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Problems 469
P8.35 Design a highpass filter to satisfy the specifications:
stopband edge: 0.4π, A s =60dB
passband edge: 0.6π, R p =0.5 dB
1. Use the dhpfd bl function of Problem P8.34 and the Chebyshev-I prototype to design
this filter. Plot the log-magnitude response in dB of the designed filter.
2. Use the cheby1 function for design and plot the log-magnitude response in dB. Compare
these two designs.
P8.36 Write a MATLAB function to determine the lowpass prototype digital filter frequencies
from an arbitrary lowpass 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] = lp2lpfre(wplp,wslp)
% Band-edge frequency conversion from lowpass to lowpass digital filter
% [wpLP,wsLP,a] = lp2lpfre(wplp,wslp)
% wpLP = passband egde for the lowpass prototype
% wsLP = stopband egde for the lowpass prototype
% alpha = lowpass to highpass transformation parameter
% wplp = passband egde for the given lowpass
% wslp = passband egde for the given lowpass
Using this function, develop a MATLAB function to design a lowpass filter from a
prototype lowpass digital filter using the bilinear transformation. The format of this
function should be
function [b,a] = dlpfd_bl(type,wp,ws,Rp,As)
% IIR lowpass filter design using bilinear transformation
% [b,a] = dlpfd_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 in radians
% ws = Stopband frequency in radians
% Rp = Passband ripple in dB
% As = Stopband attenuation in dB
Verify your function using the designs in Problem P8.33.
P8.37 Design a bandpass digital filter using the Cheby2 function. The specifications are:
lower stopband edge: 0.3π
upper stopband edge: 0.6π A s =50dB
lower passband edge: 0.4π
upper passband edge: 0.5π R p =0.5 dB
Plot the impulse response and the log-magnitude response in dB of the designed filter.
P8.38 Write a MATLAB function to determine the lowpass prototype digital filter frequencies
from a bandpass 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
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