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Problems 467
function [b,a] = mzt(c,d,T)
% Matched-Z Transformation from Analog to Digital Filter
% [b,a] = MZT(c,d,T)
% b = Numerator polynomial in z^(-1) of the digital filter
% a = Denominator polynomial in z^(-1) of the digital filter
% c = Numerator polynomial in s of the analog filter
% d = Denominator polynomial in s of the analog filter
% T = Sampling interval (transformation parameter)
Using this function, transform
H a(s) =
s +1
s 2 +5s +6
into a digital filter H(z) for the sampling intervals (in seconds): T =0.05, T =0.1, and
T =0.2. In each case obtain a plot similar to that in Figure 8.20 and comment on the
performance of this technique.
P8.27 Consider an analog Butterworth lowpass filter that has a 1 dB or better ripple at 100 Hz
and at least 30 dB of attenuation at 150 Hz. Transform this filter into a digital filter using
the matched-z transformation technique in which F s = 1000 Hz. Plot the magnitude and
phase response of the resulting digital filter and determine the exact band-edge frequencies
for the given dB specifications. Comment on the results.
P8.28 Consider an analog Chebyshev-I lowpass filter that has a 0.5 dBorbetter ripple at 500 Hz
and at least 40 dB of attenuation at 700 Hz. Transform this filter into a digital filter using
the matched-z transformation technique in which F s = 2000 Hz. Plot the magnitude and
phase response of the resulting digital filter and determine the exact band-edge frequencies
for the given dB specifications. Comment on the results.
P8.29 Consider an analog Chebyshev-II lowpass filter that has a 0.25 dB or better ripple at
1500 Hz and at least 80 dB of attenuation at 2000 Hz. Transform this filter into a digital
filter using the matched-z transformation technique in which F s = 8000 Hz. Plot the
magnitude and phase response of the resulting digital filter, and determine the exact
band-edge frequencies for the given dB specifications. Comment on the results. Is this a
satisfactory design?
P8.30 Consider the design of the lowpass Butterworth filter of Problem P8.22.
1. Use the bilinear transformation technique outlined in this chapter and the bilinear
function. Plot the log-magnitude response in dB. Compare the impulse responses of the
analog prototype and the digital filter.
2. Use the butter function and compare this design with the one in part 1.
P8.31 Consider the design of the digital Chebyshev-1 filter of Problem P8.21.
1. Use the bilinear transformation technique outlined in this chapter and the bilinear
function. Plot the log-magnitude response in dB. Compare the impulse responses of the
analog prototype and the digital filter.
2. Use the cheby1 function and compare this design with the one above.
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