Pipelining, Retiming, Look-ahead Transformation and Polyphase Decomposition - Digital Design of Signal Processing Systems: A Practical Approach - page 334

Decim a tion by 3 using IIR filter
Filtering then Decimation
Decimation using Decomposition

Int e rpol a tio n by 3 using IIR filter
Interpolation then filtering
interpolation using Decomposition

1

0.6

0.9

0.5

0.8

0.4

0.7

0.3

0.6

0.5

0.2

0.4

0.1

0.3

0

0.2

-0.1

0.1

0 10 20 30 40 50 60 70 80 90 100

0 5 10 15 20 25 30 35

n

n

(a) (b)

Figure 7.35 Results of equivalence for decimation and interpolation. (a) Decimation performing
filtering then decimation and using the decomposed structure of Figure 7.34. (b) Interpolation by first
inserting zeros then filtering and using efficient decomposition of Figure 7.34

L=99;
x=rand(1,L); % generating input samples
% Filter then decimate
y=filter(b,a,x);
yd = y(3:3:end);
% Performing decimation using decomposition technique
% Polyphase decomposition of numerator
b0=Bdash(3:3:end);
b1=Bdash(2:3:end);
b2=Bdash(1:3:end);
% Dividing input in three steams
x0=x(1:3:end);
x1=x(2:3:end);
x2=x(3:3:end);
% Filtering the streams using polyphase filters
yp0=filter(b0,1,x0);
yp1=filter(b1,1,x1);
yp2=filter(b2,1,x2);
% Adding all the samples
yp=yp0+yp1+yp2;
% Applying Nobel identity on denominator
a0=Adash0(1:3:end);
a1=Adash1(1:3:end);
a2=Adash2(1:3:end);
% Filtering output of polyphase filters through IIR
% Cascaded sections
yc0=filter(1,a0,yp); % first 1st order section
yc1=filter(1,a1,yc0);% Second 2nd order section
yc = filter(1,a2,yc1); % Third 2nd order section
% Plotting the two outputs