Suppose a digital signal is sampled with a rate of 8000 Hz f

Suppose a digital signal is sampled with a rate of 8000 Hz for 2 seconds, and the resulted data array \"d\" has a length of 16000. Suppose d is analyzed via fft, and the result is called fftd. If you want to take a look of the frequency spectrum of \"d\" from 1000Hz-2000Hz, what is the corresponding index range of fftd?

Solution

Sampling rate = 8000Hz

sampling time Ts = 1/8000 sec

in 2 sec the data point d = 16000 (periodic discrete signal with period 2 sec)

Corresponding FFT points = 16000

Since the d array is the measurement of T = 2 sec the FFT will correspond to a frequency range of 16000Hz/T sec

= 8000Hz = 16000 data points

for 1000-2000Hz frequency corresponding data point will be 2000 to 3999

In simple words, FFT taken over T seconds samples still represents the same frequency band that is the sampling frequency.