An analog signal xt has a duration of 15 ms and a bandwidth

An analog signal x(t) has a duration of 15 ms and a bandwidth of 4 kHz. Determine (there are more than one choice for each question): The suitable sampling frequency f_s The total number of samples N The approximate number of zeros that are padded to x(t) to perform FFT. The actual resolution in the frequency domain based on your design. based on the following requirements: There is no aliasing N = 2^L where L is an integer so that the FFT algorithm can be used The resolution in the frequency domain is better than 50 Hz (i.e. delta f le 50 Hz)

Solution

Fs= sampling frequency=2*4= 8 kHz

Ts= sampling time= 1/Fs=(1/8) ms

N= number of sample=15/Ts=120

n= number of zero added= 128-120=8

Resolution=8/128 =62.5

a) no alaising

b) N= length of sequence= 2^n

C) correct