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Problems 471
Using this function, develop a MATLAB function to design a bandstop filter from a
prototype lowpass digital filter using the bilinear transformation. The format of this
function should be
function [b,a] = dbsfd_bl(type,wp,ws,Rp,As)
% IIR bandstop filter design using bilinear transformation
% [b,a] = dbsfd_bl(type,wp,ws,Rp,As)
% type = ’butter’ or ’cheby1’ or ’chevy2’ or ’ellip’
% b = Numerator polynomial of the bandstop filter
% a = Denominator polynomial of the bandstop 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 P8.39.
P8.41 An analog signal
is to be processed by a
x a(t) =3sin(40πt)+3cos(50πt)
x a(t) −→ A/D −→ H(z) −→ D/A −→ y a(t)
system in which the sampling frequency is 100 sam/sec
1. Design a minimum order IIR digital filter that will pass the first component of x a(t)
with attenuation of less than 1 dB and suppress the second component to at least 50 dB.
The filter should have a monotone passband and an equiripple stopband. Determine the
system function in rational function form and plot the log-magnitude response.
2. Generate 500 samples (sampled at 100 sam/sec) of the signal x a(t) and process through
the designed filter to obtain the output sequence. Interpolate this sequence (using any
one of the interpolating techniques discussed in Chapter 3) to obtain y a(t). Plot the
input and the output signals and comment on your results.
P8.42 Using the bilinear transformation method, design a 10th-order elliptic bandstop filter to
remove the digital frequency ω =0.44π with bandwidth of 0.08π. Choose a reasonable value
for the stopband attenuation. Plot the magnitude response. Generate 201 samples of the
sequence
x(n) =sin [0.44πn] , n =0,...,200
and process thorough the bandstop filter. Comment on your results.
P8.43 Design a digital highpass filter H(z) tobeused in a
x a(t) −→ A/D −→ H(z) −→ D/A −→ y a(t)
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