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422 Chapter 8 IIR FILTER DESIGN
capk = ellipke([k.^2 1-k.^2]); % Version 4.0 code
capk1 = ellipke([(k1 .^2) 1-(k1 .^2)]); % Version 4.0 code
N = ceil(capk(1)*capk1(2)/(capk(2)*capk1(1)));
fprintf(’\n*** Elliptic Filter Order = %2.0f \n’,N)
[b,a]=u_elipap(N,Rp,As,OmegaC);
□ EXAMPLE 8.8 Design an analog elliptic lowpass filter to satisfy the following specifications of
Example 8.5:
Ω p =0.2π, R p =1dB
Ω s =0.3π, A s =16db
Solution
MATLAB script:
>> Wp = 0.2*pi; Ws = 0.3*pi; Rp = 1; As = 16;
>> Ripple = 10 ^ (-Rp/20); Attn = 10 ^ (-As/20);
>> % Analog filter design:
>> [b,a] = afd_elip(Wp,Ws,Rp,As);
*** Elliptic Filter Order = 3
>> % Calculation of second-order sections:
>> [C,B,A] = sdir2cas(b,a)
C = 0.2740
B = 1.0000 0 0.6641
A = 1.0000 0.1696 0.4102
0 1.0000 0.4435
>> % Calculation of Frequency Response:
>> [db,mag,pha,w] = freqs_m(b,a,0.5*pi);
>> % Calculation of Impulse response:
>> [ha,x,t] = impulse(b,a);
The specifications are satisfied by a 3rd-order elliptic filter whose system function
is
0.274 ( s 2 +0.6641 )
H a(s) =
(s 2 +0.1696s +0.4102) (s +0.4435)
The filter plots are shown in Figure 8.18.
□
8.3.13 PHASE RESPONSES OF PROTOTYPE FILTERS
Elliptic filters provide optimal performance in the magnitude-squared response
but have highly nonlinear phase response in the passband (which is
undesirable in many applications). Even though we decided not to worry
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