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**Technical discussion about Matlab and issues related to Digital Signal Processing.**

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first of all I would like to apologize if what I'm asking is terribly

obvious or if what I'm saying is completely wrong. I'm quite new at

discrete signal processing!

Probably it will sound quite strange to most of you since it isn't

something which usually occurs in practical situations, but I need to

get samples of a random signal whose PSD (well, I'd better say

periodogram) is given. It should be possible, isn't it? Moreover the

distribution of the recovered samples values should be normal

(gaussian), is it possible to add such a condition while recovering

the samples? How?

Of course direct suggestions are the most welcome but I will

appreciate also references suggestions provided they are

comprehensible to a novice!! :-)

Thank you,

Tony

If you send a random signal (with Psd Sx) through a LTI block with transfer

function H(f) then what comes out has a PSD Sy given by

Sy = Sx * | H(f) | ^2 This is a "well known" fact that you can find in most

books on random processes (e.g. Papoulis, Leon Garcia etc).

So take lots of samples that are iid Gaussian. Then its PSD = Fourier

Transform of Autocorrelation of iid Gaussian = Fourier Transform of delta

function = uniform over all frequencies.

Now take these samples and filter them through a filter whose frequency

response is the sqrt of the PSD you want. Then your output samples will have

the PSD you want.

Be careful of initial conditions in this filter. Throw away the first few

samples where the filter hasn't been filled with the input samples.

On 11/16/05, tony_beppe@tony... <tony_beppe@tony...> wrote:

>

> Hello everybody,

>

> first of all I would like to apologize if what I'm asking is terribly

> obvious or if what I'm saying is completely wrong. I'm quite new at

> discrete signal processing!

>

> Probably it will sound quite strange to most of you since it isn't

> something which usually occurs in practical situations, but I need to

> get samples of a random signal whose PSD (well, I'd better say

> periodogram) is given. It should be possible, isn't it? Moreover the

> distribution of the recovered samples values should be normal

> (gaussian), is it possible to add such a condition while recovering

> the samples? How?

>

> Of course direct suggestions are the most welcome but I will

> appreciate also references suggestions provided they are

> comprehensible to a novice!! :-)

>

> Thank you,

>

> Tony