Finite Impulse Response Filter Design - Digital Signal Processing: Fundamentals and Applications - page 229

0

Side lobe

Side lobe

-20

-40

Main lobe

-60

-80

0 0.5 1 1.5 2 2.5 3 3.5

Frequency (radians)

300

200

100

0

0 0.5 1 1.5 2 2.5 3 3.5

Frequency (radians)

FIGURE 7.8

Frequency responses for Example 7.3.

Program 7.1. MATLAB program for Example 7.3.

% Example 7.3
% MATLAB program to plot frequency response
%

[hz,w] ¼ freqz([-0.09355 -0.01558 0.1 -0.01558 -0.09355], [1], 512);
phi ¼ 180*unwrap(angle(hz))/pi;
subplot(2,1,1), plot(w,20*log10(abs(hz))),grid;
xlabel( ' Frequency (radians) ' );
ylabel( ' Magnitude Response (dB) ' )
subplot(2,1,2), plot(w, phi); grid;
xlabel( ' Frequency (radians) ' );
ylabel( ' Phase (degrees) ' );

To summarize Example 7.3, the magnitude frequency response demonstrates the Gibbs oscillatory
behavior existing in the passband and stopband. The peak of the main lobe in the passband is dropped
from 0 dB to approximately 10 dB, while for the stopband, the lower side lobe in the magnitude
response plot swings approximately between -18 dB and -70 dB, and the upper side lobe swings
between 25 dB and 68 dB. As we have pointed out, this is due to the abrupt truncation of the infinite
impulse sequence hðnÞ . The oscillations can be reduced by increasing the number of coefficients and
using a window function, which will be studied next.