown in Fig. 1, the vertical axis (angular frequency ω in the digital domain
2) two angular frequencies ω. (cutoff angular frequency) and π are plotted, the horizontal axis (
Corrected angular frequencies corresponding to the angular frequency ω, ) in the analog domain are wso and ■. From equation (19), wso can be expressed as follows.

ω5o=2tan(ω./2) ・・・(
20) And ωS is the corrected angular frequency ω,. and■
When taking the value of , IH(ω)12 in equation (18), which is the amplitude characteristic of the corrected transfer function H(s), is the amplitude characteristic of the transfer function in the original analog domain, lHL(fo).
l' and ]HL(f=0.5) l 2 . In this case, the following equation holds true from equation (17).

HL(f, > 12= 1/2...
(21)...(22) Furthermore, in order to calculate the coefficients α and β of equation (18), equation (1
By substituting wso and ■ as ω in 8), the following equation is established.

α=lHL(0,5) 2=hL...
(24) β From these equations (23) and (24), the two coefficients α and β
It is possible to determine the value of , and thus the amplitude characteristic of equation (18). By transforming equation (18) as follows, it can be seen that (25) the form of H(s) becomes as follows.

Finally, in equation (26), by applying the bilinear S-Z transformation (setting T = 1) of equation (12) to variable S, the transfer function H(z) in the digital domain can be obtained as follows. Desired.

(27) FIG. 2 shows an example in which the digital filter having the transfer function of equation (27) is configured as a first-order FIR type (recursive type) digital filter. In this Figure 2, the sampling period T is 1, and the input x (n) (n is an integer) is multiplied by a delay element (16) whose delay time is 1 sampling period (the same applies to other delay elements) and a coefficient B. Multiplier (1
7), the output of the delay element (6) is supplied to a multiplier (18) which multiplies the coefficient C, and the final output y (n)
is multiplied by the coefficient −A via the delay element (20).
1). and a multiplier (17), (1g
) and (21) are added to adders (19) and (22)
and the final output y (n) is obtained.

The digital filter in the example in Figure 2 is actually a DsP.
However, the transfer function H(z) in the digital domain is obtained by using linear bilinear S-Z transformation in the low frequency domain according to this example as described above in equation (27). Therefore, in the low frequency domain, the obtained transfer function H(z) in the digital domain is the transfer function HL in the analog domain.
(s) is a good approximation.

Furthermore, the cutoff angular frequency ω. and a corrected angular frequency ωso obtained based on the curve (14) in FIG. 1 at the maximum angular frequency π in the digital domain, and a corrected transfer function H whose amplitude characteristics match the original analog domain transfer function HL (s) at
(s) and performs bilinear S-Z transformation on this corrected transfer function H(s). Therefore, the transfer function H(z) in the digital domain obtained even in the high frequency domain is equivalent to the transfer function in the analog domain. There is an advantage that the function HL(s) can be well approximated.

In addition, in this example, after solving the simultaneous equations of equations (23) and (24) to obtain coefficients α and β and determining the corrected transfer function H(s) of equation (26), this corrected transfer function H(s
) can be calculated by simply applying bilinear sz transformation to the digital domain transfer numerical aperture H(z), which has the advantage of greatly shortening the calculation time compared to the case of using the least squares method.

Figure 3 is an example of the frequency characteristic of H(f)l, the square of the absolute value of the amplitude of the transfer function H(z) in the digital domain, which approximates the amplitude characteristic of a low-pass filter in the first-order analog domain using the method of this example. In this case and in the calculation example below, the sampling frequency fS (= 1/T) is 48kHz.
It is set to z. The cutoff frequency f in the analog region of this example in FIG.

(H2) i;! 10 (curve (23>1.:correspondence), 20.50.100°200, 500.1,
2, 5, 10, 20k (curve (2
4)).

G2 Second embodiment (second-order low-pass filter) The transfer function HL(s) of the analog second-order low-pass filter is given by the following equation.

The frequency characteristic of the square of the absolute value of the amplitude of this transfer function is ”hL β Next, the corrected transfer function H(S) manifest.

...(33) is expressed by the following equation. On the other hand, the frequency characteristic of the square of the amplitude of the corrected transfer function H(s) before sz conversion is expressed by the following equation.

From equation (29), when f ” f o , l HL(f
o) 12=1/2 holds, and furthermore, ω=■, that is, S
When the frequency f=0.5 after -Z transformation, (31), then α in equation (30) is calculated using ωs0 in equation (20).
, β can be calculated using the following formula.

The coefficients a-d of this equation (34) are the coefficients a-d of the example in FIG.
has a different value. Further, equation (30) can be transformed as follows.

By substituting equation (34) into equation (35), the following relational expression is derived by comparing the molecules.

(1+as+bs"Hl-as+bs")=l+ds'
...(36) From this equation (36), a becomes as follows.

b=,/7. a= σ] Te --- (37
) Similarly, C and d are found by substituting equation (34) into equation (35) and comparing the denominators, and the form of the corrected transfer function H(s) is as follows.

...(38) By applying the bilinear s-z transformation (T=1>) of equation (12) to the variable S of equation (38), the transfer function H(Z) in the digital domain can be obtained. .

The amplitude characteristics of the digital domain transfer function obtained by approximating the filter transfer function using the method of this example are shown, and the cutoff frequency f
0 is 100.200.500. 1k, 2k
.

5k, 10 shows the case of 20k (7). 1
It can be seen that the amplitude decreases rapidly compared to the next low-pass filter. Also, 1/of the sampling frequency fs
The differential becomes 0 at the frequency of 24k)Iz, which is a characteristic of digital filters.

(1+2a+4b) +(2-8b)z-'-'-,
(1-2a+4b)z-2(1+2c +4d) +
(2-86)z-' + (1-2c +4d)z-2
...(39) This is the desired transfer function. A digital filter having the transfer coefficient of equation (39) can be easily constructed by adjusting the coefficients of multipliers (2) to (5), (8), and (9) in the example shown in FIG. .

In addition, Fig. 4 shows the second-order low-pass G3 in the analog domain. Third embodiment (first-order bypass filter)
The transfer function HP (s) of the next bypass filter is as follows.

The frequency characteristic of the square of the absolute value of the amplitude of this transfer function is becomes.

On the other hand, the corrected transfer function H(S) before sz conversion
The frequency characteristic of the square of the amplitude of is expressed by the following formula.

can be determined.

From formula (41) =f.

When 1 HP (f,) When this equation (47) is subjected to bilinear sz transformation, the transfer function H(z) in the digital domain is obtained as follows.

holds, and furthermore, ω=■, that is, the frequency f after s-z transformation
When =0.5, the following formula holds true.

Then, α and β can be obtained from the following equations.

α=hyo...(44)β
10ω5o22 Also, equation (42) can be transformed as follows, −
αS2 H(s) H(-s) = β-52 (46) From this equation (46), the corrected transfer function H(s) is calculated as follows from the transfer function H( z) can be obtained by changing the coefficients of the multiplier in the digital filter shown in FIG.

Furthermore, Fig. 5 shows the amplitude characteristics of a digital transfer function that approximates the transfer numerical value of an analog first-order bypass filter, and the cutoff frequency is 10 (curve (25)) 20.5.
0.100.200.500. 1k, 2k,
5 klok (curve (26)) (biliary).

G4 Fourth embodiment (second-order bypass filter) The transfer function HP (s>) of the analog second-order bypass filter is as follows.

α and β can be determined.

a=h.

...(53) The frequency characteristic of the square of the absolute value of the amplitude of this transfer function is also: Since equation (51) can be transformed as follows, HP (f)
” = ・・・・
(50)fo'+f'. On the other hand, the corrected transfer function H(
The frequency characteristic of the square of the absolute value of the amplitude of s) is expressed by the following formula.

The corrected transfer function H(s) can be determined as follows.

Equation (50) is when f=f, then l HP(fo) I”
=-, and when ω=■, that is, f=D, 5, the following equation holds true.

By applying bilinear SZ transformation to this equation (56), the transfer function H(z) in the digital domain can be obtained.

+ 2 + (a +2b+4)+(2a-8)z-' +(a-
2b+4)z-"...(57) This is the transfer function to be sought. The transfer function of this equation (57) can be realized by the digital filter shown in the example in FIG. 11. Also in the following example, 1 The next filter is the second
This can be realized in the example shown in the figure, and the second-order filter can be realized in the example shown in FIG.

Further, FIG. 6 shows the amplitude characteristics of the transfer function in the digital domain when a second-order bypass filter is approximated, and the cutoff frequency is the same as in the example of FIG. 5.

Gs Fifth embodiment (first-order low shelping filter) Analog first-order low shelping filter
The transfer function HL S (s) of -ving) is given by the following equation.

In case 2, the following formula holds true.

201 og k = Bo”
(59) The frequency characteristic of the square of the absolute value of this transfer function is as follows.

On the other hand, the frequency characteristic of the square of the amplitude of the corrected transfer function H(s) before sz conversion is expressed by the following equation.

In equation (60), when f=fo, IHLS(fo)(
k''+1)/2 holds, and when ω=■, that is, the frequency f after sz conversion=0.5, the following equation holds.

α and β are determined.

””hLs・・・(6
3) The corrected transfer function H(s) before β sz conversion can be found from the following equation.

−12 (dB), and the cutoff frequency f. is 100
゜200, 1k, 2k, 10, 20k (
fiz) Teal. By performing bilinear S, -Z transformation on this equation, we obtain the transfer function H(z) in the digital domain.
is required.

G6 Sixth Practical M Example (Second-Order Low Shelping Filter) The transfer function HL S (s) of the analog second-order low shelping filter is given by the following equation.

1+25+(1-21/'7)z (66) FIG. 7 shows an example of the amplitude characteristics of a first-order low shelping filter in the digital domain, and curves (27) to (32) B. The values are 12, 2.5, 0.5, respectively. -0.5.
-2.5...(67) In this case, 20 lay, k = Bo holds true.

The frequency characteristic of the square of the absolute value of this transfer function is as follows.

On the other hand, the corrected transfer function H(S) before sz conversion
The frequency characteristic of the square of the amplitude of is expressed by the following formula.

In equation (68), when f=f, 1HL 5(fo
) l ”= (k2+1)/2 holds, f=0.5
The following equation holds true when .

(70) By performing bilinear S-Z transformation on this, the transfer function H(z) in the digital domain is determined as follows.

and β are calculated.

α”hLS・・・(72)
The transfer function before β sz conversion can be obtained from the following equation.

1+IjS'(1+2c+46)+(2-8d)z-' +(1-2
c+46)z-2...(75) Figure 8 shows the digital 2 approximating the analog transfer function.
An example of calculating the transfer function of the following low shelping filter is shown below. When Bo is negative, k is calculated from the absolute value of Bo and the numerator and denominator of equation (75) are reversed, as in the first-order case.

GtjR7 example (first-order high shelping filter) Analog first-order high shelping transfer function HHS
(s) is given by the following formula.

ω. 10S In this case, the following formula holds.

20 j! og k = Bo
= = (77) The frequency characteristic of the square of the absolute value of this transfer function is as follows.

On the other hand, the frequency characteristic of the square of the amplitude of the corrected transfer function H(S) before sz conversion is expressed by the following equation.

...(80) and β can be determined.

α β ”hH5 (82) The corrected transfer function H(s) before sz conversion can be calculated from the following equation.

If f=fo in equation (78), then lHH5(fo)
l 2 = (k”+1)/2 holds true.

Further, when ω=■, that is, the frequency f after sz conversion=0.5, the following equation holds true.

By performing bilinear S-Z transformation on this, the transfer function H(z) in the digital domain can be determined as follows.

FIG. 9 shows the amplitude characteristics of the transfer function of a digital first-order high shelping filter obtained by approximating the analog transfer function using the method of this example, and the values of 30 in curves (33) to (38) are 12. 2.5.0.5. -0.5°2.5. −
12 (dB), and the cutoff frequency f. is the same as the example in FIG.

When Bo is negative, k is B. Calculate by taking the absolute value of and use the formula (
Flip the denominator and numerator of 85).

G, jJ8 Actual example (second-order high shelping filter) The transfer function HHS (S) of an analog second-order high shelping filter is given by the following equation.

...(86) In this case, 20βogk=Bo holds true.

The frequency characteristic of the square of the absolute value of this transfer function is as follows.

The frequency characteristic of the square of the amplitude of the corrected transfer function H(s) before sz conversion is expressed by the following equation.

In equation (87), if f = f o, then l HH3(
fO) +2= (k2+1)/2 holds, and furthermore, ω
=■ In other words, when the frequency f after sz conversion is 0.5, the following equation holds true.

...(89) β can be determined.

α = 11as β (91) The corrected transfer function H(s) before SZ conversion can be obtained from the following equation.

1 +2a +4b + (2-8b)z-' + (
1-2a +4b)z-”1+2c+4d+(28d)
2-'+(1-2c+4d)z-"...(94) Figure 10 shows the digital 2-'+(1-2c+4d)z-"...(94)
An example of calculating the transfer function of the following high shelping filter is shown below. When Bo is negative, set k to B. Calculate by taking the absolute value of and flip the denominator and numerator of equation (94).

It should be noted that the present invention is not limited to the above-described embodiments, and it goes without saying that various configurations may be adopted without departing from the gist of the present invention.

When this is subjected to bilinear SZ transformation, a transfer function H(z) in the digital domain is obtained.

〔Effect of the invention〕

According to the present invention, the amplitude characteristics of a transfer function in an analog domain can be approximated with high accuracy from a low frequency domain to a high frequency domain, and there is an advantage that a transfer function in a digital domain can be calculated at high speed.

[Brief explanation of drawings]

FIG. 1 is a diagram showing a curve used for frequency correction in an embodiment of the present invention, and FIG. 2 is a configuration diagram showing an example of the following IIR type digital filter used in the embodiment: 3t!l to 10 are graphs showing the amplitude characteristics of the transfer numerical value in the digital domain, which approximate the transfer function in the analog domain using the method of the embodiment, and Fig. 11 shows an example of the circuit configuration of the digital filter. The configuration diagram shown in Fig. 12 is a bilinear s-
FIG. 3 is a diagram illustrating frequency distortion during z-transformation. ω. is the cutoff angular frequency, ωso is the correction angular frequency, (
1), (3), (8), (9), (16)
, (20) are delay elements, respectively, and (2). (4), (5), (10), (11), (
17), (1g), and (21) are multipliers, respectively. Agent Hidemori Matsukuma Figure 1 Figure 2 Figure 5 Figure 8 Figure 8 ItGIIJ Figure

Claims (1)

[Claims] A digital filter having a digital domain transfer function obtained by bilinear sz transformation from an analog domain transfer function that has a cutoff frequency and converges to a predetermined level at an infinite frequency. , the cutoff frequency and the maximum frequency in the digital domain are each converted to a correction frequency that corrects the distortion by bilinear sz conversion, and the amplitude characteristic in the analog domain matches the transfer function in the analog domain at the corrected frequency. A digital filter in which a corrected transfer function is obtained, and the corrected transfer function is subjected to bilinear sz transformation to become a transfer function in the digital domain.