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Continuous and discrete spectra

  1. Oct 27, 2016 #1
    Is there any way to convert a continuous, aperiodic spectrum, to a discrete spectrum, in a signal? If so, would part of he energy of this signal be lost, im this process of conversion, or would it be " distributed" amomg the various frequencies?
     
  2. jcsd
  3. Oct 27, 2016 #2

    BvU

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    Not sure I fully understand your question. Sampling the spectrum is equivalent to multiplying it with a Dirac Comb function and then the signal you get from transforming back to the time domain would be a convolution of the original signal and the FT of the comb function. If the original signal is only present for a limited time 0 - T , this would allow lossless reconstruction when the frequency samples are less than 1/(2T) apart
     
  4. Oct 27, 2016 #3
    Yes. Thanks..It s exactly what I was asking for. No losses than? Of any kind?
     
  5. Oct 27, 2016 #4

    BvU

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    No losses. It is the equivalent of Shannon's theorem but now from the frequncy domain to the time domain instead of the other way around.
     
  6. Oct 27, 2016 #5

    sophiecentaur

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    This is the equivalent of the Nyquist criterion for temporal sampling. I'm trying to get my head around how to specify the equivalent to a practical Nyquist LP filter in this process.
     
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