Question

(B) Implement Matlab code for each part as described below: i) Define the following signal in time and plot it where Ai 10, A2-3, fi-10 Hz, f2-40 Hz. part of the DFT, and discuss the results. zero. Do this carefully for both positive and negative frequencies. Call this signal G (f). ii) Compute the DFT S(f) of s (t) using the fft() function. Plot the real and imaginary ii Remove the high frequency component, that is f2 from the spectrum by setting it to Plot the spectrum. iv) Let g (t) be the inverse Fourier transform of G (f). Compute g(t) using the function ifft) and plot the signal in time. Discuss the results.

Using MATLAB, Please read carefully, EXPLAIN CODE AND ANSWERS, DISCUSS RESULTS, I NEED EVERY PART

Answer 1

clc;close all;clear all;
%plot s(t)
figure(1)
t=0:0.001:0.1
A1=10;A2=3;f1=10;f2=40;
st=(A1*(cos(2*pi*f1*t)))+(A2*(cos(2*pi*f2*t)))
subplot(321)
plot(t,st)
xlabel('t')
ylabel('s(t)')
title('s(t)')

%FFT of s(t)
%Frequency spectrum of S(f)
subplot(322)
Sf=fft(st)
k=0:1:length(t)-1
stem(k,real(Sf),'m')
title('Real(Sf)')
xlabel('k')
ylabel('real(Sf)')

subplot(323)
stem(k,imag(Sf),'g')
title('Imag(Sf)')
xlabel('k')
ylabel('Imag(Sf)')

%Remove high frequency component&perform ifft
Sf(5)=0;Sf(98)=0%Choose lowest amplitude peaks from real(Sf)
G=Sf
g=ifft(G)
subplot(324)
plot(t,g,'b')
title('Recovered signal g(t) by ifft')
xlabel('t')
ylabel('g(t)')

%Frequency spectrum of G(f)
subplot(325)
k=0:1:length(t)-1
stem(k,real(G),'m')
title('Real(Gf)')
xlabel('k')
ylabel('real(Gf)')

subplot(326)
stem(k,imag(G),'g')
title('Imag(Gf)')
xlabel('k')
ylabel('Imag(Gf)')

s(t) Real(Sf) 600 500 s 400 D 300 200 100 10 -5 -10 -15 -100 20 40 60 80 100 0.02 0.04 0.06 0.08 0.1 Recovered signal g(t) by ifft Imag(Sf) 15 10 20 E-10 -10 -20 100 0 0.02 0.04 0.06 0.08 0.1 20 40 60 80 Imag(Gf) Real(Gf) 20 600 500 400 300 200 100 -10 20 -100 20 40 60 80 100 20 40 60 80 100