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RE: [DSPEngineering] gaussian data

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  • Moshe Malkin
    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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    • Raja V Tamma
      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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      • satya ghosh
        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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