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For example if I have a $10 Hz$ signal and I sample it at $19 Hz$ (less than the Nyquist frequency) how can I determine the dominant frequency of the output and why?

If I then apply a lowpass filter, how will this allow for a dominant frequency of $10 Hz$ to be obtained again?

EDIT

If I know what the frequency of the sampled signal is, e.g. the sampled signal $x \left( t \right) = \sin \left(2 \pi \cdot 10 \cdot t \right)$, how can I determine the dominant frequency of the output signal in this case?

ZaellixA
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Major Anarchy
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1 Answers1

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For example if I have a 10Hz signal and I sample it at 19Hz (less than the Nyquist frequency) how can I determine the dominant frequency of the output and why?

not unambiguously, because you violated the necessary condition for sampling, as you say yourself.

So, not at all. Unless you know that your frequency range of interest does not include 9 Hz, you cannot know whether the signal was 10 Hz or 9 Hz; both signals would lead to exactly the same samples.

Marcus Müller
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  • Okay - what about if I am sampling a signal that I know the frequency of e.g. if I am sampling the signal x(t) = sin(102pi*t) (a signal with frequency of 10Hz only)? – Major Anarchy May 18 '22 at 16:45
  • but if you know the frequency, why would you need to detect the frequency? You just wrote it down; 10 Hz. Which is the same as 9 Hz (in the real-valued case) in $f_s=19,\text{Hz}$ discrete time. – Marcus Müller May 18 '22 at 16:47
  • I’m trying to work out how the maths works for the time being – Major Anarchy May 18 '22 at 16:49
  • there's no math working here. If you say "I have a signal that I know to be 10 Hz, what is it's frequency?" then the answer is "10 Hz, as you say". After sampling, it's still 10 Hz – but that 10 Hz is mathematically indistiguishable from 9 Hz. I might simply be missing what you're trying to figure out! – Marcus Müller May 18 '22 at 16:50
  • Well I understand that sometimes signals are sampled at less than their nyquist frequency and then passed through a lowpass filter in order to return the original signal. I’m trying to work out what happens in between sampling and being input to the lowpass filter – Major Anarchy May 18 '22 at 16:50
  • aaaaaaaaaah. I was assuming you knew that because you correctly said "Nyquist Frequency" in your question! – Marcus Müller May 18 '22 at 16:51
  • So lets say you had a device that sampled the 10Hz signal at 19Hz, and then measured the frequency after sampling, the output would have a frequency of 9Hz? Why? – Major Anarchy May 18 '22 at 16:54
  • see my comment under your question. You really should read the material where you got "Nyquist frequency" from a little further – aliasing will definitely be introduced alongside with that term! – Marcus Müller May 18 '22 at 16:55