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rates. If this is not true, we need to weight the rates of the individual subbands. The functional
to be minimized becomes
D
k
+
λ
J
=
β
k
R
k
(116)
where
β
k
is the weight reflecting the relative length of the sequence generated by the
k
th filter.
The distortion contribution from each subband might not be equally relevant, perhaps because
of the filter construction or because of the perceptual weight attached to those frequencies [
210
].
In these cases we can modify our functional still further to include the unequal weighting of
the distortion:
=
w
k
D
k
+
λ
β
k
R
k
(117)
J
14.10 Application to Speech Coding
__
G.722
ITU-T recommendation G.722 provides a technique for wideband coding of speech signals
that is based on subband coding. The basic objective of this recommendation is to provide
high-quality speech at 64 kbits per second (kbps). The recommendation also contains two
other modes that encode the input at 56 and 48kbps. These two modes are used when an
auxiliary channel is needed. These two modes provide for auxiliary channels of 8 and 16kbps,
respectively.
The speech output or audio signal is filtered to 7kHz to prevent aliasing, then sampled at
16,000 samples per second. Notice that the cutoff frequency for the anti-aliasing filter is 7kHz,
not 8kHz, even though we are sampling at 16,000 samples per second. One reason for this is
that the cutoff for the anti-aliasing filter is not going to be sharp like that of the ideal low-pass
filter. Therefore, the highest frequency component in the filter output will be greater than
7kHz. Each sample is encoded using a 14-bit uniform quantizer. This 14-bit input is passed
through a bank of two 24-coefficient FIR filters. The coefficients of the low-pass quadrature
mirror filter are shown in Table
14.7
.
The coefficients for the high-pass quadraturemirror filter can be obtained by the relationship
n
h
LP
,
n
h
HP
,
n
=
(
−
1
)
(118)
The low-pass filter passes all frequency components in the range of 0 to 4kHz, while the
high-pass filter passes all remaining frequencies. The output of the filters is downsampled by
a factor of two. The downsampled sequences are encoded using adaptive differential PCM
(ADPCM) systems.
The ADPCM system that encodes the downsampled output of the low-frequency filter uses
6 bits per sample, with the option of dropping 1 or 2 least significant bits in order to provide
room for the auxiliary channel. The output of the high-pass filter is encoded using 2 bits per
sample. Because the 2 least significant bits of the quantizer output of the low-pass ADPCM
system could be dropped and thus not be available to the receiver, the adaptation and prediction
at both the transmitter and receiver are performed using only the 4 most significant bits of the
quantizer output.
