Question

Exercises: u used to the instructor b the end of next lab. 20 102 Plot the f(t)-sinc(20r) cos(300t)sinc (10t) cos(100t) Use the fast Fourier transform to find the magnitude and phase spectrum of the signal and plot over an appropriate range. Use appropriate values for the time interval and the sampling interval. Note that in Matlab sinc(x)-, so we need to divide the argument by n to make it match the given function. Le, sinc(20t/pi) Hint: Use the parameters from example 3 and then alter them if needed an(xx), so we need to divide the argument by π to make it Example 3) Find the Fourier transform of the following signal and plot the magnitude and phase spectrum. f(t) = cos(20m), 0 t 1, and zero otherwise Fourier Transform f the modulated rectangle function 1-0 Ts= p:/200; 20-length《 ; w-pi /Ts : ws : pi/Ts-va; Frequency sampling interval Frequency vector Use the fast Fourier transform (FFT) to find spectrum % FET Shift spectrum igure (1) ubplot (211),piot (w, abs (EE),itleEET based Magnitude Spectrum' subplot : 212) ,plot(w, angle:FF》+1BO/pǐ),title ('Phase axis (i-pi/Ts pi/Ts -200 2001); xlabel', '\omega, rad/s'); Spectrum');

Answer 1

clc;clear all;close all;
Ts=1/1000
t=-1:Ts:1
No=length(t)
w=-pi:2*pi/No:pi-(2*pi/No)
f1=((20/pi).*(sinc(20*t/pi)).*(cos(300*t)))
f2=((10/pi).*((sinc(10*t/pi)).^2).*(cos(100*t)))
f=f1+f2
figure(1)
subplot(311)
plot(t,f)
xlabel('t')
ylabel('f(t)')
title('signal f(t)')

FF=fft(f);
FF=fftshift(FF);
FF=Ts*FF;

subplot(312)
plot(w,abs(FF),'m')
xlim([-0.4,0.4])
title('FFT based magnitude spectrum')
xlabel('omega(rad/s)')
ylabel('abs(FF)')
subplot(313)
plot(w,angle(FF)*180/pi,'g')
title('Phase spectrum')
xlim([-0.4,0.4])
xlabel('omega(rad/s)')
ylabel('Phase(FF)')

signal f(t) -5 -10 0.5 FFT based magnitude spectrum 0.7 0.6 L 0.5 し0.4 0.3 D0.2 0.1 0.2 0.2 0.4 omega(rad/s) Phase spectrum 200 LL 100 a -100 -200 -0.4 0.2 0.2 0.4 omega(rad/s)