Produce a PSD from Pole Zero information

[thaitam]

Hi

I am wondering how do you actually go about calculating a PSD when you know the locations of your poles and zeroes ie pzmap. I dont know if this is simple and I am not understanding something.

Thanks very much!

Thomas

 

[zorro]

Hi Thomas,

please calrify.
Are you talking about the Power Spectral Density at the output of a filter when white noise is applied to the input (ARMA process)?
regards

Z

 

[thaitam]

Z

Yes I believe this is what I am after. I basically need to produce a graph of the power spectral density and all i know is the location of the poles and zeros of the system.

Thanks

 

[zorro]

Hi Thomas,

The PSD at the output is

Syy(ω)=Sxx(ω)•|H(ω)|²

where Sxx(ω) is the PSD at the input (constant in the case it is white).

I hope this is the help you need.
Regards

Z

 

[ninju]

The pole zero info gives you H(z). Pyy=Pxx.H(z).H(1/z) . Use this to get psd. Pxx is fourier transform of the autocorrelation of the input signal. The input is usually a white noise process.

(source: statistical digital signal processing by monson hayes.)