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Window Design Techniques 333
To display the frequency-domain plots of digital filters, MATLAB
provides the freqz function, which we used in earlier chapters. Using this
function, we have developed a modified version, called freqz m, which
returns the magnitude response in absolute as well as in relative dB scale,
the phase response, and the group delay response. We will need the group
delay response in the next chapter.
function [db,mag,pha,grd,w] = freqz_m(b,a);
% Modified version of freqz subroutine
% ------------------------------------
% [db,mag,pha,grd,w] = freqz_m(b,a);
% db = Relative magnitude in dB computed over 0 to pi radians
% mag = absolute magnitude computed over 0 to pi radians
% pha = Phase response in radians over 0 to pi radians
% grd = Group delay over 0 to pi radians
% w = 501 frequency samples between 0 to pi radians
% b = numerator polynomial of H(z) (for FIR: b=h)
% a = denominator polynomial of H(z) (for FIR: a=[1])
%
[H,w] = freqz(b,a,1000,’whole’);
H = (H(1:1:501))’; w = (w(1:1:501))’;
mag = abs(H); db = 20*log10((mag+eps)/max(mag));
pha = angle(H); grd = grpdelay(b,a,w);
7.3.8 DESIGN EXAMPLES
We now provide several examples of FIR filter design using window techniques
and MATLAB functions.
□ EXAMPLE 7.8 Design a digital FIR lowpass filter with the following specifications:
ω p =0.2π,
ω s =0.3π,
R p =0.25 dB
A s =50dB
Choose an appropriate window function from Table 7.1. Determine the impulse
response and provide a plot of the frequency response of the designed filter.
Solution
Both the Hamming and Blackman windows can provide attenuation of more
than 50 dB. Let us choose the Hamming window, which provides the smaller
transition band and hence has the smaller order. Although we do not use the
passband ripple value of R p =0.25 dB in the design, we will have to check
the actual ripple from the design and verify that it is indeed within the given
tolerance. The design steps are given in the following MATLAB script.
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