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This question already has an answer here:

I am new to DSP, and I am self-studying. I came upon this question, and I am stuck at it. Could someone please help me? Here is the question:

In order to digitally create a sinusoid with frequency $f$ = 440 Hz, you will need the normalized angular frequency $\omega$. How large is $\omega$ for a sampling frequency $f_s$ = 16 kHz?

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marked as duplicate by Dan Boschen, MBaz, lennon310, Stanley Pawlukiewicz, A_A Nov 9 '18 at 9:01

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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HINT:

  1. Determine the argument of a continuous-time sinusoid with frequency $f=440$ Hz.
  2. Sample that continuous-time sinusoid by replacing $t$ by $nT$, $n\in\mathbb{Z}$, with $T=1/f_s$ being the interval between samples.

This gives you an expression $\sin(n\omega_0)$, where $\omega_0$ depends on $f$ and $f_s$. $\omega_0$ is the normalized angular frequency.

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