PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

Analog and Digital Filters 649

Example 6.19

Create the script fi le FIR_IIR that returns the magnitude plots of a 17th-order normal-

ized FIR fi lter by truncating a third-order IIR Butterworth digital fi lter with a cutoff

frequency at 0.25 rad.

Compare the plots of the 17th-order normalized FIR fi lter with the third-order IIR fi lter.

MATLAB Solution

% Script file: FIR _ IIR

% FIR from a third order normalized

% butterworth IIR FILTER with Wc=.25

[num,den] = butter(3,.25);

numad = [num zeros(1,30)];

divnumbyden = deconv(numad,den);

imp = dimpulse(num,den,30);

num9 = imp(1:19); % first 18 coefficients

% for the FIR implementation

h18 = freqz(numad,1);h = freqz(num,den);

W = 0:1/512:511/512;

plot(W,20*lo g10(a b s(h)),W,20*lo g10(a b s(h 18)))

ylabel(‘Magnitude in db’)

xlabel(‘W in rad’);

title(‘FIR IMPLEMENTATION FROM IIR’);

axis([0 1 -100 20]);grid on;

gtext(‘IIR FILTER’)

gtext(‘FIR FILTER’)

FIGURE 6.74

Phase plots of IIR normalized LP digital fi lter of order: 4, 6, 8, and 10 using the function yulewalk of Exa mple 6.18.

4

2

0

Angle

01 0.5

Order
 4

 2

 4

4

2

0

Angle

01 0.5

Order
 6

 2

 4

4

2

0

Angle

01 0.5

Order
 8

W in rad W in rad

 2

 4

4

2

0

Angle

01 0.5

Order
 10

 2

 4