Thread Subject: Power Spectral Density & Transfer Function

Hi all,

I am currently working on the spectral analysis. I would like to know whether it is a usual practice to make the unit of the power spectral density as "dB/Hz"?? I am wondering whether it is necessary to be in "dB" ????

After calculating the power spectral density , i would like to find the transfer function from it. Can i do it in the following way??

Pyy = power spectral density of output Y
Pxx = power spectral density of input X

H(transfer) = Pyy/Pxx << is it correct??

Hope someone can help me with it and point out any mistake i have made here!

Thamks

Dan <chunhoishere@yahoo.com.hk> wrote in message <31129511.1236091536284.JavaMail.jakarta@nitrogen.mathforum.org>...
> Hi all,
>
> I am currently working on the spectral analysis. I would like to know whether it is a usual practice to make the unit of the power spectral density as "dB/Hz"?? I am wondering whether it is necessary to be in "dB" ????
>
> After calculating the power spectral density , i would like to find the transfer function from it. Can i do it in the following way??
>
> Pyy = power spectral density of output Y
> Pxx = power spectral density of input X
>
> H(transfer) = Pyy/Pxx << is it correct??
>
> Hope someone can help me with it and point out any mistake i have made here!
>
> Thamks

Hi,

1. No, it is not necessary to have power spectral density (PSD) in units db/Hz. If the unit of x(t) is ux, then the unit of PSD is ux^2/Hz.
2. You may not measure "transfer function", only "frequency response" is measurable, because transfer function is a ratio of Laplace transform of output over Laplace transform of input.
3. Frequency response can be calculated as Hyx = Pyx/Pxx, Where Pxx is PSD of the signal x(t) and Pyx is cross (joint) spectral density of y(t) and x(t). See any book on signal processing.
4. Your H is, say, an amplitude characteristics (real module) of the frequency response i.e. without phase.

Hope it helps.

Mira

Hi Mira,

Thanks so much for your reply~!

Thank you for correcting me for my misunderstanding on the so-called transfer function

Actually, i have tried several ways to measure the frequency response, like using the built in "tfestimate" finction in matlab. However, i am not sure the result is correct or not. The plot in in normalized frequency, any hint for me to change it to frequency???

So, do you mean:

H = Pyy/Pxx << this is not the real frequency response?? what do you mean by amplitude characteristics(real module)??

Can you suggest me some ways to do the cross power spectral density on the input x and output y??
I have tried : "cpsd(x,y)" in matlab, however, it seems that it is not correct

Thanks,
Dan

Dan <chunhoishere@yahoo.com.hk> wrote in message <11748494.1236096638508.JavaMail.jakarta@nitrogen.mathforum.org>...
> Actually, i have tried several ways to measure the frequency response, like using the built in "tfestimate" finction in matlab. However, i am not sure the result is correct or not. The plot in in normalized frequency, any hint for me to change it to frequency???
>
> So, do you mean:
>
> H = Pyy/Pxx << this is not the real frequency response?? what do you mean by amplitude characteristics(real module)??
>
> Can you suggest me some ways to do the cross power spectral density on the input x and output y??
> I have tried : "cpsd(x,y)" in matlab, however, it seems that it is not correct
>
> Thanks,
> Dan

Hello Dan,
My answer is not complete. The reason is simple, I do not have Signal processing toolbox functions of which you tried to apply functions (tfestimate, cpsd). However, you say that there is an error in cpsd. Did you try to copy the example from the documentation and run it?

I looked on the Mathworks home page , selected Support,Browse by Product,
Signal Processing Toolbox and then in Option 2: Documentation. In Contents select Statistical Signal Processing and in it Spectral analysis. You will get good survey of it.

If you open Function Reference the in a group of functions Statistical signal processing the function cpsd is described. There is an example that you can run. If the resuilt of the run are thesame as those in documentation, you have to look for errors in your application. The similar holds for the function fpestimate. Test the example.

If the example tests don't give the same results, You would have to set up the function of welch PSD estimate you yourselves. The formulae are in the above documentation.

It is all what I can tell you now.

Best regards.

Mira