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f = 100; % frequency of the signal in Hz T = 1/f; % period of the signal in s t = 0:0.0001:5*T; % time vector x = sin(2*pi*f*t); % signal % Plot the continuous-time signal figure(1) plot(t,x) xlabel('Time (s)') ylabel('x(t)') title('Continuous-time signal') % Sample the signal at different sampling frequencies fs1 = 150; % sampling frequency 1 in Hz fs2 = 200; % sampling frequency 2 in Hz fs3 = 300; % sampling frequency 3 in Hz Ts1 = 1/fs1; % sampling period 1 in s Ts2 = 1/fs2; % sampling period 2 in s Ts3 = 1/fs3; % sampling period 3 in s n1 = 0:Ts1:5*T; % sample index vector 1 n2 = 0:Ts2:5*T; % sample index vector 2 n3 = 0:Ts3:5*T; % sample index vector 3 x1 = sin(2*pi*f*n1); % sampled signal 1 x2 = sin(2*pi*f*n2); % sampled signal 2 x3 = sin(2*pi*f*n3); % sampled signal 3 % Plot the sampled signals figure(2) subplot(3,1,1) stem(n1,x1) hold on plot(n1,x1) hold off xlabel('Time (s)') ylabel('x[n]') title(['Sampled signal 1 with fs = ',num2str(fs1),' Hz']) subplot(3,1,2) stem(n2,x2) hold on plot(n2,x2) hold off xlabel('Time (s)') ylabel('x[n]') title(['Sampled signal 2 with fs = ',num2str(fs2),' Hz']) subplot(3,1,3) stem(n3,x3) hold on plot(n3,x3) hold off xlabel('Time (s)') ylabel('x[n]') title(['Sampled signal 3 with fs = ',num2str(fs3),' Hz']) % Reconstruct the signal using sinc interpolation xr1 = zeros(size(t)); % reconstructed signal 1 xr2 = zeros(size(t)); % reconstructed signal 2 xr3 = zeros(size(t)); % reconstructed signal 3 for i = 1:length(n1) xr1 = xr1 + x1(i)*sinc((t-n1(i))/Ts1); % sinc interpolation formula end for i = 1:length(n2) xr2 = xr2 + x2(i)*sinc((t-n2(i))/Ts2); % sinc interpolation formula end for i = 1:length(n3) xr3 = xr3 + x3(i)*sinc((t-n3(i))/Ts3); % sinc interpolation formula end % Plot the reconstructed signals figure(3) subplot(3,1,1) plot(t,xr1) xlabel('Time (s)') ylabel('xr1(t)') title(['Reconstructed signal 1 with fs = ',num2str(fs1),' Hz']) subplot(3,1,2) plot(t,xr2) xlabel('Time (s)') ylabel('xr2(t)') title(['Reconstructed signal 2 with fs = ',num2str(fs2),' Hz']) subplot(3,1,3) plot(t,xr3) xlabel('Time (s)') ylabel('xr3(t)') title(['Reconstructed signal 3 with fs = ',num2str(fs3),' Hz'])
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