JPH09139653A - Band split synthesis filter - Google Patents

Abstract

PROBLEM TO BE SOLVED: To enhance the degree of freedom of selecting the number of a filter tap in the band split synthesis filter employing an acrylic filter. SOLUTION: A frequency component of an input signal is divided into bands at an equal interval by a band pass filter 1i and each signal for each band obtained by split is sampled by a switch 4i. Furthermore, an output of the switch 4i is again sampled by a switch 5i, the sampled signal is given to a band filter 2i, which extracts the component for each band and an adder 6 synthesizes the result of extraction, then a signal equivalent to the input signal is generated. The number of tap at an interval of an integer multiple of the band split number (one time, twice,...) or a sum of 1 to the interval is set to the band filters 1i, 2i being acyclic filters.

Description

Detailed Description of the Invention

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a band division / synthesis filter that divides a signal into a plurality of bands in a frequency space and restores the original signal from the divided signals for each band, and more particularly to a non-recursive filter. The present invention relates to a band division / synthesis filter using the.

[0002]

2. Description of the Related Art A band division / synthesis filter is used in a sub-band coding system, an echo canceller, and other devices that require processing for each band component of a signal. The band division / synthesis filter will be described below. FIG. 5 shows the configuration of a band division / synthesis filter in which the number of band divisions is N. In the figure, the band division / synthesis filter is the input signal X (z);
The frequency component of z = exp (j2πf / fs) is N in a specific bandwidth.
Transmission filter circuits 10 to 1N-1 to be divided and signals X0 (z) to XN-1 (z) for each band obtained by the transmission filter circuit
Switches 40 to 4N-1 for sampling at a frequency fs / N
And signals X0 (z) to XN-1 (z) sampled by the switch 4.
Is input via the block 3 for performing encoding / decoding processing and transmission, and switches 50 to 5 for sampling at the frequency fs.
N-1 and the reception filter circuits 20 to 2N-1 for extracting the components of the band of the corresponding transmission filter 1i from the signal sampled by the switch 5 and the extracted signals for each band to synthesize the input signal. It is composed of an adder 6 that restores X (z).

FIG. 6 shows that the number of divisions N is 4 in the above configuration.
7 is a diagram showing an example of the amplitude characteristic of each part in the case of FIG.
(A) is an outline of the amplitude characteristics of the filters 1i and 2i,
(B) is the outline of the signal that has passed through the filter 11, (c)
Is the outline of the signal sampled by the switch 51, (d)
Each show the outline of the signal which passed the receiving filter 21. As shown in (a) of FIG. 6, in this method, the pass characteristics of each bandpass filter are gentle cutoff characteristics in which overlap occurs only between adjacent bands.
When focusing on the filters 11 and 21, the signal X1 (z) that has passed through the filter 11 is converted by the switch 51 into a signal (Y1 (z)) in which its components are superimposed at equal intervals on the frequency axis. 21 again returns the signal in the original band (U1
(z)). At this point, the overlapping component (hatched portion in (d) of FIG. 6) of the signal Y1 (z) remains in the low band and wide band of the signal U1 (z). When combined with the signal, this overlapping component cancels out. The transmission filter 1i and the reception filter 2i are designed to cancel the overlapping components.

[0004] In this system, a non-recursive filter is used as a transmission filter and a reception filter, there are the following.

[IEEE transactions on acoustics, spee
ch, and signal processing magazine, February 1983, JHRothwiler's “polyphase quadrature filte”
r ”(reference 1) or Peter L. Chu's“ Quadrature mirror filter desig ”published in the February 1985 issue of the same magazine.
n for an arbitrary number of equal bandwidth chann
The method of "els" (reference 2) has a drawback in that a complex number calculation is required for the filter operation, and the amount of calculation increases as the number N of band divisions increases.

On the other hand, as a method in which the filter coefficient is a real number and the degree of dependence of the calculation amount on the number of divisions is small, "ICASSP 83, BOST
“Po” by Joseph H. Rothweiler and others published in “ON”
lyphase quadrature filters-a new subband coding
technique ”(reference 3) and Kenji Nakayama, JP Sho 63.
-6930, "Multi-band band-splitting filter"
(Reference 4) has been proposed. The filter of Document 3 is composed of a bandpass filter having a tap number of 4iN (i is a positive integer). Further, the filter of Document 4 has a tap number of (2i
+1) N or (2i + 1) N + 1 bandpass filters.

[0007]

The characteristics of the band division / synthesis filter can be improved by increasing the number of taps of the non-recursive filter. However, in consideration of the circuit scale of the realized filter or the amount of calculation, the tap It is desirable that the number can be set to a value as small as possible within a range in which desired accuracy can be obtained. However, in the methods of References 3 and 4, the number of taps of the non-recursive filter is 4 times the number of band divisions in Reference 3 (4 times, 8 times, ...), and 2 times the conditional interval in Reference 4 (2
However, it may be necessary to set an excessive number of taps in order to obtain a desired accuracy.

Therefore, an object of the present invention is to further increase the degree of freedom in setting the number of filter taps in a band division / synthesis filter composed of non-recursive filters.

[0009]

According to the present invention, a part of frequency components is shared between adjacent bands, and the frequency components of an input signal are divided into N (N is an integer of 2 or more) of equal width. A band splitting / synthesizing filter configured by a splitting unit that splits the band at equal intervals, and a synthesis unit that generates a signal equivalent to the input signal from a signal for each band obtained by the splitting. Operates at a frequency fs and extracts the signal components for each band from the input signal by N first acyclic filters having L taps and the N acyclic filters. A second switch for sampling the signal component for each band at a frequency fs / N, and the synthesizing unit for sampling the signal sampled by the first switch at a frequency fs;
Switch and each of the first non-recursive filter, and operates at a frequency fs.
N second acyclic types having L taps for extracting a signal component in a band corresponding to the signal component extracted by the corresponding first acyclic filter from the signal sampled by the switch A filter and an adder that synthesizes the signal components extracted by the N non-recursive filters, and the tap number L of the first and second non-recursive filters is an integer multiple of the band division number N. Alternatively, it is set to a value obtained by adding 1 to an integer multiple of the band division number N.

[0010]

BEST MODE FOR CARRYING OUT THE INVENTION Embodiments of the present invention will be described below.

FIG. 1 is a diagram showing a configuration of a band division / synthesis filter according to a first embodiment of the present invention. In the figure,
The band division / synthesis filter is a transmission filter circuit (non-recursive filter) 10 to 1N-1 that divides the frequency component of the input signal X (z) into bands of a specific width, and a band component obtained by the transmission filter circuit. The switches 40 to 4N-1 for sampling the signals X0 (z) to XN-1 (z) for each frequency at the frequency fs / N and the signals X0 (z) to XN-1 (z) sampled by the switch 4 are , Switches 50 to 5N-1 for inputting through the block 3 which performs encoding / decoding processing, transmission, etc., and sampling at the frequency fs.
And a reception filter circuit (non-recursive filter) 20 to 2N-1 that filters the signal sampled by the switch 5 with the characteristic corresponding to the transmission filter circuit 1 and the signal filtered by the reception filter circuit are added. Input signal X (z)
And an adder 6 for generating a signal equivalent to

In this band division / synthesis filter, the number of taps L of the transmission filter 1i and the reception filter 2i can be set to an integer multiple of the number of band divisions N (or a value obtained by adding 1 thereto), and the number of taps is set. The degree of freedom is improved. The realization of such a filter will be described below.

First, the filter coefficient is h (n) (0≤n <L)
Set the basic low-pass filter of. h (n) is | ω |> π / N, the stopband normalized by the sampling frequency fs is | ω | = π / 2N, and H (z) obtained by z-transforming h (n) is H (ex
It is assumed that p (jω)) = 0 (π / N ≦ | ω | <π) and the filter coefficient is h (n) = h (L-1-n).

(Condition 1) The characteristic H (z) of the basic low-pass filter is shifted on the frequency axis so that the entire frequency region including negative frequencies is evenly distributed.
A band pass characteristic Hi (z) divided into 2N pieces is obtained.

[0015]

(Equation 3)

In FIG. 1, the bandpass characteristics Fi and Gi of the transmission filter 1i and the reception filter 2i are represented by appropriate linear combinations of the equations 3a and 3b. Among them, the following case is adopted in which all filter coefficients are real numbers.

[0017]

(Equation 4)

At this time, from the inverse z transformation of the equations 4a and 4b,
The filter coefficient is as follows.

[0019]

(Equation 5)

In FIG. 1, when the input signal is X (z), the signal Yi (z) obtained by interpolating 0 to N times after thinning out the output of the transmission filter 1i by 1 / N is It is expressed as follows.

[0021]

(Equation 6)

Here, when the signal of the equation (6) passes through the reception filter 2i, the signal Ui (z) becomes as follows, considering the condition 1.

[0023]

(Equation 7)

[0024] Here, the first,
The second term is a component of the original signal Xi (z), the third and fourth terms are low-frequency side overlapping components, and the fifth and sixth terms are high-frequency side overlapping components. However,
Equation 6 is a case where i is 1 ≦ i ≦ N−2, and when i = 0, the overlapping component on the low frequency side becomes 0, and when i = N−1, the overlapping component on the high frequency side becomes 0 respectively. .

The input signal is correctly re-synthesized between the adjacent bands Ui-1 and Ui (0 <i <N) and the overlapping component on the high frequency side of Ui-1 (z) and Ui (z). z) and the overlapping component on the low frequency side,
It's time to cancel each other out. The condition can be expressed by the following equation from Equation 7.

[0026]

(Equation 8)

Equation 8 is replaced with the following equation.

[0028]

(Equation 9)

From the equations 3a, 3b, 4b and 9a,

[0030]

(Equation 10)

The first and third terms of the equation 10 are 0 according to the condition 1.
Therefore, the following equation is obtained.

[0032]

[Equation 11]

(Condition 2) Assuming Condition 2, H + i (z) · H-i (z) = 0 (0 <i <N
−1), the output signal U (z) is as follows.

[0034]

(Equation 12)

Here, the following conditions are set.

[0036]

(Equation 13)

(Condition 3) At this time, the response characteristic of the band division / synthesis filter system (U
The inverse z transformation of (z) / X (z)) is expressed in the following form.

[0038]

[Equation 14]

However, the inverse z-transforms of U (z) and H2 (z) are defined as u (n) and h2 (n), respectively. In Equation 13, the parentheses on the right side are impulse trains with an interval N starting from n = 0. Especially, in the case of φ = πk (k = {0,1}), starting from n = 0, φ = Πk (k = 1/2, 3/2), the impulse sequence is an interval 2N starting from n = N. Also, Equation 1
H2 (n) on the right side of 3 is n = L ± 2Nk (k
Is an integer other than 0) and can take a 0 value. Equation 14 (inverse z of the response characteristic of the band division / synthesis filter)
(Conversion) is a response of 1 impulse, in the right side of the same equation, the parenthesized “n” and h2 (n) of the same equation
It is only necessary to properly match “n” where 0 becomes 0. The condition is shown in the following formula.

[0040]

(Equation 15)

(Condition 4) According to the above Conditions 1 to 4, when the output signals of the reception filter 2i are added, the overlapping components between the adjacent bands are canceled and a signal equivalent to the input signal X (z) is generated. A band division / synthesis filter to be generated is configured. Also, in condition 4, an arbitrary integer M
On the other hand, since m and k are always obtained, the value of the filter tap number L can be determined to be an integral multiple of the band division number N or a value obtained by adding 1 to it. The method of Document 3 described above corresponds to the case of k = 0 in the above Condition 4, and the method of Document 4 corresponds to the case of k = {1/2, 3/2}.

Using the above conditions 1 to 4, the characteristics of the filters 1i and 2i shown in FIG. 1 are obtained. First, H (z), Fi (z), Gi
(z) is expressed in the following format.

[0043]

(Equation 16)

Here, fi (n) and gi (n) are expressed by equation 4a and equation 4
Calculated from b.

From the condition 4, L = M · N + s (s =
{0 | Tap number L is odd}, {1 | Tap number L is even}}
Then, set M as follows.

M = 2 (2m + k) (where, k = {0, 1/2, 1, 3/2}; m is a positive integer) ... (Equation 17) From Equation 17 and the conditions 2 and 3, , Constants ai and ci can be obtained.

When k = 1/2, 3/2,

[0048]

(Equation 18)

When k = 0,1,

[0050]

[Equation 19]

At this time, fi (n) and gi (n) are as follows.

[0052]

(Equation 20)

For example, when k = 1/2 and s = 1, the equation 2
From 0a and number 20b,

[0054]

(Equation 21)

Is as follows.

The equations 18 and 19 are one of the solutions,
Exchange of ai and ci, sign reversal of ai and ci, and ai and ci
For the exchange of and the sign inversion, the solution satisfies the conditions,
Fi (n) and gi (n) can be obtained for each.

Next, specific examples of the transmission filter circuit 1i and the reception filter circuit 2i will be described. In FIG. 1, each of the transmission filter circuits 1i has an input signal X (n) input to one end thereof, and (L-1) delay units 7 connected in series at a time of 1 / fs and an input signal X (n). Further, it can be configured by the multipliers 100 to 10L-1 that perform an operation on the output signal of each delay device 7 and the adder 6 that adds each output of the multiplier 10. Here, the multiplier 10n forming the transmission filter 1i includes
The multiplier determined by fi (n) of the equation 19 is set. Similarly,
The reception filter 2i is a delay unit of time 1 / fs and a multiplier 200 to 20L in which a multiplier determined by gi (n) of equation 19 is set.
-1 and an adder.

Next, a band / separation filter according to the second embodiment of the present invention will be described.

In the above-described first embodiment, the calculation of the filter of equation 20a can be summarized as follows.

[0060]

(Equation 22)

Expression 21 is a kind of discrete cosine transform, which is a fast calculation algorithm of discrete Fourier transform (hereinafter, FFT).
It is well known that is applicable. Similarly, the number 20
Since the a and the equation 20b are discrete cosine transform or discrete sine transform, FFT can be applied.

The transfer function H (z) of the basic low-pass filter is represented by the equation 16a of the first embodiment, and the transfer function F'i (z of the non-recursive filter when FFT is applied to the band division / synthesis filter is shown. ), G'i (z) is expressed as follows.

[0063]

(Equation 23)

Inverse z transformation f'i (n) of F'i (z), G'i (z),
g'i (n) is expressed as follows.

[0065]

(Equation 24)

As an example, when k = 1/2 and s = 1, f'i
(n) and g'i (n) have the following values.

[0067]

(Equation 25)

FIG. 2 shows the configuration of a band division / synthesis filter based on the above idea. In FIG. 2, blocks 3 to 7 are
This is the same as described with reference to FIG. Blocks 8 and 11
Is a Fourier transformer, and the transformer 11 performs the inverse transformation of the transformer 8. Block 90i and block 91i (i = 0, 1,
, N-1) is a non-recursive filter circuit having the number of taps L as shown in FIGS. By setting the multipliers obtained by the equation 23 in the multipliers forming these non-recursive filters, a band division / synthesis filter having the same characteristics as the first embodiment is realized.

In this case, L = [{2 (2m + k) N + s} / between the number of band divisions N and the number of filter taps L.
N] (where s = {0,1}; m is an arbitrary positive integer; k =
{0, 1/2, 1, 3/2}; [x] is the maximum integer that does not exceed x), so the number of taps L of the filter is
Can be set to any positive integer.

As described above, according to the first embodiment, when a non-recursive filter is used, the number of taps of the filter can be set at intervals of an integral multiple of the number of band divisions, and
According to the second embodiment, the number of filter taps can be set to an arbitrary positive integer by combining orthogonal transformation methods such as FFT. That is, according to the present invention, it is possible to realize a band division / synthesis filter having a higher degree of freedom in design than the conventional method.

The band division / synthesis filter described above can also be realized by program processing such as DSP (digital signal processor).

[0072]

According to the present invention, the degree of freedom in setting the number of filter taps can be further increased in a band division / synthesis filter composed of a non-recursive filter.

[Brief description of the drawings]

FIG. 1 is a configuration diagram of a band division / synthesis filter according to a first embodiment of the present invention.

FIG. 2 is a configuration diagram of a band division / synthesis filter according to a second embodiment of the present invention.

3 is a configuration diagram of a bandpass filter 90 in FIG.

FIG. 4 is a configuration diagram of a bandpass filter 91 in FIG.

FIG. 5 is a configuration diagram of a parallel band division filter.

FIG. 6 is a diagram showing an amplitude characteristic example of each part when N = 4 in the filter of FIG. 5;

[Explanation of symbols]

1i Non-cyclic filter for band division of band i 10k Non-cyclic filter for band division of band 0
i-th filter coefficient 2i Non-cyclic filter for band synthesis of band i 20n Non-cyclic filter for band synthesis of band 0
n-th filter coefficient 3 The part of the signal divided into each band that performs processing such as coding and transmission 4n Sampling frequency converter that passes the signal once for every N times of the signal 5n Passes the signal once Sampling frequency converter for interpolating 0 for each (N-1) times 6 adder 7 delay device 8 Fourier transform device 90i, 91i acyclic filter X (z) input signal Xi (of band division / synthesis filter system z) Transmit filter output signal of band i Yi (z) Receive filter input signal of band i Ui (z) Receive filter output signal of band i U (z) Output signal of band division / synthesis filter system

Claims (4)

[Claims] 1. A part of frequency components is shared between adjacent bands, and the frequency components of an input signal are equal in width to N (N).
Is an integer greater than or equal to 2)
A band splitting / synthesizing filter configured by a synthesizing unit that generates a signal equivalent to the input signal from a signal for each band obtained by splitting, wherein the dividing unit operates at a frequency fs and The N first acyclic filters with the number of taps L for extracting the signal components for each band and the signal components for each band extracted by the N acyclic filters at a frequency fs / N A second switch for sampling the signal sampled by the first switch at a frequency fs, and a first non-recursive filter. A signal component in a band corresponding to the signal component extracted by the corresponding first acyclic filter is extracted from the signal provided correspondingly and operating at the frequency fs and sampled by the second switch. N taps with L A second non-recursive filter, an adder for combining the extracted signal components in the N pieces of FIR filters, number of taps of said first and second non-recursive filter L
Is a band division / synthesis filter, which is set to an integer multiple of the band division number N or a value obtained by adding 1 to the integer division of the band division number N. 2. A frequency component of a part is shared between adjacent bands, and the frequency components of an input signal are equal in width to N (N).
Is an integer greater than or equal to 2)
A band splitting / synthesizing filter configured by a synthesizing unit that generates a signal equivalent to the input signal from a signal for each band obtained by splitting, wherein the dividing unit operates at a frequency fs and The N first acyclic filters with the number of taps L for extracting the signal components for each band and the signal components for each band extracted by the N acyclic filters at a frequency fs / N A second switch for sampling the signal sampled by the first switch at a frequency fs, and a first non-recursive filter. A signal component in a band corresponding to the signal component extracted by the corresponding first acyclic filter is extracted from the signal provided correspondingly and operating at the frequency fs and sampled by the second switch. N taps with L A filter coefficient of a basic low-pass filter that has a second acyclic filter and an adder that combines the signal components extracted by the N acyclic filters, and that determines the characteristics of the first acyclic filter. Where h (n) is the filter coefficient fi of the first and second acyclic filters
(n), gi (n) (i = 0,1, ..., N-1; n = 0,1, ...,
L-1) is a band division characterized by being obtained by the following equation:
Synthesis filter. (Equation 1) 3. A frequency component of a part is shared between adjacent bands, and the frequency components of an input signal are equal in width to N (N).
Is an integer greater than or equal to 2)
A band splitting / synthesizing filter configured with a synthesizing unit that generates a signal equivalent to the input signal from a signal for each band obtained by splitting, wherein the dividing unit inputs the input signal from one end, (N-1) delay devices connected in series, a first switch for sampling the input signal and the output signal of each delay device at a frequency fs / N, and operating at a frequency fs / N Then, each of the N signals sampled by the first switch is filtered by the N first non-recursive filters having L taps and by the first non-recursive filter. A first orthogonal transformer that generates a signal for each band based on the signal, and the combining unit performs an inverse transform of the orthogonal transform on the signal generated by the first orthogonal transformer. A second orthogonal transformer,
N taps, each of which is provided corresponding to each of the first non-recursive filters, operates at a frequency fs / N, and filters a signal inversely transformed by the second orthogonal transformer, the tap number being L. Second non-cyclic filter and a second acyclic filter for sampling the signal extracted by the second non-cyclic filter at a frequency fs.
Switch and means for adding to each of the N signals sampled by the second switch with the same delay as the delay amount given by the delay device, and combining the taps of the acyclic filter. The number L is a band division / synthesis filter characterized in that it can be set to an arbitrary integer. 4. The band division / synthesis filter according to claim 3, wherein the filter coefficient of the basic low-pass filter that determines the characteristic of the first acyclic filter is h (n), And the filter coefficient fi 'of the second acyclic filter
(n), gi '(n) (i = 0,1, ..., N-1; n = 0,1, ...,
L-1) is a band division characterized by being obtained by the following equation:
Synthesis filter. (Equation 2)