JPH0770957B2 - FIR filter - Google Patents

Description

TECHNICAL FIELD The present invention relates to a digital filter, and more particularly, to a FIR (Finite Impulse Response) filter in which the transfer function of the digital filter is represented as a finite sequence of impulse responses.

BACKGROUND ART Filters used for digital audio and the like generally require linear phase characteristics. Therefore, an FIR filter with excellent linear phase characteristics is used.

A case where a low-pass filter is obtained by using the FIR filter will be described.

^Assuming that the required frequency response H (e ^jωT ) of the FIR filter repeats with a period ωs, the frequency response is represented by a Fourier series as follows.

However, h (nT) is an impulse response and is given by the following equation.

Here, if e ^jωT = z, then equation (1) is Therefore, if the frequency response H (e ^jωT ) of the FIR filter described above is given as the design specification, the impulse response h (nT) can be obtained. Therefore, the coefficient a _n of the coefficient multiplier of the FIR filter shown later is set to a _n = h (nT)
By defining that, the required digital filter can be configured.

By the way, it is necessary to cut off the impulse response with a finite number of terms due to the circuit configuration of the FIR filter which is generally configured by the non-recursive type. The higher the order N of the FIR filter, the closer it is to the ideal low-pass filter characteristic, but the number of Fourier series is cut off by N, and the amplitude characteristic has protrusions or excessive fluctuations near the discontinuity point. The so-called Gibbs phenomenon occurs. It is known that this phenomenon is inevitably caused by Fourier expansion.

Therefore, we try to suppress the occurrence of Gibbs phenomenon by using a so-called window function or Chebyshov approximation that exchanges a finite impulse response using a kind of time domain function.

FIG. 2 shows the ideal frequency response (amplitude characteristic) of the target low-pass filter. In FIG. 2, the vertical axis represents the predetermined attenuation amount normalized by the signal pass band attenuation amount, and the horizontal axis represents the predetermined angular frequency ω at the sampling frequency ωs (= 2π / T). It is represented by a normalized normalized frequency. This filter characteristic has an attenuation of 1 in the pass band and 0 in the stop band.

FIG. 3 shows an example of the actual frequency-attenuation characteristic of the FIR filter obtained by determining the value of the impulse response using the Chebyshov approximation based on the frequency response shown in FIG.

As shown in this characteristic example, ripples due to the finite word length of Fourier expansion or digital operation occur in the actually designed actual filter characteristic. The ripple causes a portion where the above-mentioned normalized attenuation exceeds 1.

When the maximum input level of the frequency band corresponding to this portion is supplied to the filter, the arithmetic output of this filter overflows, causing a large distortion.

Therefore, δ is reduced by the amplitude 2δ of the ripple so that the attenuation does not exceed 1, and the frequency vs. attenuation characteristic shown in FIG. 3 is corrected to obtain a characteristic diagram as shown in FIG. Inverse conversion is performed to obtain a time axis response (pulse response) characteristic as shown in FIG. Coefficient value α (+6) shown in this characteristic
.Alpha. (-6) is the coefficient of the coefficient multiplier of the FIR filter.

An example of the structure of such an FIR filter is shown in FIG. Figure 5 shows F
The IR filter consists of a 13th-order non-recursive type and is known as a transversal filter.

The input data sampled at the frequency ωs are sequentially delayed by the delay elements 1 to 12 which are connected to each other in series and operate in synchronization with the clock of the frequency ωs. Input data and output data of each delay element are coefficient multiplier
21 to 33, and the coefficient values α (+6) to α (−6) are multiplied. The multiplication outputs of the coefficient multipliers 21 to 33 are added by the adder 40 and become output data.

By the way, since the device is required to be downsized and low priced, the FIR filter is configured by a digital IC. In this case, instead of having 13 coefficient multipliers as described above, the time division processing of the arithmetic circuit can be used for 13
It is configured to multiply times.

However, the multiplication requires a relatively long time, and the number of multiplications that can be performed within one sample time is limited.

Therefore, the number of multiplications is reduced by devising the circuit configuration as shown in FIGS. 6 and 7.

The FIR filter shown in FIG. 6 utilizes the so-called linear phase characteristic, and the coefficient value shown in FIG.
(-6) = α (+6), α (-5) = α (+5), α
(-4) = α (+4), ..., α (-1) = α (+1)
Taking advantage of the above relationship, the coefficient multipliers 21 to 26 are deleted and the adders 41 to 46 are used instead to reduce the number of multiplications to 7 to obtain the same calculation result. In this case, the addition circuit has a simpler circuit configuration than the multiplication circuit, and
Because the calculation time of addition is shorter than that of multiplication, FIR
Data processing time in the filter is reduced.

The FIR filter shown in FIG. 7 further has the coefficient values α (± 6), α (± 4), and α (± 2) in FIG. The adders 42, 44 and 46 and the multipliers 29, 31 and 33 are omitted from the circuit configuration shown in the figure.
As a result, the number of multiplications is reduced to four. The reason why such a circuit can be omitted is that the normalized frequency characteristic as shown in FIG. 3 becomes a symmetrical characteristic centered on the normalized frequency 0.25 and the attenuation 0.5. The corresponding parts in FIGS. 5 to 7 are designated by the same reference numerals.

As shown in FIG. 8, the correction filter characteristic obtained by such an FIR filter has the attenuation amount not exceeding 1, so that the above-mentioned overflow problem does not occur.

However, the maximum value of ripple in the attenuation region is 2σ, and the attenuation characteristic is about 6 as compared with the characteristic shown in FIG.
[DB] gets worse.

As another overflow prevention measure, the input data is multiplied by a coefficient of 1 or less to reduce the value of the input data in advance, and the gain is adjusted by multiplying the reciprocal of the coefficient in the output data processing in the subsequent stage. There is a so-called scaling method to prevent this. However, in this case, there is a problem that the number of multipliers increases, and it is difficult to apply it to a high-order FIR filter.

SUMMARY OF THE INVENTION Therefore, an object of the present invention is to provide an FIR filter in which overflow does not occur in the signal pass band and attenuation characteristics do not deteriorate in the signal pass stop band.

In order to achieve the above object, the FIR filter of the present invention selects a delay means for sequentially delaying sample values to obtain a series of delayed sample values, and n units from the delayed sample values.
Arithmetic means for obtaining a series of output data by adding each of the multiplication values obtained by multiplying the selected n delay sample values by a predetermined coefficient for each delay sample value, and obtaining each of the predetermined coefficients as desired. In the FIR filter determined based on the filter characteristic, assuming that the amplitude value of the ripple of the obtained real normalized filter characteristic is 2δ, 1 / (1
It is characterized by being multiplied by + δ).

Examples Examples of the present invention will be described below. First, the actual filter characteristic of the designed FIR filter as shown in FIG. 3 is obtained from the desired filter characteristic as shown in FIG. 2 by the same procedure as the conventional one.

Further, the attenuation amount characteristic shown in FIG. 3 is normalized by the maximum value (1 + δ) in the pass band. δ represents the half value of the amplitude value of the ripple described above. FIG. 1 shows the correction filter characteristics after normalization. In FIG. 1, δ ′ is δ / (1+
δ) is represented.

As is clear from this correction filter characteristic, the attenuation amount does not exceed 1 in the pass band, and the attenuation amount in the pass stop band is from 2δ to δ / (1
+ Δ), and the filter characteristics are improved.

The time-axis domain characteristic obtained by inverse Fourier transforming the correction filter characteristic is the time-axis domain characteristic as shown in FIG.
In this case, the new time-axis coefficients α ′ (+ 6) to α ′ (− 6) obtained by the inverse Fourier transform are 1 / each of the above-mentioned time-axis coefficients α (+6) to α (−6). It is multiplied by (1 + δ).

By setting the time axis coefficients α '(+ 6) to α' (-6) in the corresponding coefficient multipliers of the FIR filter shown in FIGS. 5 to 7, a more preferable correction filter as shown in FIG. The characteristics are obtained.

Thus, the correction for the ripple component as shown in FIG. 3 is changed from the conventional method of subtracting the ripple component from the actual filter characteristic as in the present invention, and there is no overflow and the amount of attenuation in the signal blocking region is large. The filter characteristic is obtained.

Further, since an additional circuit such as a multiplier is not required for improving the filter characteristic, the calculation speed is not relatively reduced, and it is preferable for an FIR filter which usually has a high order.

The time-axis coefficients α (+6) to α (−6) already obtained as shown in FIG. 4 are not subjected to the inverse Fourier transform again.
By multiplying each of them by 1 / (1 + δ) and α ′ (+ 6) to α ′
By calculating (-6) and correcting the coefficient of the coefficient multiplier by the calculated value, the same correction filter characteristic as in FIG. 1 can be obtained. 1 / (1 + δ), which is a value smaller than 1.
Multiplying by the neighborhood value of has a similar effect.

Effect of the Invention As described above, the FIR filter of the present invention first determines the time-axis coefficient of each coefficient multiplier based on the desired normalization filter characteristic to obtain the real normalization filter characteristic, and the real normalization filter characteristic. When the amplitude value of the ripple of 2 is set to 2δ, a new coefficient obtained by multiplying each of the above time axis coefficients by 1 / (1 + δ) is reset to each coefficient multiplier, so that distortion due to overflow is eliminated. Moreover, it is preferable because it does not deteriorate the attenuation characteristics.

[Brief description of drawings]

FIG. 1 is an explanatory diagram for explaining the filter characteristic of the FIR filter of the present invention, FIG. 2 is an explanatory diagram for explaining the desired filter characteristic, and FIG. 3 is designed based on the desired filter characteristic. FIG. 4 is an explanatory view for explaining a characteristic example of the FIR filter, FIG. 4 is an explanatory view for explaining a time axis region characteristic of the filter characteristic shown in FIG. 3, and FIGS. Block diagram showing a circuit configuration example of a filter, eighth
The figure is an explanatory view for explaining an example of filter characteristics of a conventional FIR filter. Description of symbols of main parts 1 to 12 ... delay element 21 to 33 ... coefficient multiplier 40, 40a, 41 to 46 ... adder

 ─────────────────────────────────────────────────── ─── Continuation of the front page (56) Reference JP 62-178006 (JP, A) JP 52-144945 (JP, A) JP 62-172809 (JP, A) JP 62- 69713 (JP, A) JP 63-290403 (JP, A) JP 61-224511 (JP, A)

Claims (1)

[Claims] 1. A delay means for sequentially delaying sample values to obtain a series of delay sample values, and n delay sample values are selected from each of the delay sample values. An FIR filter that includes each of the multiplication values obtained by multiplying the predetermined coefficient and obtains a series of output data, and is an FIR filter in which each of the predetermined coefficients is determined based on a desired normalization filter characteristic. The amplitude value of the ripple of the obtained real normalization filter characteristic is 2
An FIR filter, wherein each of the predetermined coefficients is multiplied by 1 / (1 + δ), where δ.