Sampled data system freq response

[likephysics]

Can someone please explain the frequency response of sampled data system.

Why is there a spectrum at 0, Fs, 2Fs, 3Fs. (Fs - nyquist sampling frequency).
Shouldn't it be just from zero to Fs/2 ?

See fig. 2a in this link - http://www.maxim-ic.com/app-notes/index.mvp/id/928

 

[AlephZero]

After you have sampled the data, you can't tell the difference between signal with frequences 0 and Fs. They both have all the samples with the same constant value. That's what Figure 2a is about.

Similarly you can't tell the difference between signals with frequencies f and (Fs-f), (Fs + f), (2Fs - f), (2Fs + f), etc.

So for practical work, you need to filter out frequencies > Fs/2 from the analog data before you convert it into digital samples. That way, you know that a frequency between 0 and Fs/2 in the sampled data really was a signal at that frequency, not an unknown higher frequency.

You are right that in practice usually "you only look at frequencies up to Fs/2". The point of the web page is to show the assumptions behind that, and what happens if the data doesn't satisfy those assumptions.

 

[sophiecentaur]

A sampling waveform will consist of a series of pulses This waveform will contain a large (infinite) number of harmonics. When you sample, you are effectively amplitude modulating this waveform so the result will contain all of the harmonics of the sampling waveform, each of which has sidebands due to the sampled (modulating) waveform plus a 'baseband' component.
After any digital messing about with these samples, you will get a modified set of sample pulses. Often, the samples are 'boxcar' waveform, which then require some equalisation but they would ideally be impulses - just like the original sampling pulses. The output wavefrom will contain a whole lot of harmonics, which would normally be low-pass filtered out before actually using the resulting analogue (continuous) signal (to avoid overload at frequencies that the analogue circuitry couldn't handle.