Digital Signal Processing Reference
In-Depth Information
subplot(4,1,1);plot(speech);grid,ylabel(
'
x(n)
'
);axis([0 20000 -20000 20000]);
subplot(4,1,2);plot(sb_low);grid,ylabel(
'
x0(m)
'
); axis([0 10000 -20000 20000]);
subplot(4,1,3);plot(sb_high);grid, ylabel(
'
x1(m)
'
); axis([0 10000 -2000 2000]);
subplot(4,1,4);plot(rec_sig);grid, ylabel(
'
xbar(n)
'
),xlabel(
'
Sample number
'
);
axis([0 20000 -20000 20000]);
NN
¼
min(length(speech),length(rec_sig));
err
¼
rec_sig(1:NN)-speech(1:NN);
SNR
sum(speech.*speech)/sum(err.*err);
disp(
¼
PR reconstruction SNR dB
¼
>
);
'
'
SNR
10*log10(SNR)
This two-band composition method can easily be extended to a multiband filter bank using a binary
tree structure.
Figure 13.12
describes a four-band implementation. As shown in
Figure 13.12
,
the filter
banks divide an input signal into two equal subbands, resulting the low (L) and high (H) bands using
PR-QMF. This two-band PR-QMF again splits L and H into half bands to produce quarter bands: LL,
LH, HL, and HH. The four-band spectrum is labeled in
Figure 13.12
(b). Note that the HH band is
actually centered in
½p=
2
;
3
p=
4
instead of
½
3
p=
4
;p
.
In signal coding applications, a dyadic subband tree structure is often used, as shown in
Figure 13.13
,
where the PR-QMF bank splits only the lower half of the spectrum into two equal bands at any level.
Through continuation of splitting, we can achieve a coarser-and-coarser version of the original signal.
¼
↓
2
↑
H
2
G
0
↓
↑
H
2
2
G
0
↓
2
↑
H
2
G
1
xn
()
xn
()
↓
2
↑
H
2
G
1
Analysis stage
Synthesis stage
FIGURE 13.13
Four-band implementation based on a dyadic tree structure.
13.3
SUBBAND CODING OF SIGNALS
Subband analysis and synthesis can be successfully applied to signal coding.
Figure 13.14
presents an
example of a two-band case. The analytical signals from each channel are filtered by the analysis filter,
downsampled by a factor of 2, and quantized using quantizers
Q
0
and
Q
1
each with a assigned number
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