Efficient LPC Quantization Methods - Digital Speech: Coding for Low Bit Rate Communication Systems - page 131

Table 5.13 Percentage of energy con-
tained in frequency bands: A < 25Hz,
25Hz ≤ B < 50 Hz, 50 Hz ≤ C < 100Hz and

D ≥ 100 Hz

Frequency band

LSF
parameters A B C D

f 1 94.52 4.24 1.07 0.17

f 2 95.44 3.61 0.83 0.12

f 3 96.67 2.71 0.54 0.08

f 4 96.81 2.56 0.54 0.09

f 5 98.10 1.51 0.33 0.05

f 6 97.46 1.99 0.45 0.10

f 7 96.36 2.88 0.64 0.12

f 8 95.54 3.28 0.71 0.47

f 9 94.64 4.41 0.98 0.24

f 10 92.72 3.97 1.13 2.18

above, a low pass filtering as a preprocessing stage prior to decimation has
been proposed [15] to alleviate the possible spectral overlapping distortion.
Of course one may question the use of low-pass filtering when the same
can be achieved by increasing the analysis window length with overlapping.
Increasing the analysis window length, i.e. to greater than two and a half
times the average pitch, would increase the frequency resolution, but in the
time domain, the speech signal would have evolved considerably during a
longer analysis window. Even though a largewindowmay result in smoothed
spectra, important details within the frame will not be modelled accurately.
In addition, even if the window length was increased there would still be no
guarantee that the high frequency components of the LSF tracks would not
be present. Al-Naimi's proposal of the use of a low-pass filter with a cut-off
frequency that is dependent on the LSF vector transmission rate, is therefore
justifiable [15].
The following set-up has been used to show the effect of low-pass filtering
over 8 seconds of speech [15]. First the LSF vectors f were extracted every
frame from the tracks f i which are formed by calculating the LSFs every
sample. Next, filtering was applied in the frequency domain separately for
each LSF track, f i , with a cut-off frequency that is dependent on the LSF
vector transmission rate and another set of LSFs g

g 1 ,g 2 ,g 3 , ... ,g p were
extracted. In order to avoid the rectangular windowing effect at the edges of
the blocks, one large FFT transformation was used for whole of the 8 seconds.
Figures 5.20-5.23 show a section of the variations of certain LSF tracks for
both classic f i and low-pass filtered g i methods. It is evident in these figures
that significant variations exist in the LSF tracks produced by the classic

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