JPH1051269A - Low-pass filter - Google Patents

Abstract

PROBLEM TO BE SOLVED: To set a pass-band characteristic and a block-band characteristic of an LPF characteristic to a desired characteristic by changing a discrete and nearly constant high-gain region of an FIE digital filter to have a characteristic where a high-frequency side has swollen up. SOLUTION: An FIR digital filter 2 whose gain-frequency characteristic has a feature is connected to a post-stage of a CIC digital filter 1. A weighted error frequency function ECIC(e<jwt> ) can be obtained for a pass band of the filter 1, based on a specific equation. A high-frequency side end and a low-frequency side end of a high-gain region are slightly swollen up by adding the function ECIC(ejwt ) to a conventional filter as a correction characteristic part. A filter coefficient for a filter 2 is obtained by using the weighted error frequency function E(ejwt ) for the filter 1 and a gain-frequency characteristic of the digital filter 2 is obtained by the coefficient found this way.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a digital low-pass filter which performs filtering and decimation processing on an oversampled digital signal and returns the signal to the original sampling frequency, and more particularly to a CIC (Cascade Integrator and CIC). The present invention relates to a low-pass filter configured by combining a digital filter of a Comb) type and a digital filter of a FIR (Finite Impulse Response) type.

[0002]

2. Description of the Related Art In the technical field of digital audio, generally, an FIR type filter having excellent linear phase characteristics is used. In addition, the filter is required to have a low-pass filter characteristic having a steep amplitude frequency characteristic as shown in FIG. Conventionally, a digital filter having such characteristics is configured to input a digital signal that is oversampled at an integer multiple of the sampling frequency and perform decimation to return the signal to the original sampling frequency.

By the way, for example, in the low-pass filter characteristic of FIG. 5, the upper limit of the pass band frequency fp = 20 KHz,
Stopband lower limit frequency fc = 24.1 kHz, sampling frequency Fs = 44.1 kHz, stopband attenuation is 100 dB or more, and passband ripple is ± 0.0005 d.
B, if this is one FI for decimation
In order to realize this with an R-type digital filter, it is necessary to configure it with 256 or more taps.

[0004] However, such a method using one FIR type digital filter requires 256 or more registers, and has a problem that the circuit scale becomes extremely large, and one sampling period (1 / Fs). Since a problem due to the processing speed that 256 or more multiplications must be performed per time also occurs, it has become less realistic as a digital audio integrated circuit that is becoming faster and smaller in recent years.

[0005] Therefore, the above-mentioned frequency characteristics are converted to a plurality of FIR
A method is used in which a digital filter is used to perform decimation in several steps. In this case, each FI
It is said that the R-type digital filter can be constituted by a relatively small-scale circuit, and that the multiplication processing per one sampling period can have a margin in time. In particular, when a CIC type digital filter and a FIR type digital filter configured by combining a comb filter and an integrating circuit are used, there is an advantage that the circuit scale can be significantly reduced.

Next, gain frequency characteristics of the above-mentioned conventional FIR digital filter and CIC type digital filter will be described. The transfer z function H _FIR (z) of the FIR type digital filter is represented by H _FIR (z) = Σ (n = 0 to N−1) h _n z ⁻ⁿ (1) Here, Σ (n = 0 to N−1) indicates that n is applied from 0 to N−1 and cumulatively added. Also, n
Denotes the number of taps, h _n denotes a filter coefficient at the ^n- th tap, and z ⁻ⁿ denotes a signal delay amount (n-sampling time delay amount) at the n-th tap. Equation (1) is used to determine the gain frequency characteristic H
_When converted into _FIR (e ^jwT ), the following equation (2) is obtained. Note that jwT = j2πfT. H _FIR (e ^jwT ) = Σ (n = 0 to N−1) h _n e ^-jwnT (2)

Generally, the filter coefficient h can be obtained by a weighted Chebyshev approximation method. ^Assuming that the ideal gain frequency characteristic of the target filter is D (e ^jwT ), the gain frequency characteristic of the filter obtained by the approximation method is H (e ^jwT ), and the weight frequency function for the approximation error is W (e ^jwT ), The attached error frequency function E (e ^jwT ) is defined as follows. E (e ^jwT ) = W (e ^jwT ) [D (e ^jwT ) −H (e ^jwT )] (3) In the above-mentioned weighted Chebyshev approximation method, the weighted error frequency function error E (e ^jwT ) , The filter coefficient h is determined so that the absolute value in the specified frequency band becomes the minimum, but the ideal gain frequency characteristic D (e
^jwT ) is set to 1 in the pass band and 0 in the stop band.
A weight frequency function W (e ^jwT ) is specified to weight the ripple of each band.

On the other hand, the transmission z of the CIC type
The function H _CIC (z) is expressed by H _CIC (z) = (1−z ^−N ) / (1−z ⁻¹ ) (4). Here, N is a sampling rate.
When the equation (4) is converted into the gain frequency characteristic H _CIC (e ^jwT ), the following is obtained. H _CIC (e ^jwT ) = [sin (NwT / 2)] / [N sin (wT / 2)] (5)

Conventionally, when a digital signal oversampled at a sampling frequency of 16 Fs is decimated to a signal of the original sampling frequency, as shown in FIG.
And a low-pass filter configured by cascade-connecting the CIC type desirta filter 1 with the filter. The CIC type filter filter 1 performs filtering and decimation on a digital signal input at a sampling frequency of 16 Fs, and outputs the digital signal at a sampling frequency of 2 Fs. F
The IR digital filter 3 has a sampling frequency of 2F
The digital signal input at s is subjected to filtering and decimation, and output at the sampling frequency Fs.

Here, a low-pass filter having a cascade connection configuration of these two digital filters has a pass band upper limit frequency fp = 20 KHz and a stop band lower limit frequency fc =
24.1KHz, sampling frequency Fs = 44.1K
Hz, the passband ripple is within ± 0.0005 dB, and the stopband attenuation is 100 dB as the overall frequency characteristics.
Consider the case where the above is true.

[0011] CIC type digital filter filter 1 in order to meet the above specifications, it is 10-stage configuration, the gain frequency characteristic becomes _{^{H CIC (e jwT) -1 0}} . Further, since the sampling frequency is converted from 16Fs to 2Fs, the sampling rate N = 8. By substituting these into the equation (5) to obtain the gain frequency characteristic of the CIC type desirta filter 1 alone, as shown in FIG. 7, the frequency is 0 times or an odd multiple of the sampling frequency Fs of the input digital signal. Has a characteristic in which a peak gain whose value decreases as the frequency increases increases discretely.

Regarding the FIR digital filter 3,
When the filter coefficients for satisfying the above specifications are obtained from equation (3), and these coefficients are substituted into equation (2), the FI
As shown in FIG. 8, the gain frequency characteristic of the R-type digital filter 3 is such that, as shown in FIG. 8, a substantially constant low gain (about -100 dB) is discretely obtained in a region before and after a frequency which is an odd multiple of the sampling frequency. Almost constant high gain (about 0d
B) is a characteristic obtained discretely. The number of taps n =
It is about 120.

Then, the CIC type desilter filter 1 and F
The total gain frequency characteristic H _ALL (e ^jwT ) when the IR digital filters 3 are cascaded is a combination of both frequency characteristics, and H _ALL (e ^jwT ) = H _CIC (e ^jwT ) · H _FIR (e ^jwT) From (6), the result is as shown in FIG.

[0014]

However, in the configuration in which the CIC type digital filter 1 and the FIR type digital filter 3 are simply connected in cascade as described above, the final output gain characteristic is simply the frequency characteristic of each filter. 9, the characteristics of the FIR digital filter 3, which is originally designed so that the attenuation of the pass band is 0 dB, are affected by the slowly attenuating characteristics of the CIC digital filter 1. As shown in (A), there is a problem that the signal is attenuated by several dB in the high-pass portion of the pass band.

Therefore, in order to correct the attenuation of several dB and improve the frequency characteristics, a circuit as a compensator is provided at the subsequent stage of the FIR type digital filter circuit 3 or the like.
Although it is separately added, this method has another problem that the advantage of reducing the circuit scale is sacrificed.

The present invention has been made in view of the above points, and an object thereof is to set the output frequency characteristic of a filter to a characteristic close to an ideal, and to add a special correction circuit without requiring a circuit scale. An object of the present invention is to provide a low-pass filter capable of taking advantage of the reduction.

[0017]

According to a first aspect of the present invention, there is provided a CIC which discretely obtains a peak gain whose value decreases as the frequency increases at a frequency of 0 times or an odd number times the sampling frequency of an input digital signal. Type digital filter and an FIR type digital filter in which a substantially constant low gain is discretely obtained in a region before and after a frequency which is an odd multiple of the sampling frequency, and a substantially constant high gain is discretely obtained in another region. In the connected low-pass filter, the discrete almost constant high-gain region of the FIR digital filter is changed to a characteristic in which at least the high-frequency side is raised.

In a second aspect based on the first aspect, the amount of swelling of the gain frequency characteristic of the FIR digital filter corresponds to an error of a passband gain frequency characteristic of the CIC digital filter with respect to a target gain frequency characteristic. Was set.

[0019]

Embodiments of the present invention will be described below. FIG. 1 is a diagram showing a configuration of a low-pass filter according to the embodiment. The same components as those in FIG. 5 are denoted by the same reference numerals. In the present embodiment, the CIC digital filter 1 is the same as that shown in FIG. 5, and an FIR digital filter 2 having a characteristic gain frequency characteristic is connected to the subsequent stage.

Next, these total frequency characteristics will be described. Gain frequency characteristic H _ALL (e
^jwT ) is intended to set the gain frequency characteristic to 1 in the pass band and to 0 in the stop band as described above.
Therefore, the weighted error frequency function E (e ^jwT ) for this frequency characteristic is as shown in the following equation (7). E (e ^jwnT ) = W _P (e ^jwT ) [1-H _ALL (e ^jwT )] (pass band) = W _S (e ^jwT ) [0-H _ALL (e ^jwT )] (stop band) (7) Here, W _P (e ^jwT ) represents a weight function frequency function in a pass band, and W _S (e ^jwT ) represents a weight frequency function in a stop band.

By substituting equation (6) into equation (7), the following equation (8) can be obtained. E (e ^jwnT ) = W _P (e ^jwT ) [1-H _CIC (e ^jwT ) · H _FIR (e ^jwT )] (pass band) = W _S (e ^jwT ) [0−H _CIC (e ^jwT ) · H _FIR (e ^jwT )] (stop band) (8)

This equation (8) can be further transformed into the following equation (9). E (e ^jwnT ) = W _P (e ^jwT ) · H _CIC (e ^jwT ) [1 / H _CIC (e ^jwT ) −H _FIR (e ^jwT )] (pass band) = W _S (e ^jwT ) · H _CIC (E ^jwT ) [0-H _FIR (e ^jwT )] (stop band) (9)

Here, when the relationship between the expressions (9) and (3) is ^summarized , the weight frequency function W (e ^jwT ) for the approximation error and the ideal gain frequency characteristic D (e ^jwT ) are as ^follows .
Is obtained. W (e ^jwT ) = W _P (e ^jwT ) · H _CIC (e ^jwT ) (pass band) = W _S (e ^jwT ) · H _CIC (e ^jwT ) (stop band) (10) D (e) ^jwT ) = 1 / H _CIC (e ^jwT ) (pass band) = 0 (stop band) (11)

On the other hand, the weighted error frequency function E _CIC (e ^jwT ) of the CIC type digital filter 1 is E _CIC (e ^jwT ) = W (e ^jwT ) [D (e ^jwT ) −H _CIC (e ^jwT )]. (12) Therefore, by substituting the equation (10) into the equation (12), a weighted error frequency function E _CIC (e ^jwT ) in the pass band of the CIC digital filter 1 is obtained. be able to.

Therefore, the weighted error frequency function E
_CIC (e ^jwT ) is ^converted to a conventional FIR digital filter 3
By taking into account the characteristics to be corrected for the characteristics of
As shown in FIG. 2, it is possible to obtain a gain frequency characteristic in which the high-frequency end and the low-frequency end of the high gain portion are slightly raised. This swell portion is a weighted error frequency function E
_CIC (e ^jwT ) is added.

As described above, the filter coefficient of the FIR digital filter 2 is obtained by using the weight function W (e ^jwT ) of the error of the CIC digital filter 1, and the filter coefficient thus obtained is obtained. Thus, the gain frequency characteristic of the FIR digital filter 2 shown in FIG. 2 is obtained.

In FIG. 2, in order to make a comparison with the conventional frequency characteristic, the specification is similar to the characteristic shown in FIG.
Pass band upper limit frequency fp = 20 KHz, stop band lower limit frequency fc = 24.1 KHz, sampling frequency Fs =
A low-pass filter of 44.1 KHz is used. The swell is several tens per pass band upper limit frequency fp.
It is about dB.

Thus, the total frequency characteristic of the low-pass filter shown in FIG. 1 is obtained by synthesizing the gain frequency characteristic of the CIC type digital filter 1 shown in FIG. 7 and the gain frequency characteristic of the FIR digital filter 2 shown in FIG. The characteristic shown in FIG. The amplitude frequency characteristic in the pass band is flat and shows around 0 dB. In addition, the attenuation in the stop band is sufficiently 100 dB or more. Further, FIG. 4 shows the ripple in the pass band, which is also within ± 0.0005 dB, which sufficiently satisfies the specification. In this manner, unnecessary attenuation does not occur in the pass band, and sufficient attenuation occurs in the stop band.

In the above description, the specifications of the digital filter device, the number of taps of the FIR digital filter, the decimation ratio of each filter, and the like are not fixed, and the same effect can be obtained in other cases. Of course.

[0030]

As described above, according to the present invention, the gain frequency characteristic of the FIR digital filter is set so that at least the high-frequency end of the discrete high gain portion is raised. The pass band characteristics and the stop band characteristics of the low pass filter characteristics obtained by the combination can be set to desired characteristics. Also, the FIR
By setting the amount of rise of the digital filter in accordance with the error of the passband amplitude frequency characteristic of the CIC digital filter with respect to the target amplitude frequency characteristic, a flat passband frequency characteristic can be accurately obtained.

[Brief description of the drawings]

FIG. 1 is a block diagram of a low-pass filter according to an embodiment of the present invention.

FIG. 2 is a characteristic diagram of gain frequency characteristics of the FIR digital filter shown in FIG.

FIG. 3 is a characteristic diagram of an overall gain frequency characteristic of the low-pass filter shown in FIG.

FIG. 4 is a characteristic diagram of a ripple frequency characteristic of a pass band of the low-pass filter shown in FIG.

FIG. 5 is a characteristic diagram of an amplitude frequency characteristic required for a low-pass filter.

FIG. 6 is a block diagram of a conventional low-pass filter.

FIG. 7 is a characteristic diagram of a gain frequency characteristic of a CIC type degilter filter.

FIG. 8 is a characteristic diagram of a gain frequency characteristic of a general FIR type digital filter.

9 is a characteristic diagram of a total gain frequency characteristic of the low-pass filter shown in FIG.

[Explanation of symbols]

1: CIC-type digital filter, 2, 3: FIR-type digital filter.

Claims (2)

[Claims] 1. A peak gain that discretely obtains a value that decreases as the frequency increases at a frequency that is 0 times or an odd multiple of the sampling frequency of an input digital signal.
An IC type digital filter and an FIR type digital filter in which an almost constant low gain is discretely obtained in a region before and after a frequency which is an odd multiple of the sampling frequency and an approximately constant high gain is discretely obtained in another region. In the cascade-connected low-pass filter, the discrete almost constant high-gain region of the FIR digital filter is changed to a characteristic in which at least the high-frequency side is raised. 2. The method according to claim 1, wherein the swell amount of the gain frequency characteristic of the FIR digital filter is set in accordance with an error of a pass band gain frequency characteristic of the CIC digital filter with respect to a target gain frequency characteristic. Item 1
The low-pass filter according to 1.