We want to compute an N-point DFT of a one-second-duration compact disc (CD) aud

Question

We want to compute an N-point DFT of a one-second-duration compact disc (CD) audio signal x(n), whose sample rate is fs = 44.1 kHz, with a DFT sample spacing of 1 Hz.
(a)What is the number of necessary x(n) time samples, N? (b)What is the time duration of the x(n) sequence measured in seconds?Hint: This Part (b) of the problem is trickier than it first appears. Think carefully. We want to compute an N-point DFT of a one-second-duration compact disc (CD) audio signal x(n), whose sample rate is fs = 44.1 kHz, with a DFT sample spacing of 1 Hz.
(a)What is the number of necessary x(n) time samples, N? (b)What is the time duration of the x(n) sequence measured in seconds?Hint: This Part (b) of the problem is trickier than it first appears. Think carefully. We want to compute an N-point DFT of a one-second-duration compact disc (CD) audio signal x(n), whose sample rate is fs = 44.1 kHz, with a DFT sample spacing of 1 Hz.
(a)What is the number of necessary x(n) time samples, N? (b)What is the time duration of the x(n) sequence measured in seconds?Hint: This Part (b) of the problem is trickier than it first appears. Think carefully.

Explanation / Answer

Given sample rate fs = 44.1 k HZ,sample spacing = 1HZ

a) frequency axis variables f = n/N ts = n fs/N

    sample spacing of x(n) = fs/N = 1Hz

      N = fs/1 = 44.1*103

b) periodicity is fs HZ then the time sample period ts = 1/fs = 1/44.1k = 22.6*106 seconds

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