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Lowpass Filter Design Using MATLAB 447
The system function is
H(z) = 0.1797 ( 1+0.5574z −1 + z −2)( 1 − 1.0671z −1 + z −2)
(1 − 0.4183z −1 +0.1503z −2 )(1− 1.1325z −1 +0.7183z −2 )
which is the same as in Example 8.19. The frequency-domain plots were shown
in Figure 8.28.
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□ EXAMPLE 8.24 Digital elliptic lowpass filter design:
>> % Digital Filter Specifications:
>> wp = 0.2*pi; %digital Passband freq in rad
>> ws = 0.3*pi; %digital Stopband freq in rad
>> Rp = 1; %Passband ripple in dB
>> As = 15; %Stopband attenuation in dB
>> % Analog Prototype Specifications:
>> T = 1; %Set T=1
>> OmegaP = (2/T)*tan(wp/2); %Prewarp Prototype Passband freq
>> OmegaS = (2/T)*tan(ws/2); %Prewarp Prototype Stopband freq
>> % Analog Elliptic Filter order calculations:
>> ep = sqrt(10^(Rp/10)-1); %Passband Ripple Factor
>> A = 10^(As/20); %Stopband Attenuation Factor
>> OmegaC = OmegaP; %Analog Prototype Cutoff freq
>> k = OmegaP/OmegaS; %Analog Prototype Transition Ratio;
>> k1 = ep/sqrt(A*A-1); %Analog Prototype Intermediate cal.
>> capk = ellipke([k.^2 1-k.^2]);
>> capk1 = ellipke([(k1 .^2) 1-(k1 .^2)]);
>> N = ceil(capk(1)*capk1(2)/(capk(2)*capk1(1)));
>> fprintf(’\n*** Elliptic Filter Order = %2.0f \n’,N)
*** Elliptic Filter Order = 3
>> % Digital Elliptic Filter Design:
>> wn = wp/pi; %Digital Passband freq in pi units
>> [b,a]=ellip(N,Rp,As,wn); [b0,B,A] = dir2cas(b,a)
b0 = 0.1214
B = 1.0000 -1.4211 1.0000
1.0000 1.0000 0
A = 1.0000 -1.4928 0.8612
1.0000 -0.6183 0
The system function is
H(z) = 0.1214 ( 1 − 1.4211z −1 + z −2)( 1+z −1)
(1 − 1.4928z −1 +0.8612z −2 )(1− 0.6183z −1 )
which is the same as in Example 8.20. The frequency-domain plots were shown
in Figure 8.29.
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