代做Use MATLAB to implement sampling and reconstruction of the following signal代写留学生Matlab语言

Question 3

Use MATLAB to implement sampling and reconstruction of the following signal

f(t):=cos(2t)e-t²,            0≤t≤2π

and is defined to be causal for t≥0 and assumed to be zero for t>2π.

(a) Use MATLAB to plot this signal for 0 ≤ t ≤ 2π

(b) Use MATLAB to plot the amplitude spectrum |f(α)|.

(c) Is  f(t) time-limited or band-limited, explain your reasoning?

(d) Pick a suitable sampling rate such that f(t) can be reconstructed from the samples and plot the sampled signal using MATLAB.

(e) Choose a suitable value Mo based on previous part as a threshold for low-pass filter.Use MATLAB to reconstruct the original signal using Shannon's sampling formula.

(f) Plot the reconstructed signal and superimpose the original signal f on the same graph using MATLAB.Comment on the results.