AssignmentIn this assignment, we will investigate basic principles of sampling.1) Sampling of a...

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AssignmentIn this assignment, we will investigate basic principles of sampling.1) Sampling of a cosine. The object of this part is to show that you can recover a signal from its samples if the signal is bandlimited and you sample above the Nyquist rate of twice the highest frequency in the signal. a. With Matlab, create a 1-Hz cosine, x(t) = cos(2rt), over a time interval —2 a. Repeat part 1, sampling the 1-Hz cosine at exactly the Nyquit rate of 2 Hz. Can you still reconstruct the signal from its samples? b. Repeat part 2, sampling the 1-Hz sine at exactly the Nyquit rate of 2 Hz. Can you still reconstruct the signal from its samples? c. What do you conclude about your ability to reconstruct signals sampled exactly at the Nyquist rate? 6) Effect of the reconstruction filter bandwidth. The criterion for chosing the bandwidth of the reconstruction filter is that you pass the baseband replica of Xs (w) while rejecting the sidebands. In previous examples, you've set the bandwidth of the ideal reconstruction filter in the digital-to-analog converter to one-half the Nyquist rate. Now, we'll explore using other bandwidths. a. Produce a plot that corresponds to sampling the 1-Hz cosine at a rate of 8 Hz, but this time, set the bandwidth of the reconstruction filter to 2 Hz instead of 4 Hz (which would be one-half the sampling frequency). Can you reconstruct the cosine from its samples? Why or why not? b. Repeat the previous part, but with the bandwidth of the reconstruction filter set to 0.5 Hz. Can you still reconstruct the cosine from its samples? Why or why not?

David · Accepted Answer

Here is the MATLAB code that you can use in each of these questions. fs is sampling frequency in each 
case and f is the frequency of the signal. 
tmin = -1; 
tmax = 1; 
t = tmin:0.001:tmax; 
f = 1; 
xa = sin(2*pi*f*t); 
plot(t,xa); 
hold on 
fs = 2; 
Ts = 1/fs; 
n = tmin/Ts:tmax/Ts;

Assignment In this assignment, we will investigate basic principles of sampling. 1) Sampling of a cosine. The object of this part is to show that you can recover a signal from its samples if the...

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