Homework SourseWe want to compute an Npoint DFT of a onesecondduration comp
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.
Solution
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
