$$ x \left[ n \right] = 3 \sin \left( 4 \pi n \right) + 2 \cos \left(0.36 \pi n \right), ~~~ 0 \leq n \leq 100 $$

The fact that my signal is composed of both sine and cosine makes it tricky for me.

  • $\begingroup$ Hello bob and welcome to DSP SE. There's a couple of things to make note of here. First and probably most important is that the combination of those two "signals" ($\sin$ and $\cos$) is linear. Additionally, the only difference between a $\sin$ and a $\cos$ is a phase difference of $\pi/2$, which essentially means that you (somewhat arbitrarily) change the $\cos$ to $\sin$ and try again. $\endgroup$
    – ZaellixA
    Oct 9, 2022 at 10:39
  • 1
    $\begingroup$ Sounds like homework: Can you please show what you have done already? Can you finde the period for each component separately? $\endgroup$
    – Hilmar
    Oct 9, 2022 at 11:03

1 Answer 1


This is a homework type question, so here are a few hints instead of a complete answer:

  1. Determine the period of the cosine term. If you don't know how to do that then learn it, it's important.

  2. Compute a few samples of the sine term. Do you notice anything special? Draw your conclusions concerning the period of the given signal.


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