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Math Help - Delta Function Integration

  1. #1
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    Delta Function Integration

    Working on Fourier Series and Transforms and have come across an integral that I can't seem to evaluate, I understand that integrating the delta function simply gives you 1 but don't seem to have any real joy with that.

    the integral is between minus infinity and plus infinity and is this,

    {[sin(omega(t-tau))]/pi(tau-KTs)}delta(tau-KTs) dtau

    apologies for the terrible way I have written this out, but I don't know how to use symbols or if you can on this

    also don't know if this helps but

    omega is wavelength, K is a constant from part of a sum and takes values from - infinity to +infinity

    Ts is a constant

    and the integral came from trying to convolve the bit in the curly brackets with the delta func.

    I tried converting sine into exponential form but so far no luck.

    If anyone can decipher what I've written above and can help I'd appreciate it,

    thanks
    Rich
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by rnadams View Post
    Working on Fourier Series and Transforms and have come across an integral that I can't seem to evaluate, I understand that integrating the delta function simply gives you 1 but don't seem to have any real joy with that.

    the integral is between minus infinity and plus infinity and is this,

    {[sin(omega(t-tau))]/pi(tau-KTs)}delta(tau-KTs) dtau

    apologies for the terrible way I have written this out, but I don't know how to use symbols or if you can on this

    also don't know if this helps but

    omega is wavelength, K is a constant from part of a sum and takes values from - infinity to +infinity

    Ts is a constant

    and the integral came from trying to convolve the bit in the curly brackets with the delta func.

    I tried converting sine into exponential form but so far no luck.

    If anyone can decipher what I've written above and can help I'd appreciate it,

    thanks
    Rich
    To make things easier I have attempted to translate this to LaTeX:
    \int_{-\infty}^{\infty} \frac{sin( \omega (t - \tau))}{\pi (\tau - KT_s)}~\delta ( \tau - KT_s)~d \tau

    Please correct me if I'm wrong.

    -Dan
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  3. #3
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    yea, thats correct
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  4. #4
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    Quote Originally Posted by topsquark View Post
    To make things easier I have attempted to translate this to LaTeX:
    \int_{-\infty}^{\infty} \frac{sin( \omega (t - \tau))}{\pi (\tau - KT_s)}~\delta ( \tau - KT_s)~d \tau

    Please correct me if I'm wrong.

    -Dan
    Use the sifting property: Sifting Property -- from Wolfram MathWorld
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