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Short Time Fourier Transform - invertible?

  1. Mar 9, 2010 #1
    Short Time Fourier Transform -- invertible?

    On Wikipedia,
    http://en.wikipedia.org/wiki/Short-time_Fourier_transform" [Broken]

    However, it's also said



    That is to say, Gabor is invertible, it's able to obtain the original signal, but modulated.

    original signal is obviously x(t),
    w(t-τ) is the window function used to extract a local signal within this window,
    which can also be looked on as a kind of modulation.

    Therefore, in the above function (attached picture),
    x(t)w(t-τ) can be computed, from the Gabor transformed data,
    But, I'm dropping questions to ask, whether the true original data x(t) can be finally recovered?
    as it's declared by Wiki itself

    Can anybody help to make me clarified?


    Best Regards
    JIA Pei
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 10, 2010 #2
    Re: Short Time Fourier Transform -- invertible?

    I'll answer your question by asking you another question.

    Let's say I have a time-varying signal. I multiply it by a gaussian then send it to you. Will you be able to recover the original signal?
     
  4. Mar 10, 2010 #3
    Re: Short Time Fourier Transform -- invertible?

    Sorry for my stupidity.

    Your word "multiply" hints me. !!

    This is a "element-wise" multiplication!! Right??? Yes, it should be.

    Thanks for your answering to clarify my doubts.

    Best Regards
    JIA Pei


     
  5. Mar 15, 2010 #4
    Re: Short Time Fourier Transform -- invertible?

    Yes, it's element-wise.
     
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