# How do I determine the dominant frequency of a signal after sampling?

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?

• After our discussion below: That's aliasing, and I bet if you're familiar with the term "Nyquist frequency", it will be introduced a few paragraphs before or after that term. May 18, 2022 at 16:54
• Does this answer your question? Properties of Discrete-time Sinusoidal Signal May 18, 2022 at 16:54
• hmm I can’t see aliasing anywhere in my lecture notes! May 18, 2022 at 17:00
• That would really be surprising! I don't think your lecturer would say "and if you violate the condition to sample at more than the Nyquist frequency, a kitten feels pain"; the motivation for that is exactly that: Aliasing! (do be nice to your kittens, though) May 18, 2022 at 17:03
• I think I kind of understand the link that you sent, but don’t really get how it applies to this situation May 18, 2022 at 17:08

• 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. May 18, 2022 at 16:47