ell1mag

magnitude of elliptic filter

Calling Sequence

[v]=ell1mag(eps,m1,z)

Arguments

:eps passband ripple= 1/(1+eps^2) : :m1 stopband ripple= 1/(1+(eps^2)/m1) : :z sample vector of values in the complex plane : :v elliptic filter values at sample points :

Description

Function used for squared magnitude of an elliptic filter. Usually m1=eps*eps/(a*a-1). Returns v=real(ones(z)./(ones(z)+eps*eps*s.*s)) for s=%sn(z,m1).

Examples

`deff`_('[alpha,BeTa]=alpha_beta(n,m,m1)',...
'if 2*int(n/2)==n then, BeTa=K1; else, BeTa=0;end;...
alpha=%k(1-m1)/%k(1-m);')
epsilon=0.1;A=10;  //ripple parameters
m1=(epsilon*epsilon)/(A*A-1);n=5;omegac=6;
m=`find_freq`_(epsilon,A,n);omegar = omegac/`sqrt`_(m)
`%k`_(1-m1)*`%k`_(m)/(`%k`_(m1)*`%k`_(1-m))-n   //Check...
[alpha,Beta]=alpha_beta(n,m,m1)
alpha*`%asn`_(1,m)-n*`%k`_(m1)      //Check
`sample`_=0:0.01:20;
//Now we map the positive real axis into the contour...
z=alpha*`%asn`_(`sample`_/omegac,m)+Beta*`ones`_(`sample`_);
`plot`_(`sample`_,ell1mag(epsilon,m1,z))

See Also

• buttmag Power transmission of a Butterworth filter