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Problems 465
function [b,a] =afd(type,Fp,Fs,Rp,As)
%
% function [b,a] =afd(type,Fp,Fs,Rp,As)
% Designs analog lowpass filters
% type = ’butter’ or ’cheby1’ or ’cheby2’ or ’ellip’
% Fp = passband cutoff in Hz
% Fs = stopband cutoff in Hz
% Rp = passband ripple in dB
% As = stopband attenuation in dB
Use the afd butt, afd chb1, afd chb2, and afd elip functions developed in this chapter.
Check your function using specifications given in Problems P8.12 through P8.17.
P8.21 We want to design a Chebyshev-I prototype lowpass digital filter operating at a sampling
rate of 8 kHz with a passband edge of 3.2 kHz, a passband ripple of 0.5 dB, and a minimum
stopband attenuation of 45 dB at 3.8 kHz.
1. Using the impulse invariance transformation with T =1sec, design the digital filter. Plot
the magnitude and the log-magnitude responses as functions of analog frequency in kHz.
2. Repeat part 1 using T =1/8000 sec.
3. Compare the above two designs in parts 1 and 2 in terms of their frequency responses.
Comment on the effect of T on the impulse invariance design.
P8.22 Design a Butterworth digital lowpass filter to satisfy the specifications:
passband edge: 0.4π, R p =0.5 dB
stopband edge: 0.6π, As =50dB
Use the impulse invariance method with T =2.Determine the system function in the
rational form, and plot the log-magnitude response in dB. Plot the impulse response h(n)
and the impulse response h a(t) ofthe analog prototype and compare their shapes.
P8.23 Write a MATLAB function to design digital lowpass filters based on the impulse invariance
transformation. The format of this function should be
function [b,a] =dlpfd_ii(type,wp,ws,Rp,As,T)
%
% function [b,a] =dlpfd_ii(type,wp,ws,Rp,As,T)
% Designs digital lowpass filters using impulse invariance
% type = ’butter’ or ’cheby1’
% wp = passband cutoff in Hz
% ws = stopband cutoff in Hz
% Rp = passband ripple in dB
% As = stopband attenuation in dB
% T = sampling interval
Use the afd function developed in Problem P8.20. Check your function on specifications
given in Problems P8.21 and P8.22.
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