% % Filename: example9.m % % Description: m-file to demonstrate how the DFT of a sampled analog signal % can be used to determine the approximate frequency content % (FT) of the analog signal. % ** Use an AM signal for example ** figure(1); clf; clear; fm = 20e3; fc = 100e3; tstep = 100e-9; tmax = 200e-6; t = 0:tstep:tmax; xam = (1 + cos(2*pi*fm*t)).*cos(2*pi*fc*t); k = k + 1; subplot(2,1,1); plot(t,xam); axis([0 200e-6 -2 2]); grid; xlabel('tMATLAB Plots Generated:'); ylabel('xam(t) '); title('AM Modulated Signal'); % Plot Frequency Spectrum of xam(t), XAM(f) subplot(2,1,2); stem(1000*[-120 -100 -80 80 100 120], pi*[.5 1 .5 .5 1 .5]); grid; xlabel('f '); ylabel('|Xam(f)|'); title('Magnitude Spectrum of xam(t)'); % ** Sample AM signal every 1usec ** figure(2); clf; clear; fm = 20e3; fc = 100e3; T = 1e-6; N = 200; nT = 0:T:N*T; xn = (1 + cos(2*pi*fm*nT)).*cos(2*pi*fc*nT); % Plot Sampled Signal subplot(2,2,1); stem(nT,xn); axis([0 200e-6 -2 2]); grid; xlabel('t '); ylabel('x[n]'); title('xam(t) Sampled Every T=1e-6 '); % Plot DFT of Sampled Signal Vs k Xk = dft(xn); k = 0:length(xn)-1; subplot(2,2,2); stem(k, abs(Xk)); grid; xlabel('k'); ylabel('|Xk|'); title('DFT of x[n], T=1e-6 '); % Plot ZOH Approximation of x(t) subplot(2,2,3) plot(nT, xn); grid; xlabel('t '); ylabel('x_zoh(t)'); title('ZOH Reconstruction of x(t), T=1e-6 '); % Plot DFT of Sampled Signal Vs f Xk = dft(xn); k = 0:length(xn)-1; subplot(2,2,4); stem(k/(length(xn)*T), abs(Xk)); grid; xlabel('f = k/(NT) '); ylabel('|Xk|'); title('DFT of x[n], T=1e-6 '); % Sample AM signal every 4usec figure(3); clf; clear; fm = 20e3; fc = 100e3; N = 52; T = 4e-6; nT = 0:T:N*T; xn = (1 + cos(2*pi*fm*nT)).*cos(2*pi*fc*nT); % Plot Sampled Signal subplot(2,2,1); stem(nT,xn); axis([0 200e-6 -2 2]); grid; xlabel('t '); ylabel('x[n]'); title('xam(t) Sampled Every T=4e-6 '); % Plot DFT of Sampled Signal Vs k Xk = dft(xn); k = 0:length(xn)-1; subplot(2,2,2); stem(k, abs(Xk)); grid; xlabel('k'); ylabel('|Xk|'); title('DFT of x[n], T=4e-6 '); % Plot ZOH Approximation of x(t) subplot(2,2,3) plot(nT, xn); axis([0 200e-6 -2 2]); grid; xlabel('t '); ylabel('x_zoh(t)'); title('ZOH Reconstruction of x(t), T=4e-6 '); % Plot DFT of Sampled Signal Vs f Xk = dft(xn); k = 0:length(xn)-1; subplot(2,2,4); stem(k/(length(xn)*T), abs(Xk)); grid; xlabel('f = k/(NT) '); ylabel('|Xk|'); title('DFT of x[n], T=4e-6 ');