Z-transform of time domain data

Hi!

I have a vector x which consist of an impulse response to an unknown system, and a transfer function A in terms of its coefficients. What I now want to do is to calculate IDFT(X(z)/A(z)), ie. evaluate the transfer function X(z)/A(z) at some discrete points z.

I have already looked at FREQZ and FILTER, but those functions assume that the coefficients of the transfer functions are known. INVFREQS is maybe a possible solution to get X(z) but the problem is that my impulse response x is in time domain.

Any help appreciated.

Answer 1

[Wayne King]

If you have a finite-length vector which is the impulse response of a discrete time system, then you have an FIR filter. The values of the impulse response vector are the coefficients of the finite-order polynomial in z^{-1} that is the z-transform, so you can just do

   freqz(B,1)

where B is your impulse response vector.

For example, assume you have a simple 10-point moving average FIR filter where the impulse response is

   1/10*ones(10,1)

but

    B = 1/10*ones(10,1);
    impz(B,1)

It's trivial. Unless you really don't have the impulse response (or you have a truncated impulse response, which is really IIR)

Answer 2

[Rajiv Singh]

Try this:

 data =  iddata(x,[],Ts) % ts:= sampling time
 Filter = armax(data, [na nc]) % na, nc are filter design parameters

 Value = evalfr(Filter, z) % evaluate response at complex number z

 Values = freqresp(Filter, w) % evaluate frequency response at frequencies w