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Message from discussion stochastic signal transform in time domain
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NZTideMan  
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 More options Oct 28 2009, 4:05 pm
Newsgroups: comp.soft-sys.matlab
From: NZTideMan <mul...@gmail.com>
Date: Wed, 28 Oct 2009 13:05:43 -0700 (PDT)
Local: Wed, Oct 28 2009 4:05 pm
Subject: Re: stochastic signal transform in time domain
On Oct 28, 11:25 pm, "Aymen " <aymenkoo...@gmail.com> wrote:

> Hi everybody,

> i'm having the following problem :

> i want to transform a stochastic signal (a PSD : two column vector, first one for frequency values, second for amplitude values) from Frequency domain to time domain using the "ifft", but i have no idea how to get the initial phases of the signal to do that. In fact the transformation in time domain has not a unique solution, it depends on initial conditions, is it right ?
> any idea how could i encounter this problem ?

> thanks

Since its stochastic, you can just use random phases.
The 2nd order statistical properties (standard deviation and variance)
will be preserved, no matter what the phases are.

But before hitting it with ifft, you need to compose a vector of
complex numbers.
The composition of this vector depends upon what you have already.
Does the frequency go from zero to the Nyquist, then negative?
Or are all the frequencies positive?
And is the first frequency zero?

Basically, if Y is a column vector of complex numbers prepared from
the amplitudes with the first frequency being greater than zero, then
your vector for ifft should look like this:
Y1=[0;Y;flipud(conj(Y))];
If there is a zero frequency, it will look like this:
Y1=[Y;flipud(conj(Y(2:end)))];


 
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