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# freq

frequency response

### Syntax

```[x]=freq(A,B,C [,D],f)
[x]=freq(NUM,DEN,f)```

### Arguments

A, B, C, D

real matrices of respective dimensions `nxn, nxp, mxn, mxp`.

NUM,DEN

polynomial matrices of dimension `mxp`

x

real or complex matrix

### Description

`x=freq(A,B,C [,D],f)` returns a real or complex `mxp*t` matrix such that:

`x(:,k*p:(k+1)*p)= C*inv(f(k)*eye()-A)*B + D`.

Thus, for `f` taking values along the imaginary axis or on the unit circle `x` is the continuous or discrete time frequency response of `(A,B,C,D)`.

`x=freq(NUM,DEN,f)` returns a real or complex matrix `x` such that columns `k*(p-1)+1` to `k*p` of `x` contain the matrix `NUM(f(k))./DEN(f(k))`

### Examples

```s=poly(0,'s');
sys=(s+1)/(s^3-5*s+4)
rep=freq(sys("num"),sys("den"),[0,0.9,1.1,2,3,10,20])
[horner(sys,0),horner(sys,20)]
//
Sys=tf2ss(sys);
[A,B,C,D]=abcd(Sys);
freq(A,B,C,[0,0.9,1.1,2,3,10,20])```