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468 Chapter 8 IIR FILTER DESIGN
P8.32 Design a digital lowpass filter using elliptic prototype to satisfy the requirements:
passband edge: 0.3π, R p =0.25 dB
stopband edge: 0.4π, As =50dB
Use the bilinear as well as the ellip function and compare your designs.
P8.33 Design a digital lowpass filter to satisfy the specifications:
passband edge: 0.45π, R p =0.5 dB
stopband edge: 0.5π,
As =60dB
1. Use the butter function and determine the order N and the actual minimum stopband
attenuation in dB.
2. Use the cheby1 function and determine the order N and the actual minimum stopband
attenuation in dB.
3. Use the cheby2 function and determine the order N and the actual minimum stopband
attenuation in dB.
4. Use the ellip function and determine the order N and the actual minimum stopband
attenuation in dB.
5. Compare the orders, the actual minimum stopband attenuations, and the group delays
in each of the above designs.
P8.34 Write a MATLAB function to determine the lowpass prototype digital filter frequencies
from an highpass digital filter specifications using the procedure outlined in this chapter.
The format of this function should be
function [wpLP,wsLP,alpha] = hp2lpfre(wphp,wshp)
% Band-edge frequency conversion from highpass to lowpass digital filter
% [wpLP,wsLP,a] = hp2lpfre(wphp,wshp)
% wpLP = passband egde for the lowpass prototype
% wsLP = stopband egde for the lowpass prototype
% alpha = lowpass to highpass transformation parameter
% wphp = passband egde for the highpass
% wshp = stopband egde for the highpass
Using this function develop a MATLAB function to design a highpass digital filter using the
bilinear transformation. The format of this function should be
function [b,a] = dhpfd_bl(type,wp,ws,Rp,As)
% IIR Highpass filter design using bilinear transformation
% [b,a] = dhpfd_bl(type,wp,ws,Rp,As)
% type = ’butter’ or ’cheby1’ or ’chevy2’ or ’ellip’
% b = Numerator polynomial of the highpass filter
% a = Denominator polynomial of the highpass filter
% wp = Passband frequency in radians
% ws = Stopband frequency in radians (wp < ws)
% Rp = Passband ripple in dB
% As = Stopband attenuation in dB
Verify your function using the specifications in Example 8.27.
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