Question

Hello, I need the Matlab code of the Fourier Transform without using the Matlab functions fft and dft. Applied to discrete signals. If you can with an example.Thank you!!

Answer 1

Program :

clc;
clear all;
x = input('Enter the input sequence = ');
N = length(x);
for k = 1:N
y(k) = 0;
for n = 1:N
y(k) = y(k)+x(n)*exp(-1i*2*pi*(k-1)*(n-1)/N);
end
end
%code block to plot the input sequence
t = 0:N-1;
subplot(2,2,1);
stem(t,x);
ylabel('Amplitude ---->');
xlabel('n ---->');
title('Input Sequence');
grid on;
magnitude = abs(y); % Find the magnitudes of individual FFT points
disp('FFT Sequence = ');
disp(magnitude);
%code block to plot the FFT sequence
t = 0:N-1;
subplot(2,2,2);
stem(t,magnitude);
ylabel('Amplitude ---->');
xlabel('K ---->');
title('FFT Sequence');
grid on;
R = length(y);
for n = 1:R
x1(n) = 0;
for k = 1:R
    x1(n) = x1(n)+(1/R)*y(k)*exp(1i*2*pi*(k-1)*(n-1)/R);
end
end
%code block to plot the IFFT sequence
t = 0:R-1;
subplot(2,2,3);
stem(t,x1);
disp('IFFT Sequence = ');
disp(x1);
ylabel('Amplitude ---->');
xlabel('n ---->');
title('IFFT sequence');
grid on;

Output :

Enter the input sequence = [1 4 2 5 2]

FFT Sequence =
   14.0000    2.8124    4.3692    4.3692    2.8124

IFFT Sequence =
Columns 1 through 4

   1.0000 - 0.0000i   4.0000 - 0.0000i   2.0000 - 0.0000i   5.0000 + 0.0000i

Column 5

   2.0000 + 0.0000i

Waveforms: