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So I have signal with frequency of $15Hz$ and sample rate frequency is $20Hz$.

What happens if we sample the signal at a frequency that is lower that the Nyquist rate? We will have aliasing. Sample rate frequency should be at least bigger than $2*f_{max}$.

I understand that part but I'm confused how that will look like. Can someone help me with that?

Alen
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  • Hi! Um, yes, you probably have some slides and a textbook that say that aliasing will happen. It's very likely that these have illustrations. If you can, read these – it's easier to stay within a given didactic framework than getting to know a new notation for stuff for every question :) basically, it's just a fold-over https://en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem – Marcus Müller Jan 20 '18 at 13:22
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    Here is a sound illustration with aliasing http://ews.illinois.edu/~serwy/aliasing/ The assertion "I have signal with frequency of 15Hz" is not quite precise. Is that a mere sine, or the maximum frequency of a signal? – Laurent Duval Jan 20 '18 at 13:37
  • Does this answer answer your question? – Matt L. Jan 20 '18 at 14:38

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You have aliasing for sampling signals of any frequency: a signal of 5Hz sampled at 20Hz is indistinguishable from a signal of 15Hz of opposite phase.

It's common in audio usage to work with "lowpass signals" only and consider "aliasing" for frequencies more distant from DC, but in reality sampling of anything is ambiguous by multiples of the sample frequency regardless of the original signal. You can perfectly well sample signals of 15Hz with a sampling frequency of 20Hz as long as you make sure that the signal only contains frequencies between 10Hz and 20Hz (for example).

For any detected signal component, increasing/decreasing its frequency by multiples of the sampling frequency will not cause any change at the sampled time points. Hence you want to prefilter the signal such that adding multiples of the sampling frequency to any signal component leads to something that cannot be present in the signal: that way the sampled values represent the signal uniquely.