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Problem

The sampling frequency of a continuous-time signal is $S$ kHz, what does $\frac{\pi}{4}$ radians/sample in DTFT domain represent in Hz in frequency domain? Prove the relationship.

Doubts

I am confused with DTFT domain and frequency domain and I do not how to put all these domains together.

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If this is a homework problem, shield your eyes.

Otherwise, it is a simple units issue.

S has units of 1k samples per second.

Your frequency is expressed in radians per sample.

There are $ 2 \pi $ radians per cycle.

So the puzzle now is to find the relationship between $\frac{samples}{second}$, $\frac{radians}{sample}$, $\frac{radians}{cycle}$, and your goal of $\frac{cycles}{second}$,

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