JPS5840914A - Band dividing and synthesizing filter - Google Patents

Abstract

PURPOSE:To obtain an original signal which is free from the folded noise, by using the noncyclic filters of an odd number of taps to both low and high band- pass filters within the band dividing and synthesizing filter blocks respectively. CONSTITUTION:An input signal X(Z) of frequency fS is supplied to noncyclic filters 201 and 301 having odd number of taps with transmission functions H(Z) and H(-Z) within a band dividing filter block 100 via an input terminal 10. The outputs of the filters 201 and 301 are thinned to fS/2kHz respectively through sampling frequency thinning switches 401 and 402 and then fed to a band synthesizing filter block 200 via a signal processing circuit 300. Then 0 is inserted into each input with every second sample through sampling frequency interpolation switches 501 and 502 and then added by an adder 60 via noncyclic filters 202 and 302 having the same structure as the filters 201 and 301.

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention, for example, divides a signal into a plurality of bands, and then combines the signals of each band again through a signal processing circuit for encoding transmission and decoding. This paper relates to band division/synthesis filters used to obtain .

Band division coding method (
(subband encoding method) is known.

The principle of this method is that the audio signal is divided into bands by multiple filters, and each band signal is encoded by assigning the optimal number of encoding bits according to the signal output of each filter. Therefore, it is possible to encode high-quality speech at a low transmission rate.

This is a method for reducing or eliminating aliasing noise occurring at the end of the passband of each filter, which is the most important dotted line when implementing this subband encoding method. In May 1977, Hartford in the United States discovered that it was possible to remove aliasing noise by using a filter called a quadrature mirror filter (hereinafter referred to as QMF).
) was held at the International Academic Conference (IEEE Intern).
ational Conf@r@ncson Acou
sticm, Sp@ech, and Signal
Proc@ssing) l), 131t@ba
Paper published by N. and C. Qaland”, Appl.
cation of Quadratur@M
error filtersto 5plit 1l
and voice Codlng 3eh@mes
' is described in detail.

However, as stated in the above-mentioned reference, only a transversal lid filter with an even number of taps could be used as a conventional QMF. It was believed that a transversal filter with an odd number of taps could not eliminate aliasing noise.

SUMMARY OF THE INVENTION Therefore, it is an object of the present invention to provide a band division/synthesis filter for eliminating aliasing noise using a filter with nine odd taps, which has not been possible in the past.

Another object of the present invention is to provide a band division/synthesis filter which can simplify the hardware by time division multiplexing.

Next, the present invention will be described in detail with reference to the drawings.

FIG. 1 is a block diagram for explaining the present invention in detail. Since the filter shown in Figure 1 is a sample value system,
Expression using two functions is possible. The input signal X(2) from the input terminal 10 is input to the low-pass filter 2o1 and the high-pass filter 301 in the band-splitting filter pack 100. The sampling frequency of the input signal X(2) at this time is assumed to be fs)h. However, z wx @J"l'
It is l. Data from the outputs of these filters 20m and 30 is discarded every other sample by switches 401 and 40m, and the sampling frequency is fs/2H.
output from the filter block 100 as a signal of z,
These signals are input to switches 501 and 50m in the synthetic filter block 20-0, data with the value @0# is inserted every other sample, and the signal is returned to the signal of the sampling frequency fs. These signals are added or subtracted by an adder 60 via a low-pass filter 20 and a high-pass filter 30, and are outputted to the output terminal 70 of the filter block 200 as a signal Y(2). Low pass filters 201, 201 and high pass filter 301
．． The 30 mm have transfer functions H(2) and K(2), respectively, and the passband width is f1/4.

FIG. 2 is a diagram for explaining the operation of the circuit shown in FIG. 1; Figure 2 ■ The spectrum of Hiro input signal No. 2
and ■ are the output vectors of the filter 201 and the switch 401, respectively, 0 in the figure is the amplitude frequency characteristic of the filter 30530m, and ■ and ■ are the amplitude frequency characteristics of the filter 30530m, respectively.
The output vectors of 0-fold and switch 40-fold are shown in the same figure■
and ■ are the output vectors of the filters 20I and 303, respectively, and O and ■ in the figure show the spectra of the output signal Y (23) with and without aliasing noise, respectively. The shaded area in ~o represents aliasing noise.

Next, the mathematical representations of each part of FIG. 1 will be shown. First, input signal X (
The sampling frequency of 2) is fs, )h, so X(
2) are two series X5 of sampling frequency f-/2-
(Z") and )(x(Z")Ke can be expressed as the following equation.

X(Z)-X@(Z")+Z-'・Xs CZ"
) (1) Also, the sampling frequency ft1b
Similarly, the H(2) filter and the K(2) filter respectively have the sampling frequency fs/2HsO transfer characteristic H
e (Z") and Hx (Z") and two filters with transfer characteristics Ko (Z')' and 1es (Z"). Therefore, H (2) and K (2
) is expressed as the following equation:

H(23-He(Z")+Z-'Hx(Z")
(21K(Zl−＠(Z”)+Z−”Kl
(Z”) (31 is K (23 is H (2
) by fs/4- and use nine, then K(Z)-H(-Z") ==xHs (Z")-Z-" Hz (Z")
(4) holds true. Therefore, formula (3),
(From 41, Ke (Z”) = H* (Z”)
(51 to 1 (Z") - Hx (Z"
) 161 is obtained.

The output of the filter of formula +11, (2) and fiH(2) is expressed as the following formula.

)E@)E)=(Xs(Z)+Z−”X5E)[He(
2hZ−”Ht(Z))=(X e (ZH@(Z
)+Z −”X t (Z)I(1(z))+Z−'
[X@(Z)Hx(2H-Xs(Z)He(Z))=(
X[Z) )E-+-X(-Z)H(-Z') )/2
+(XtZ))IZ)-X(-Z)H(-Z'))
/2(7) However, in equation (7), the following equation holds true.

X@(Z) He(Z)+Z-'XtlZ)Hs(Zl
-(XtZ))[Z)+X(-Z')HC-Z) )/
2 (81Z-”[X@(Z)Hs(2)+X
5 (Z) HoE) = OE abuse x (-Z) H (-Z))/
2 (91 Also, from equation (11, (4+), K(2
) is expressed as the following equation.

)QZ) KIZ=(Xs(Z)+-Z-'X5(Z)
) (He(Z)-Z-"Ht(Z))-(Xs(Z)
He(Z)−Z″″″X t (Z) Hs (Z))
10Z-' [-X@(ZIF(x(Z)+X*(Z)H
o(Zl)-[X[Z)H(-Z)+X(-Z))[Z
)/2+(χZ)H(-Z)-X(-Z))1211/
2(10) However, in equation (10), the following equation holds true.

X@-*(2hZ-”XsI:gHs@-(X[Z)H
(-Z)+X(-Z)brain)/2 (11)Z-
” (-X@(ZIHtkenX5(Z)He(2))-(
X[ZIH(-z)-X(-Z)HE)/z
(12) At this point, the sampling frequency thinning switches 401 and 401 in FIG. Depending on whether it is taken out, it can be divided into the following four cases. Furthermore, depending on whether the outputs of the filters KH and K(2) are added or subtracted, different M results are obtained as shown below.

(1) The first term of the filter output of H■ (Equation (8)),
When extracting the first term (Equation (11)) of the filter output of K(2), Y(Z)=(X(Z)H(Zl+X(-Z)H(-Z')
))/2-)E±01H(Z)+X(-Z)Naw)/2-
Since H(-Z), (13) (the first term of the filter output of 11H(2) (Equation (8))
, K(2) and the second term of the filter output (Equation (12)), Y(Z)-(X[Z)H(Z)+X(-Z)H(-Z)
)/2-H(Z)±[X(23H(-Z)-X(-Z)
Ia)/2-H(-Z)'MtK1 (14) (I) @The second term of the filter output (Equation (9)) in the figure, and the first term of the K's filter output (Equation (11)) When generating MR, Y(Z)-(X(23H(Z)-X(-Z)H(-Z'
) ) / 2 lilo ± (X (ZIH (-Z) + X (-Z))
E)/2-H(-Z) Therefore, the second term of the filter output of GV)H(2) (Equation 9)),
When extracting the second term (Equation (12)') of the filter output of K■, Y(Z)= (X(23H(Z)-X(-Z)H(-Z
) )/2-H[Z)±(X(Z)H(-Z)-X(-
Z)H(Z))/2-H(-Z) Therefore, in the output Y(2) of (I) to (goods) obtained above, (
The term XeZ)H(2)H(-Z)) represents aliasing noise. Therefore, in all of the above four cases, aliasing noise can be completely eliminated from the output Y(2) by selecting one of the addition and subtraction X-rays. l
! lFi is a summary of these results. So H
Assuming that the filter for (Z) is an N-tap acyclic filter with symmetrical coefficients, the transfer function of this filter can be expressed as follows.

H(Z)=a@Z"+at Z-'10amZ-"+s
e s+aN-IZ-(N-")-, q, , kf+,
z thousand, +,, +,, -, z-Np) = 2-shot・G(2
) (17) However, G(Z3=& @zJp +atZ1P-" +...
... 10&N-*Z-hour (18) a1=am-t-1 (&i is a real number: 1-0.1.---
, N-1) (19) and \, the amplitude frequency characteristics of H■ and H (-Z') are expressed by the formula % () (20) ) (21) However, -1w2w:fI. Also G(・j′T)
-1). Therefore, from equations (20) and (21), tl
The amplitude frequency aq# of H(2)1±H(-Z)") is (H"(・j"?)-1J(connection-,j"1)),(,j
ω′)−(N−”)e”(−−t;(−eJωT )−
('-1)e "Pl(lJa, ff1-go-)±(1
)'-"G'(-@/2))e-j("-1)"(22
) becomes. In Equation (22), two cases will be considered: when N is an even number and when N is an odd number.

■When N is an even number, Hl(・j″?) 倀1(−・jo) [union) 1 go1(−
慟Vclause>)C8)'tr(o) In equation (23), for 0≦ω≦ωm/2, the
Although it is possible to design a filter with −+−s/2) m 1゛, it is also possible to
It is impossible to design a filter as the sum 1(ω+#l/2) z l .

Therefore, IH” (ej-”)-H”(-e””)l-1(24
) It becomes possible to design a filter H■ that satisfies the following.

■When N is an odd number, H"(@j""MH"(-ej") = (e"riJ"(-
s/2))8゜-j (s-s voice'
(25) In equation (25), the same thing as ■ can be said for 0≦ω≦ωs/2, so IH"(ej"") 1 H"(-ej"?) 1-1
It becomes possible to design a filter H■ that satisfies (26).

When the results obtained above, equations (24) and (26), are made to correspond to Table 1, the following can be seen.

In the cases (I) and QV) in Table 1, the original signal can be restored without aliasing noise by Umikoto K using an acyclic filter with even number of taps. Therefore, addition 116G in FIG. 1 is made to be a subtraction operation. On the other hand, in the case of (11 and 1) in Table 1, the original signal is restored and colored without aliasing noise by using an acyclic filter with odd number of taps. Therefore, the adder 60 in FIG. 1 performs an addition operation. As for cases (1) and side, what has been known so far is (
In the case of group (1), it has conventionally been considered impossible to restore the original signal without aliasing noise.

However, as explained in detail above, (I) and (
In the case of 1), also according to the configuration described below! 0 (1) and similar results as in the case of side are obtained.

FIG. 3 shows one embodiment of the invention, in which all reference numerals that are the same as in FIG. 1 indicate the same functions. The adder 60 performs an addition operation, and the filters 201 and 20! is the transfer function H(2)
Odd tap acyclic low pass filter, filter 30
K and 30 are odd-tap acyclic high-pass filters with transfer functions) [-Z). Switches 40*, 40, 50t, and 50m all operate synchronously.')
, 0N10FF every T (-1/f a ) seconds, respectively.
and repeat through/zero. The state shown in Figure 3 is
Sampling frequency thinning switch 401 and 40m
are in the ``ON'' state FF state, and the sampling frequency interpolation switches 501 and 50g are in the 1-through state and the value 1 zero state, respectively.For the next 7 seconds, all The switches operate to change to the opposite state from the current state. , the band division filter block 100 and the band synthesis filter block 200.
A signal processing circuit 300 is inserted between the circuit 30 and
0 indicates functions such as input signal encoding/decoding and transmission path. Any encoding/decoding method may be used here. It is also possible to dynamically change the number of encoding bits.

In FIG. 3, input signal X(2) is passed through input terminal 10 to H(2) odd tap filter 201 and H(-2
) is fed to the odd tap filter. This is H(-Z
The high-pass filter of H(2) is obtained by shifting the frequency of the low-pass filter of H(2) by fs/2)h. Sampling frequency thinning switch 40s and 4
The two output streams decimated to fs/2KHz rate by the operation of 01 are as described in the above operation principle (1) or (rin).
This corresponds to the case of .

That is, when equation (8) is taken out as the output of filter 201 of H(2), equation (12) is taken out as the output of 30 filters of H(-Z), so (11
Corresponding to the case, when equation (9) is taken out as the output of the filter 20s of H(z), the filter 3 of H(-Z)
Since equation (11) is extracted as the output of 01 (corresponds to case 11), as an actual operation, (Il
Whether it becomes 1 or 1 depends on the initial state of the switch.

The two output sample value series of the signal processing circuit 300 are processed by the sample frequency interpolation switches 501 and 50.
A value 1 zero'' is inserted every other sample.Further filters 20m and H(-Z'') of H(2), respectively.
The adder 60 adds the outputs of both filters through the filter 30 (2) and outputs Y(2) to the output terminal 70. By using an acyclic filter with an odd number of taps that satisfies equation (26) as a filter for H(2),
Y(2) does not include aliasing noise, and the input signal X(2) can be completely restored.

Incidentally, in the conventional method using an even-numbered tap acyclic filter, the sample frequency thinning switch 401',
40m and sample frequency interpolation switches 501, 50
1 is different from that shown in FIG. That is,
The above four switches operate in synchronization.J)T
Repeat @0N10FF" or 1 through/zero every (-1/fs) seconds, respectively. However, as shown in the fs1 diagram, in the state shown in the figure, the sample frequency thinning switches 401 and 401 are both in the @ON" state, and the sample frequency interpolation switches 501 and 50 are both in the 'through' state. ing. For the next 7 seconds, all switches operate to change to the opposite state.

In other words, switches 401 and 40! When both are in the @OFF' state, both the switches 501 and 50sd have a value of 1 zero. Therefore, it corresponds to the case of (1) or Tei shown in Table 1. 60 needs to perform a subtraction operation.

This invention further has the following advantages.

In the band division filter block 100 of FIG. 3, the sampling frequency thinning switches 401 and 40 alternately repeat 'ON' and 'OFF'.Therefore, the two output sample value series of the band division filter block 100 are controlled by the selector. The time switches 401 and 40m are included in the selector function.Furthermore, the two output sample value series of the signal processing circuit 300 can be easily time-division multiplexed using When division multiplexing is performed, sampling frequency interpolation switch 5
01 and 50 snow, H(2
) and T((-Z) filter inputs can be obtained by 6g. This operation can be realized with two AND elements. Therefore, the invention of band division and synthesis suitable for extended time division multiplexing Can provide filters.

FIG. 4 shows another embodiment of the invention, reference numeral 100.
t, 100g, φ..., 100ma are band division filter pulls, reference numbers 200u, 200m, respectively.

...-, 200 are respectively band synthesis filter blocks, reference numerals 300 are widening signal processing circuits, reference numerals 10 and 7.
0hiro shows the input terminal and output terminal, respectively.

FIG. 4 shows an example in which a signal input through the input terminal 10 is divided into eight bands. The band division/synthesis filter pulls 1001 and 200 are paired,
The sampling frequencies before and after band division are fs-out and f
s/2-Aishi. Also, the bandwidth wII/synthetic filter block 100m, 200 snow, 100 torture and 2001
are a pair, and the sampling frequencies before and after band division are both fs/2Hz and fs, 741 m. Furthermore, band division/synthesis filter block 10°0
4 and 2004.1001 and 200 Gun, 100・and 200- and 100 Ma and 200! are each a pair, and the sampling frequencies before and after band division are both Kfs/4.
- and fs/8 output.

The band of the signal input through the input terminal 10 is divided into two by a band division filter pull 1001, and the bands are supplied to two band division filter pulls 100 and 1008, respectively. The good signal inputted to the band division filter block 100 is further divided into two bands, and is supplied to the band division filter pulls 1004 and 100, respectively. Also, band division filter boot 1001. Similarly, the band of the input signal is further divided into two and supplied to band division filter blocks 1006 and 100, respectively. The good signals inputted to the band division filter blocks 100a, 100m, 100, and 100m have their bands further divided into two, and all are supplied to the signal processing circuit 300.

Four pairs of sample value sequences each having a sampling frequency of fs/8- are input to the signal processing circuit 300. As mentioned above, the signal processing circuit 300 includes functions such as encoding/decoding of input data series and signal transmission.

Band division filter blocks 1004, 1001, 100
The pair of output sample value series of . .

The outputs of band synthesis filter blocks 2004 and 2001 are both fed to band synthesis filter block 200,
The outputs of band synthesis filter blocks 2006 and 200 are both provided to band synthesis filter pull 200-. In addition, the band synthesis filter block 200 and 200
- output appears at output terminal 70 via band synthesis filter block 200K.

As described above, after dividing the input signal into eight bands, it is possible to combine them again to obtain the original signal without aliasing noise. Here, the band division filter blocks 100x, 10
0, ass, 100v have the same configuration as the band division filter block 100 in FIG. 3, and band synthesis filter blocks 200s, 200m, .
0ma has the same configuration as the band division filter 200 shown in FIG. However, it is assumed that the operating speed of the band division/synthesis filter pull corresponds to the sampling frequency of input/output data.

In addition, as explained in FIG. 3, the band division filter blocks 100*, 100°, .
, 200v can each be subjected to time division multiplex processing.

Furthermore, the band division filter pull is divided into a first group consisting of 1001, a second group consisting of 1001 and 100-, and a third group consisting of 1004, 100i, 100@ and 100ma. If one piece of hardware is prepared for each of the third groups and time division multiplexing is performed on a plurality of band division filter blocks, then the first Since the clock rates of the hardware in the second and third groups cannot be made the same, the hardware can be simplified.

Furthermore, similar time division multiplexing processing can also be applied to the band synthesis filter, thereby making it possible to standardize the p-rate and simplify the hardware.

Furthermore, in FIG. 4, the number of band divisions can be reduced by sequentially removing the pair of band division and synthesis filter blocks having the lowest sampling rate. For example, if the pair of band division filter pull 1004 and band synthesis filter block 2004 is removed, the number of divisions becomes 17. Furthermore, a band division filter block 100- and a band synthesis filter block 20-
If the pair of 0m is removed, the number of divisions becomes 6, and when the pair of band division filter block 100 and band synthesis filter block 200 is removed, the number of divisions is further reduced to 5.
Become an individual.

In Fig. 4, an example is shown in which the band is divided into 8 bands to simplify the explanation, but based on the principle described above, the band is divided into N bands (N is any integer greater than or equal to 2). It is clear that it is possible to do so.

As described in detail above, according to the present invention, it is possible to provide a band division/synthesis filter that does not generate aliasing noise by using a transparsal type filter with an odd number of taps, which has not been possible in the past. Furthermore, the band division and
The synthesis filter is suitable for time division multiplexing and can simplify hardware.

[Brief explanation of the drawing]

FIG. 1 is a block diagram for explaining the invention in detail,
FIG. 2 is a diagram showing a signal spectrum for explaining the circuit operation of FIG. 1, FIG. 3 is a block diagram showing one embodiment of the invention, and FIG. 4 is a diagram showing another embodiment of the invention. FIG. 10: Input terminal, 70: Output terminal, 20120 bird: Low pass filter, 301301: High pass filter, 4o
14o1: Sampling frequency thinning switch, 50
150! : Sampling frequency interpolation switch, 60:
Adder, 100s to 100y: band division filter block, 200w 200s to 200ma: band synthesis filter block, 300: signal processing circuit. Patent Applicant NEC Corporation Agent Takashi Kusano 71 Figure 73 Figure 72

Claims (1)

[Claims] (11 input signal cycle value series is divided into two bands by the low-pass filter #11 and the high-pass filter #!1, and the sample value series of the sample sheet 1/2 of the input signal is divided into two bands. a ninth band dividing means for obtaining an output bear; a low-pass filter in tube 2 for receiving a sample value series input bear having the same sample rate as the sample value series output bear; and a second low-pass filter for performing sample value interpolation. band synthesis means for adding the outputs of the high-pass filters to obtain an output signal sample value series having the same sample rate as the input signal sample value series; and a signal processing circuit that combines the band division means and the band synthesis means. In the band division/synthesizing filter, the outputs of the first low-pass filter and the first low-pass filter are alternately removed to obtain the 172 times the sample. means for obtaining a sample value series output bear of the rate; and means for alternately performing sample value interpolation between one sample value series and the other sample value series of the sample value series input bears; A band division method characterized in that an original signal at risk of aliasing noise is obtained by using a non-recursive filter with an odd number of taps as the low-pass filter and the first and second high-pass filters.・Synthesis filter.