4. Sampling, Aliasing, and Reconstruction: In this problem we want to consider the signal x(t) = cos(275000 t) and make plots at different sampling rates. For each part below you

will create a plot. All of your plots should be appear on the same figure as subplots, one below the other. Use the subplot (4,1,p) command which will create 4 rows and 1 column of plots. The value of p gives the specific plot number from top to bottom. a) For the first subplot make a plot of x(1) sampled at 100 kHz from 0 to 1 msec (0.001 seconds). Plot both the sample values as stems and the linear interpolation between the samples (Use stem(t, x); hold on; plot (t,x); hold off;) b) Repeat part (a) in the second subplot using a sampling frequency of 25 kHz. c) Repeat part (a) in the third subplot using a sampling frequency of 10 kHz. d) Repeat part (a) in the fourth subplot using a sampling frequency of 8 kHz. e) The plot in part (d) is under-sampled and shows aliasing. Find the frequency of the aliased signal and add it to this plot. For plotting the aliased signal use a 100 kHz sampling frequency so it appears continuous.