## RE: [DSPEngineering] gaussian data

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• Well, the dft is a linear transformation and it is known that a linear transformation of gaussians results gaussians as well. see probability and random
Message 1 of 4 , Nov 27, 2002
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Well, the dft is a linear transformation and it is known that a linear
transformation of gaussians results gaussians as well.
see "probability and random processes for electrical engineers" by
Leon-Garcia
-----Original Message-----
From: statis2003 [mailto:wz_2002@...]
Sent: Tuesday, November 26, 2002 7:39 PM
To: dspengineering@yahoogroups.com
Subject: [DSPEngineering] gaussian data

hello, all , I am now a student, and want to ask for a question
for a gaussian serie such as x[n], the mean is 0 and the varianace
is delta,
and how about the DFT of the x[n], is it still the gaussian?
thanks

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• For a linear system (a DFT is a linear operation), a Gaussian input produces a Gaussian output. Hence, the DFT of x[n] must be Gaussian with a certain mean and
Message 2 of 4 , Nov 28, 2002
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For a linear system (a DFT is a linear operation), a Gaussian input produces a
Gaussian output. Hence, the DFT of x[n] must be Gaussian with a certain mean
and variance.

--- statis2003 <wz_2002@...> wrote:
> hello, all , I am now a student, and want to ask for a question
> for a gaussian serie such as x[n], the mean is 0 and the varianace
> is delta,
> and how about the DFT of the x[n], is it still the gaussian?
> thanks
>
>
>

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• Hai, Fourier transform of any gaussian rv(Random Variable) is gaussain...And any linear operation on Gaussian rv is also gaussain....So Dft of Gaussain rv will
Message 3 of 4 , Nov 28, 2002
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Hai,
Fourier transform of any gaussian rv(Random Variable)
is gaussain...And any linear operation on Gaussian rv
is also gaussain....So Dft of Gaussain rv will
have Gaussian distribution b'coz DFT is nothing but
linear opeartion.

Regards,
Satya

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