How to Use FFT in MATLAB: Syntax, Example, and Tips

In MATLAB, use the fft function to compute the fast Fourier transform of a signal. Call Y = fft(x) where x is your input data vector, and Y is the frequency domain result.

Syntax

The basic syntax for the fast Fourier transform in MATLAB is:

• Y = fft(x): Computes the FFT of vector x.
• Y = fft(x, n): Computes the FFT with length n, padding or truncating x as needed.
• Y = fft(x, [], dim): Computes FFT along dimension dim of array x.

Explanation: x is your input data, usually a time-domain signal. Y is the complex frequency-domain output. The optional n controls the FFT length, and dim specifies which dimension to transform for multi-dimensional data.

matlab

Y = fft(x)
Y = fft(x, n)
Y = fft(x, [], dim)

Example

This example shows how to compute the FFT of a simple sine wave and plot its magnitude spectrum.

matlab

Fs = 1000;            % Sampling frequency in Hz
T = 1/Fs;             % Sampling period
L = 1000;             % Length of signal
t = (0:L-1)*T;       % Time vector

f = 50;               % Frequency of sine wave
x = 0.7*sin(2*pi*f*t); % Generate sine wave

Y = fft(x);           % Compute FFT

P2 = abs(Y/L);         % Two-sided spectrum magnitude
P1 = P2(1:L/2+1);     % Single-sided spectrum
P1(2:end-1) = 2*P1(2:end-1); % Adjust amplitude

f_axis = Fs*(0:(L/2))/L; % Frequency axis

plot(f_axis, P1)
title('Single-Sided Amplitude Spectrum of x(t)')
xlabel('Frequency (Hz)')
ylabel('|P1(f)|')

Output

A plot window showing a peak at 50 Hz in the amplitude spectrum

Common Pitfalls

Common mistakes when using fft in MATLAB include:

• Not normalizing the FFT output, which can lead to incorrect amplitude interpretation.
• Ignoring that FFT output is complex; you usually want the magnitude abs(Y) or power spectrum.
• Not using the single-sided spectrum for real signals, which doubles the amplitude except at DC and Nyquist.
• Confusing the frequency axis scale; you must create it based on sampling frequency and FFT length.

matlab

%% Wrong: Plot raw FFT output without magnitude or normalization
Y_wrong = fft(x);
plot(abs(Y_wrong))
title('Incorrect FFT Plot')

%% Right: Plot normalized magnitude spectrum
P2 = abs(Y_wrong/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);
plot(f_axis, P1)
title('Correct Single-Sided Amplitude Spectrum')

Output

First plot shows magnitude of complex values (not normalized), second plot shows correct amplitude spectrum

Quick Reference

Remember these tips when using fft in MATLAB:

• Use abs(fft(x)) to get magnitude.
• Normalize by dividing by signal length for correct amplitude.
• Use single-sided spectrum for real signals.
• Generate frequency axis with Fs*(0:(N/2))/N.

Key Takeaways

Use fft(x) to compute the fast Fourier transform of signal x in MATLAB.

Normalize the FFT output by signal length and use the magnitude abs(Y) for correct amplitude.

For real signals, use the single-sided spectrum by taking the first half of the FFT result and doubling amplitudes except at DC and Nyquist.

Create the frequency axis based on sampling frequency and FFT length to interpret the spectrum correctly.

Avoid plotting raw complex FFT output without processing, as it is not meaningful visually.