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Two different definitions for sinc ?

  1. Dec 17, 2011 #1
    i've seen in some texts they use
    sin(pi t)/pi t = sinc(t)
    and in some they've used just
    sin(t)/t = sinc(t)
    each gives different answer
    for example
    if i want to find FT of rect(t/tow)
    using former one gives
    sinc(w tow/2 pi)
    and if i use former one i get
    sinc (w tow / 2)

    so how to know which one to use ??
    Thnx. . . .
     
  2. jcsd
  3. Dec 17, 2011 #2

    I like Serena

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    Check how the text defines the sinc.
    If it is a proper text, it should define it.

    According to wiki, your first variant is used in digital signal processing and information theory, while the second is used in mathematics.
     
  4. Dec 18, 2011 #3
    I can confirm I Like Serena's post. First is the definition of sinc function in signal processing. I think we like that because sin(pi*t)/pi*t effectively eliminates the pi from the period. And you get "nice" numbers on the x-axis.

    Although sinc isn't periodic, but sin is.
     
  5. Dec 18, 2011 #4
    but these two are not equivalent right.
    i mean first one goes to zero @ 1,2,3,4. . . .
    And second one goes to zero at pi, 2pi,3pi. . . . .
    So
    sinc function in math is different from sinc function in signal processing ??????
     
  6. Dec 18, 2011 #5

    I like Serena

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    Correct.

    This is not the only function that is ambiguous.
    Consider the log function, which can either be the natural log or the 10-log.
    Often this is not even specified, so you are supposed to deduce it from the context.
     
  7. Dec 18, 2011 #6

    AlephZero

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    It would be better to say that the sinc function in analog signal processing theory is (sometimes) different from the sinc function in digital signal processing.

    In DSP the "obvious" way to number the sampled data points is 0, 1, 2, 3, etc, not 0, π, 2π, 3π, etc.
     
  8. Dec 18, 2011 #7

    marcusl

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    It is analogous to defining the Fourier transform, which differs in signal processing and physics by details like normalization by 1, 1/2π or sqrt(1/2π).
     
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