freq

frequency response

Calling Sequence

[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])

See Also

• repfreq frequency response
• horner polynomial/rational evaluation