Scilab Function
Last update : 07/11/2006

ell1mag - magnitude of elliptic filter

### Calling Sequence

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

### Parameters

- `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`,