Sampling and spectrum replication

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Discussion Overview

The discussion centers on the phenomenon of frequency spectrum replication in sampled signals, particularly in the context of signals that have been low-pass filtered and sampled above the Nyquist rate. Participants explore the underlying reasons for this replication and seek clarification on the implications of sampling in the frequency domain.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question why the frequency spectrum of a sampled signal is replicated, particularly when the signal is low-pass filtered and sampled above the Nyquist rate.
  • One participant suggests that the replication occurs because each waveform is assumed to be identical, leading to a low-frequency version of the waveform being constructed from successive samples.
  • A participant requests clarification on the frequency at which the signal was sampled and suggests that the source of the signal may also be sampled at the same frequency, potentially causing similar results.
  • Another participant rephrases the question to focus on why sampling produces multiple spectra at intervals of 1/T, where T is the sampling rate, and references the Fourier Transform of an impulse train as a possible explanation for the observed spectra at -fs and +fs.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the reasons for spectrum replication, and multiple competing views remain on the topic. The discussion does not reach a consensus on the underlying mechanisms.

Contextual Notes

Limitations include assumptions about the uniformity of waveforms and the dependence on the definitions of sampling and frequency representation. The discussion does not resolve the mathematical implications of the Fourier Transform in this context.

likephysics
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Why is the frequency spectrum of a sampled signal replicated?
We have a Low pass filtered signal sampled well above nyquist rate. I can't understand why the spectrum is replicated.
 
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I haven't done this, but I understand they assume that each waveform is the same as the next one and so they take one sample off successive waves but progressing across the wave in each case.
So, if they look at the incoming waves and look a little later at each wave, they build up a low frequency version of the waveform that follows the shape of the waveform reasonably well.

This is how sampling oscilloscopes work.
 
likephysics said:
Why is the frequency spectrum of a sampled signal replicated?
We have a Low pass filtered signal sampled well above nyquist rate. I can't understand why the spectrum is replicated.


can you explain at which frequency you got this well sampled signal, and what is your source may be it si also sampled as the same frequency that is why you get the same result.
 
mustafa, let me rephrase -
Why does sampling produce multiple spectrum at 1/T, where T is the sampling rate.
If you look at the sampled data spectrum is should look like this -
http://en.wikipedia.org/wiki/File:ReconstructFilter.png
Why are there spectrum at -fs and +fs?
I think this is bcoz the FT of an impulse train is also an impulse train spaced 1/T apart in the Freq domain.
 

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