FFT Magnitude and Phase Spectrum using MATLAB

• 📘 Overview & Theory
• 🧮 MATLAB Code 1
• 🧮 MATLAB Code 2
• 📚 Further Reading

 

MATLAB Code 

% Developed by SalimWireless.Com

clc;
clear;
close all;

% Configuration parameters
fs = 10000; % Sampling rate (Hz)
t = 0:1/fs:1-1/fs; % Time vector creation

% Signal definition
x = sin(2 * pi * 100 * t) + cos(2 * pi * 1000 * t);

% Calculate the Fourier Transform
y = fft(x);
z = fftshift(y);

% Create frequency vector
ly = length(y);
f = (-ly/2:ly/2-1) / ly * fs;

% Calculate phase while avoiding numerical precision issues
tol = 1e-6; % Tolerance threshold for zeroing small values
z(abs(z) < tol) = 0;
phase = angle(z);

% Plot the original Signal
figure;
subplot(3, 1, 1);
plot(t, x, 'b');
xlabel('Time (s)');
ylabel('|y|');
title('Original Messge Signal');
grid on;

% Plot the magnitude of the Fourier Transform
subplot(3, 1, 2);
stem(f, abs(z), 'b');
xlabel('Frequency (Hz)');
ylabel('|y|');
title('Magnitude of the Fourier Transform');
grid on;

% Plot the phase of the Fourier Transform
subplot(3, 1, 3);
stem(f, phase / pi, 'b');
xlabel('Frequency (Hz)');
ylabel('Phase (radians)');
title('Phase of the Fourier Transform');
grid on;

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

Output 

 

 

 

Copy the MATLAB Code above from here

% Developed by SalimWireless.Com clc; clear; close all; % Configuration parameters fs = 10000; % Sampling rate (Hz) t = 0:1/fs:1-1/fs; % Time vector creation % Signal definition %x = cos(2 * pi * 15 * t - pi/2) + sin(2 * pi * 40 * t); x = sin(2 * pi * 100 * t) + cos(2 * pi * 1000 * t); % Calculate the Fourier Transform y = fft(x); z = fftshift(y); % Create frequency vector ly = length(y); f = (-ly/2:ly/2-1) / ly * fs; % Calculate phase while avoiding numerical precision issues tol = 1e-6; % Tolerance threshold for zeroing small values z(abs(z) < tol) = 0; phase = angle(z); % Plot the original Signal figure; subplot(3, 1, 1); plot(t, x, 'b'); xlabel('Time (s)'); ylabel('|y|'); title('Original Messge Signal'); grid on; % Plot the magnitude of the Fourier Transform subplot(3, 1, 2); stem(f, abs(z), 'b'); xlabel('Frequency (Hz)'); ylabel('|y|'); title('Magnitude of the Fourier Transform'); grid on; % Plot the phase of the Fourier Transform subplot(3, 1, 3); stem(f, phase / pi, 'b'); xlabel('Frequency (Hz)'); ylabel('Phase (radians)'); title('Phase of the Fourier Transform'); grid on; web('https://www.salimwireless.com/search?q=fourier%20transform', '-browser');

 

Another MATLAB Code

clc;
clear;
close all;

% Parameters
fs = 100;           % Sampling frequency
t = 0:1/fs:1-1/fs;  % Time vector

% Signal definition
x = cos(2*pi*15*t - pi/4) - sin(2*pi*40*t);

% Compute Fourier Transform
y = fft(x);
z = fftshift(y);

% Frequency vector
ly = length(y);
f = (-ly/2:ly/2-1)/ly*fs;

% Compute phase

z(abs(z) < 1e-6) = 0;
phase = angle(z);

% Plot magnitude of the Fourier Transform
figure;
subplot(2, 1, 1);
stem(f, abs(z), 'b');
xlabel('Frequency (Hz)');
ylabel('|y|');
title('Magnitude of Fourier Transform');
grid on;

% Plot phase of the Fourier Transform
subplot(2, 1, 2);
stem(f, phase, 'b');
xlabel('Frequency (Hz)');
ylabel('Phase (radians)');
title('Phase of Fourier Transform');
grid on;

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

 

Output 

Copy the MATLAB Code above from here

% The code is written by SalimWireless.Com clc; clear; close all; % Parameters fs = 100; % Sampling frequency t = 0:1/fs:1-1/fs; % Time vector % Signal definition x = cos(2*pi*15*t - pi/4) - sin(2*pi*40*t); % Compute Fourier Transform y = fft(x); z = fftshift(y); % Frequency vector ly = length(y); f = (-ly/2:ly/2-1)/ly*fs; % Compute phase z(abs(z) < 1e-6) = 0; phase = angle(z); % Plot magnitude of the Fourier Transform figure; subplot(2, 1, 1); stem(f, abs(z), 'b'); xlabel('Frequency (Hz)'); ylabel('|y|'); title('Magnitude of Fourier Transform'); grid on; % Plot phase of the Fourier Transform subplot(2, 1, 2); stem(f, phase, 'b'); xlabel('Frequency (Hz)'); ylabel('Phase (radians)'); title('Phase of Fourier Transform'); grid on; web('https://www.salimwireless.com/search?q=fourier%20transform', '-browser');  

Further Reading

1. Fourier Transform of Sine or Cosine
2. Definition of the Fourier Series
3. Cooley-Tukey algorithm for Fast Fourier Transform (FFT) in MATLAB
4. Fourier Spectral Analysis
5. Power Spectral Density Calculation Using FFT in MATLAB
6. Autocorrelation and Periodicity of a Signal