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freq

frequency response

Syntax

x = freq(A, B, C, f)
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])