- #1
zaka
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Hi, I have the following question:
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 fs = 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
fk = k (fs / N)
= (1)*(120/6) = 20Hz
For k=5
fk = (k-N)*(fs / 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 fk for that = 120*(2000/1000)
or fk for that = (120-1000)*(2000/1000)
or something else completely?
Any help would be much appriciated.
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 fs = 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
fk = k (fs / N)
= (1)*(120/6) = 20Hz
For k=5
fk = (k-N)*(fs / 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 fk for that = 120*(2000/1000)
or fk for that = (120-1000)*(2000/1000)
or something else completely?
Any help would be much appriciated.