U. Glaeser

In the MPEG-1 encoder an efficient polyphase filter bank realization is implemented, using the following
steps:
1. Thirty-two new input samples x(n) are shifted into a 512-point FIFO buffer.
2. Five hundred and twelve samples x(n) are multiplied by the modified (the so-called analysis
window) coefficients C(n).
© 2002 by CRC Press LLC
(27.50a)
where C(n) = −h(n) if the integer part of n/64 is odd, otherwise C(n) = h(n), n = 0, 1,…,511.
3. Intermediate result is calculated
4. Thirty-two new output samples are computed
(27.50b)
(27.50c)
where M i(k) = cos{[(2i + 1)(k − 16)π]/64} are the modulation (or analysis) matrix coefficients.
Sampling Rate Conversion
Z( n)
= C( n)x(
n)
Y( k)
= Z( k+ 64j)
for k = 0, 1,…, 63
Currently, digital audio signals are used with various sampling rates. Typical values are 8, 16, 22.05, 32,
44.1, 48, and even 96 ksamples/s. Thus, an “online” sampling rate conversion is a very important task in
digital audio signal processing algorithms. This, task can nowadays be realized using modern digital signal
processors [6]. Generally, three different approaches are possible:
• Natural approach based on, first, interpolation with factor integer M, and then, decimation with
factor N (Fig. 27.23),
• Time-domain approach based on direct interpolation (or decimation) in time, i.e., on the realization
of a sequence of noninteger delays (Fig. 27.24),
FIGURE 27.23 Basic system for sampling rate conversion.
FIGURE 27.24 Time relationships between input and output samples.
7
∑
63
j=0
∑
Si = Mi( k)Y(
k)
for i = 0, 1,…, 31
k=0
x (m)
M
Lowpass filter
M
ω
ωc
N
y(n)
...
∆ ti
ti ti+
1
Tout
Tin
∆ ti+
1
...
time