- 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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[Non-text portions of this message have been removed] - 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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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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