MATLAB script for creating Figure 1 and Figure 2 in DSP Lab 2
clc; clear all; close all; %%%%%% TIME DOMAIN PLOT (FIGURE 1) %================================================== %PLOT THE ORIGINAL CONTINUOUS TIME DOMAIN SIGNAL x(t) %================================================== f1=1/2; % frequency f1 in Hz f2=2.5; % frequency f2 in Hz fs=1000*f2; %sampling frequency. When plotting the time-domain signal we %take a very high sampling frequency so that the plotted signal %will appear continuous to the eye. t=[0:1/fs:10]; %plot 10 seconds x=3*sin(2*pi*f1*t)+2*sin(2*pi*f2*t); %time domain signal we are %sampling. figure('color',[1 1 1]); %Note: Open new figure. Set background color to %white. subplot(3,1,1) h=plot(t,x); ylabel('x(t)','FontSize',16) xlabel('t [sec]','FontSize',16) axis tight set(gca,'FontSize',16) grid on %================================================== %Sampling at fs=2.5*fmax=2.5*f2 %================================================== fs = 2.5*f2; % Sampling Frequency t_samp=[0:1/fs:10]; %plot 10 seconds. xs = 3*sin(2*pi*f1*t_samp)+2*sin(2*pi*f2*t_samp); %create sampled signal subplot(3,1,2); n_vector=t_samp*fs; %sampled index array: n=[0, 1, 2, 3, ...., N] h=plot(n_vector,xs,'r.','markers',13); ylabel('x(nT)','FontSize',16) xlabel('n','FontSize',16) axis tight set(gca,'FontSize',16) grid on %================================================== %Reconsturcted signal %================================================== xr=x; %reconstructed signal xr(t) equals the original continuous time domain %signal x(t) because the sampling condition is met subplot(3,1,3) h=plot(t_samp,xs,'r.',t,x,'b','markers',13); str = {'x(nT) and', 'Reconstructed'}; ylabel(str,'FontSize',13) xlabel('t [sec]','FontSize',16) axis tight set(gca,'FontSize',16) grid on % %%%%%% FREQUENCY DOMAIN PLOT (FIGURE 2) %================================================== %PLOT SPECTRUM OF ORIGINAL CONTINUOUS TIME DOMAIN SIGNAL x(t) %================================================== figure('color',[1 1 1]); %Note: Open new figure. Set background color to %white fs=1000*f2; %sampling frequency. When creating the continuous time-domain %signal we take a very high sampling frequency so that the plotted signal %will appear continuous to the eye. t=[0:1/fs:30]; %plot 30 seconds (for frequency domain plots, you want to %simulate many periods of the signal so that your frequency domain plots %have a high resolution (frequency tones appear "sharp") x=3*sin(2*pi*f1*t)+2*sin(2*pi*f2*t); %time-domain signal N=2^20; %good general value for FFT (Leave this number alone for Lab 1) y=fft(x,N); %compute FFT! There is a lot going on "behind the scenes" with %this one line of code. z=fftshift(y); %Move the zero-frequency component to the center of the %array. This is used for finding the double-sided spectrum (as opposed to %the single-sided spectrum). f_vec=[0:1:N-1]*fs/N-fs/2; %Create frequency vector (this is an array of %numbers. Each number corresponds to a discrete point in frequency in which we %shall evaluate and plot the function.) amplitude_spectrum=abs(z)/length(x); %Extract the amplitude of the spectrum %Here we also apply a scaling factor of 1/length(x), so that the amplitude %of the FFT at a frequency component equals that of the ideal double-sided %spectrum. subplot(3,1,1) plot(f_vec,amplitude_spectrum); set(gca,'FontSize',13) %set font size of axis tick labels to 15 xlabel('Freq [Hz]','fontsize',13) title('Continuous time spectrum (original signal):','fontsize',17) %ylabel('Spectrum of x(t)','fontsize',13) grid on %axis tight xlim([-6.25/2,6.25/2]) %================================================== %Sampling at fs=2.5*fmax=2.5*f2 %================================================== fs = 2.5*f2; % Sampling Frequency t_samp=[0:1/fs:30]; xs = 3*sin(2*pi*f1*t_samp)+2*sin(2*pi*f2*t_samp); %create sampled signal N=2^20; y=fft(xs,N); z=fftshift(y); amplitude_spectrum=abs(z)/length(xs); w_vec=[0:1:N-1]*pi/N-pi/2; %create discrete time frequency (omega hat) subplot(3,1,2) plot(w_vec,amplitude_spectrum); set(gca,'FontSize',13) %set font size of axis tick labels to 15 xlabel(['$$\hat{\omega}$$'],'Interpreter','Latex','fontsize',13) str = {'Spectrum of', 'sampled signal'}; %ylabel(str,'fontsize',13) title('Discrete time spectrum (sampled signal):','fontsize',17) grid on %axis tight xlim([-pi/2,pi/2]) %================================================== %Reconsturcted signal %================================================== f_vec=w_vec*fs/pi; %Scale frequency axis subplot(3,1,3) plot(f_vec,amplitude_spectrum); grid on xlim([-fs/2,fs/2]) xlabel('Freq [Hz]','fontsize',13) title('Continuous time spectrum (reconstructed signal):','fontsize',17) set(gca,'FontSize',13) %set font size of axis tick labels to 15
