Question

Consider the finite duration signal x(n) = (0.9)ⁿcos(0.1πn) for 0 ≤ n ≤ 31. Using MATLAB:

a.) Plot the signal

b.) Plot the real part of the DFT of x(n), the imaginary part of the DFT of x(n) and the DCT of x(n). All transforms are length N = 32.

Answer 1

%code

clc;
clear all;
for n = 1:32
x(n) = 0.9*(n-1)*cos(0.1*pi*(n-1));
end

%code for part a)

figure()
plot(x);xlabel('time');ylabel('amplitude');title('Input signal');

%code for part b)

figure()
plot(real(fft(x,32)));xlabel('frequency');ylabel('amplitude');title('Real part of fft of the signal');
figure()
plot(imag(fft(x,32)));xlabel('frequency');ylabel('amplitude');title('Imaginary part of fft of the signal');
figure()
plot(dct(x,32));xlabel('frequency');ylabel('amplitude');title('DCT of the signal');