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Why is that 'The higher the sidelobes, the greater the "cross-talk" between channels' when transmitting signals via hardware electronics?

where,

  • Cross-talk: a signal transmitted on one circuit or channel of a transmission system creates an undesired effect and/or interference in another circuit or channel.
  • Sidelobes: The sidelobes (spectral leakage) introduced to signal frequency spectrum after application of window functions to the transmission signal.
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Convolution theorem states convolution in time domain is the same as multiplication in Fourier domain, also the multiplication in time domain is a convolution in Fourier domain.

So when you truncate a signal (multiply it by a window), your signal's spectrum will be convoluted with the window's spectrum which widen your signal's spectrum depending on the main lobe width and also replicate signal spectrum depending on the side lobe height which is called frequency leak. if you consider different channels over different bandwidth, when you truncate the signal the frequency leak will cause channel cross-talk.

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  • $\begingroup$ Thanks for your reply, Does this confirm that cross-talk can be frequency dependent? $\endgroup$
    – S Fateri
    Aug 31, 2017 at 7:42
  • $\begingroup$ what do you mean by "frequency dependent"? $\endgroup$
    – Mohammad M
    Sep 1, 2017 at 14:30
  • $\begingroup$ That cross talk changes at each operating frequency. $\endgroup$
    – S Fateri
    Sep 4, 2017 at 7:59

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