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spectrum of rectangular pulse

Discussion in 'Electronic Basics' started by thejim, Feb 25, 2006.

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  1. thejim

    thejim Guest

    What do we mean by saying that the spectrum of rectangular pulse is
    sinc(x) function?
  2. Figaro

    Figaro Guest

  3. It isn't, always. It depends on how it is distributed over 0. For a
    balanced rectangle:


    : | :
    : | :
    : | :
    : | :
    <-------------------+--------------------> x
    -t | +t

    I think the transform is 2*a*t*sinc(2*PI*f*t).

    If you shift the rectangle to be asymmetric around x=0, then the
    transform will be different.

  4. Hi,
    Sinc(x) is Sin(x)/x.

    So compare the shape of this function with the envelope of the
    components in the spectrum of a narrow rectangular pulse and all
    should be clear.

    Cheers - Joe
  5. In case you are just wondering what the whole idea is, at all...

    A Fourier transform can be just a frequency domain representation of a
    time domain function. Time and frequency are... kin and conjugate to
    each other.

    The spectral width in one domain times the spectral width in the other
    domain will be greater than a finite constant (1, usually), which
    implies that something narrow in terms of time information will be
    wide in terms of frequency information and the converse. The
    transform of the rectangle, 2*a*t*sinc(2*PI*f*t), exhibits this
    spectral area product in the "f*t" unitless term inside the sinc()
    function. Narrowing 't' spreads out the result over broader 'f'.

  6. redbelly

    redbelly Guest

    That would change the relative phases of the frequency components, but
    their amplitudes would still be a sinc function.

  7. Bob Masta

    Bob Masta Guest

    To add to all the other replies, if you want to get a
    "hands-on" feel for this, check out my DaqGen
    freeware signal generator. You can set up any
    sort of rectangular pulse you want (or just about
    any other sort of waveform) and toggle between
    waveform and spectrum views. (DaqGen uses
    your sound card, so you can listen to the signal
    as well... but I'd guess it might be really annoying
    in this case!)

    Best regards,

    Bob Masta

    D A Q A R T A
    Data AcQuisition And Real-Time Analysis
    Home of DaqGen, the FREEWARE signal generator
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