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+//Example 2.2 page 23
+//
+//Assuming that an analog signal is given by
+//x(t) = 5 cos (2*%pi*2000*t) + 3*cos(2*%pi*3000*t),for t>=0
+//and it is sampled at the rate of 8,000 Hz,
+//a. Sketch the spectrum of the sampled signal up to 20 kHz.
+//b. Sketch the recovered analog signal spectrum if an ideal lowpass filter with
+//a cutoff frequency of 4 kHz is used to filter the sampled signal
+//(y(n) = x(n)in this case) to recover the original signal.
+
+clc;
+clear;
+close;
+fs = 8000;//Hz
+t = 1:(1/fs):10;
+x = 5*cos(2*%pi*2000*t)+ 3*cos(2*%pi*3000*t);
+//before sampling
+
+//c1 and f1 are derived using the euler's identity which gives
+//  x(t) = 1.5 * %e^(-%i*2*%pi*3000t)+ 2.5 * %e^(-%i*2*%pi*2000t)+ 2.5 * %e^(%i*2*%pi*2000t) + 1.5 * %e^(%i*2*%pi*3000t)
+
+c1 = [1.5 2.5 2.5 1.5];
+f1 = [-3 -2 2 3];//kHz
+
+//after sampling
+c2 = repmat(c1,1,5);
+f2 = [f1-16 f1-8 f1 f1+8 f1+16];
+ax=gda();
+ax.thickness = 2;
+ax.y_location = "origin";
+ax.x_location = "origin";
+
+subplot(2,1,1)
+plot2d3(f2,c2)
+xtitle('Spectrum of the sampled signal in Example 2.2(a)','f(kHz)','X(f)');
+//Since Sampling theorem is satisfied, we can recover the original spectrum using reconstruction low pass filter.
+subplot(2,1,2)
+plot2d3(f1,c1)
+xtitle('Spectrum of the recovered signal in Example 2.2(b)','f(kHz)','X(f)');