Question

Given signal x(t) = sinc(t):

1. Find out the Fourier transform of x(t), find X(f), sketch them.

2. Find out the Nyquist sampling frequency of x(t).

3. Given sampling rate fs, write down the expression of the Fourier transform of xs(t), Xs(f) in terms of X(f).

4. Let sampling frequency fs = 1Hz.

Sketch the sampled signal xs(t) = x(kTs) and the Fourier transform of xs(t), Xs(f).

5. Let sampling frequency fs = 2Hz. Repeat 4.

6. Let sampling frequency fs = 0:5Hz. Repeat 4.

7. Let sampling frequency fs = 1:5Hz. Repeat 4.

8. Let sampling frequency fs = 2/3Hz. Repeat 4.

8.1 Design Matlab programs to illustrate items 4-8

8.2 plot all the graphs.

9. Design a Matlab function to calculate the Fourier transform of a sampled signal
xs(t), Xs(f) = Σ k x(kTs) exp(-j2πf . kTs).

NOTE: In Matlab and this experiment, sinc(t) is defined as sinc(t) = sin(π t)/(πt). Under
this definition: sinc(2Wt) 1/(2W) rect( f/2W )

Answer 1