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How to Find the Fourier Transform of Any Signal

 

MATLAB Code

This is a simple MATLAB code snippet that computes the Fourier Transform of any signal. I will show you different examples below the main code. Remember, to find the Fourier Transform of any signal using this code snippet, you need a sampled signal and its corresponding sampling frequency.

n = length(signal);

f = (-n/2:n/2-1)*(fs/n); % Frequency axis centered at 0

S_f = abs(fftshift(fft(signal)/n));  % Normalize FFT

S_f_dB = 20*log10(S_f / max(S_f));  % dB scale with normalization


Example for finding FFT of a sine wave

clc;

clear all;

close all;


fm = 10;      % Message signal frequency (Hz)

fs = 1000; % Sampling frequency (100 kHz)

t = 0:1/fs:1-1/fs; % Time vector over 1 second

signal = sin(2*pi*fm*t);


% Compute frequency spectrum in dB

n = length(signal);

f = (-n/2:n/2-1)*(fs/n); % Frequency axis centered at 0

S_f = abs(fftshift(fft(signal)/n));  % Normalize FFT

S_f_dB = 20*log10(S_f / max(S_f));  % dB scale with normalization


% Plot normalized spectrum in dB

figure(1);

plot(f, S_f);

title('Normalized Frequency Spectrum of PAM Signal');

xlabel('Frequency (Hz)');

ylabel('Magnitude (dB)');

grid on;


figure(2);

plot(f, S_f_dB);

title('Normalized Frequency Spectrum (dB) of PAM Signal');

xlabel('Frequency (Hz)');

ylabel('Magnitude (dB)');

grid on;

web('https://www.salimwireless.com/search?q=fft%20fourier%20transform', '-browser');


Another Example Code

clc;
clear all;
close all;

fm = 10;      % Message signal frequency (Hz)
fs = 1000; % Sampling frequency (100 kHz)
t = 0:1/fs:1-1/fs; % Time vector over 1 second


choice = input('Enter a choice (add, sub, or mul): ', 's');

% Initialize return variable
signal = [];

switch choice
    case 'add'
        disp('You selected option 1.');
        signal = sin(2*pi*fm*t) + cos(2*pi*fm*t);
        
    case 'sub'
        disp('You selected option 2.');
        signal = sin(2*pi*fm*t) - cos(2*pi*fm*t);
        
    case 'mul'
        disp('You selected option 3.');
        signal = sin(2*pi*fm*t) .* cos(2*pi*fm*t);
        
    otherwise
        disp('Invalid choice.');
        signal = sin(2*pi*fm*t);
end


% Compute frequency spectrum in dB
n = length(signal);
f = (-n/2:n/2-1)*(fs/n); % Frequency axis centered at 0
S_f = abs(fftshift(fft(signal)/n));  % Normalize FFT
S_f_dB = 20*log10(S_f / max(S_f));  % dB scale with normalization

% Plot normalized spectrum in dB
figure(1);
plot(f, S_f);
title('Normalized Frequency Spectrum of PAM Signal');
xlabel('Frequency (Hz)');
ylabel('Magnitude (dB)');
grid on;

figure(2);
plot(f, S_f_dB);
title('Normalized Frequency Spectrum (dB) of PAM Signal');
xlabel('Frequency (Hz)');
ylabel('Magnitude (dB)');
grid on;
web('https://www.salimwireless.com/search?q=fft%20fourier%20transform', '-browser');

Further Reading


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