- #1

zaka

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A signal x(t) which is band-limited to 10kHz is sampled with a sampling frequency of 20kHz. The DFT (Discrete Fourier Transform) of N= 1000 samples of x(n) is then computed. To what analogue frequency does the index k=120 respond to?

I'm trying to relate the above to a previous worked example that I encountered, the question was similar as follows:

The sampling frequency, is f

_{s}= 120 Hz. The DFT of N=6 samples. To what analogue frequency does the index

k=1 correspond to? What about index k=5 ?

For k =1

f

_{k}= k (f

_{s}/ N)

= (1)*(120/6) = 20Hz

For k=5

f

_{k}= (k-N)*(f

_{s}/ N)

= (5-6)*(120/6) = -20Hz

Why for k=5 was k subtracted from N. Is there a general forumla for this sort of question?

And what does this mean for the question I'm trying to resolve?

Is f

_{k}for that = 120*(2000/1000)

or f

_{k}for that = (120-1000)*(2000/1000)

or something else completely?

Any help would be much appriciated.