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470 Chapter 8 IIR FILTER DESIGN
function [wpLP,wsLP,alpha] = bp2lpfre(wpbp,wsblp)
% Band-edge frequency conversion from bandpass to lowpass digital filter
% [wpLP,wsLP,a] = bp2lpfre(wpbp,wsbp)
% wpLP = passband egde for the lowpass prototype
% wsLP = stopband egde for the lowpass prototype
% alpha = lowpass to highpass transformation parameter
% wpbp = passband egde frequency array [wp_lower, wp_upper] for the bandpass
% wsbp = passband egde frequency array [ws_lower, ws_upper] for the bandpass
Using this function, develop a MATLAB function to design a bandpass filter from a
prototype lowpass digital filter using the bilinear transformation. The format of this
function should be
function [b,a] = dbpfd_bl(type,wp,ws,Rp,As)
% IIR bandpass filter design using bilinear transformation
% [b,a] = dbpfd_bl(type,wp,ws,Rp,As)
% type = ’butter’ or ’cheby1’ or ’chevy2’ or ’ellip’
% b = Numerator polynomial of the bandpass filter
% a = Denominator polynomial of the bandpass filter
% wp = Passband frequency array [wp_lower, wp_upper] in radians
% ws = Stopband frequency array [wp_lower, wp_upper] in radians
% Rp = Passband ripple in dB
% As = Stopband attenuation in dB
Verify your function using the design in Problem P8.37.
P8.39 We wish to use the Chebyshev-I prototype to design a bandstop digital IIR filter that meets
the following specifications:
0.95 ≤|H(e jω )|≤1.05, 0 ≤|ω| ≤0.25π
0 ≤|H(e jω )|≤0.01, 0.35π ≤|ω| ≤0.65π
0.95 ≤|H(e jω )|≤1.05, 0.75π ≤|ω| ≤π
Use the cheby1 function and determine the system function H(z) ofsuch a filter. Provide a
plot containing subplots of the log-magnitude response in dB and the impulse response.
P8.40 Write a MATLAB function to determine the lowpass prototype digital filter frequencies
from a bandstop digital filter specifications using the functions given in Table 8.2 and the
procedure outlined for highpass filters. The format of this function should be
function [wpLP,wsLP,alpha] = bs2lpfre(wpbp,wsblp)
% Band-edge frequency conversion from bandstop to lowpass digital filter
% [wpLP,wsLP,a] = bs2lpfre(wpbp,wsbp)
% wpLP = passband egde for the lowpass prototype
% wsLP = stopband egde for the lowpass prototype
% alpha = lowpass to highpass transformation parameter
% wpbp = passband egde frequency array [wp_lower, wp_upper] for the bandstop
% wsbp = passband egde frequency array [ws_lower, ws_upper] for the bandstop
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