Digital Signal Processing Reference
In-Depth Information
% Compute the new polynomial as power of z^-3
Adash0=conv(p0, rP0);% conv performs poly multiplication
% Combine pole pair to form poly with real coefficients
p1 = conv([1 -p(1)], [1 -p(2)]);
% Generate requisite poly for first conjugate pole pair
rP1 = conv([1 p(1) p(1)^2], [1 p(2) p(2)^2]);
% Generate polynomial in z^-3 for first conjugate pole pair
Adash1 = conv(p1, rP1);
% Repeat for second pole pair
p2 = conv([1 -p(3)], [1 -p(4)]); %
rP2 = conv([1 p(3) p(3)^2], [1 p(4) p(4)^2]);
Adash2 = conv(p2, rP2);
% The modified denominator in power of 3
Adash = conv(conv(Adash0, Adash1), Adash2);
% Divide numerator with the composite requisite polynomial
Bdash = conv(conv(conv(b, rP0), rP1), rP2);
% Frequency and Phase plots
figure (1)
freqz(Bdash, Adash, 1024)
figure (2)
freqz (b,a,1024);
hold off
The B
0
(z) is implemented as a polyphase decimation filter, whereas 1/A
0
(z) is either implemented
as single-order all-pole IIR filter or converted into serial form for effective realization in fixed-
point arithmetic.
Figure 7.34 shows the optimized realization of decimation by 3 using the decomposition and Noble
identity where the denominator is implemented as a cascade of three serial filters. The multiplexer
runs at the input data rate, whereas the FIR and IIR part of the design works at a slower clock.
The MATLAB
code below implements the decimation using the structure given in Figure 7.34
and the result of decimation on a randomly generated data sample is shown in Figure 7.35(a). The
figure shows the equivalence of
this technique with the standard procedure of filtering
then decimation.
0.00
17
0.0
90
5
0.432
0
0.26
76
0.606
4
0.0121
x
x
x
x
x
x
y[n]
+
+
+
+
+
+
+
+
x[n]
0.036
7
0
0.2989
0.6093
0.4099
0.0559
x
x
x
x
x
x
x
+
x
+
x
+
+
+
+
-0.3194
0.6095
1.6589
0.0108
x
x
0.1789
0.5449
0.532
8
0.1414
x
x
x
x
x
x
0.6881
0.2474
+
+
+
+
clk
Figure 7.34
Optimized implementation of a polyphase fifth-order IIR filter in decimation by a
factor of 3
Search WWH ::
Custom Search