[SI-LIST] Re: power spectral density of random signal with finite rise/fall time
- From: Luca Giacotto <lgiacott@xxxxxxxxx>
- To: SI-List <si-list@xxxxxxxxxxxxx>
- Date: Thu, 31 Jan 2002 01:45:11 +0100
Jan,
it is a while that my book about signal theory is closed, but I would
think that the shape of your pulses enters linearly, and as a
deterministic component of the signal. As such I think you may just
multiply your PSD by the power spectrum of the filter that degrades your
ideal signal to the real one.
Or, in time domain, convolute the two respective autocorrelation
functions.
Equivalently, you may directly multiply your pulse-shape power spectrum
bye the PSD of the aleatory dirac's train.
Hope this is helpful.
Luca
On Wed, 30 Jan 2002 14:44:41 +0100
"Jan Vercammen" <jan.vercammen.jv1@xxxxxxxxxxxxxxxx> wrote:
>
> hello si-list (communication engineers),
>
>
> I was wondering if someone knows a reference (article, paper, book, ...)
> where the power spectral density
> of a random digital signal with finite rise-fall time is described. It is
> easy to find information on ideal random
> digital signals. Here ideal means "with ideal steps" or unit-steps.
>
> The ideal case is easy to calculate using the Wiener-Khichine theorem which
> states that the autocorrrelation
> function and the power spectral density form a fourier transform pair.
> Ideal digital pulses have a triangular
> autocorrelation function, but I was wondering what it would be if the
> pulses have a finite rise-fall time. The
> autocorrelation function would be "triangular-like", but is it possible (1)
> to describe it analytically and, if so,
> (2) is it possible to calculate it's fourrier transform?
>
>
> thank you,
>
> Jan Vercammen
> EMC/PCB engineer
> Agfa-Gevaert NV, Belgium
>
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--
Luca Giacotto <lgiacott@xxxxxxxxx>
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