Sampling and spectrum replication

In summary, the conversation discusses the replication of frequency spectrum in a sampled signal. The speaker mentions a low pass filtered signal being sampled well above the Nyquist rate, resulting in a low frequency version of the waveform. This is how sampling oscilloscopes work. The question is then raised about the multiple spectra at 1/T, with a suggestion that it is due to the FT of an impulse train.
  • #1
likephysics
636
2
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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  • #2
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.
 
  • #3
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.
 
  • #4
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.
 

Related to Sampling and spectrum replication

1. What is sampling in the context of spectrum replication?

Sampling refers to the process of converting an analog signal into a digital one by measuring and recording its amplitude at regular intervals.

2. Why is sampling necessary for spectrum replication?

Sampling is necessary because it allows for the discrete representation of an analog signal, which is required for digital processing and replication of the spectrum.

3. What is the relationship between sampling rate and spectrum replication?

The sampling rate, or the number of samples taken per second, directly affects the accuracy of spectrum replication. A higher sampling rate results in a more accurate representation of the original signal's spectrum.

4. Can spectrum replication be achieved without sampling?

No, spectrum replication cannot be achieved without sampling. In order to replicate the spectrum of an analog signal, it must first be converted into a digital signal through sampling.

5. What are the potential limitations of sampling in spectrum replication?

Sampling can introduce errors and distortions in the replicated spectrum due to the discrete nature of digital signals. Additionally, the Nyquist-Shannon sampling theorem states that the sampling frequency must be at least twice the highest frequency component in the signal to avoid aliasing, which can be a limitation in certain cases.

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