How to Plot Frequency Spectrum in MATLAB: Simple Guide

To plot the frequency spectrum in MATLAB, use the fft function to compute the Fast Fourier Transform of your signal, then plot the magnitude against frequency using plot. You typically calculate the frequency axis based on the sampling rate and signal length to label the spectrum correctly.

Syntax

The basic syntax to plot a frequency spectrum in MATLAB involves these steps:

• Y = fft(x): Computes the Fast Fourier Transform of signal x.
• P2 = abs(Y/L): Calculates the two-sided amplitude spectrum, where L is the length of x.
• P1 = P2(1:L/2+1): Extracts the single-sided amplitude spectrum.
• f = Fs*(0:(L/2))/L: Creates the frequency axis, where Fs is the sampling frequency.
• plot(f, P1): Plots the frequency spectrum.

matlab

Y = fft(x);
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);
f = Fs*(0:(L/2))/L;
plot(f, P1);

Example

This example shows how to plot the frequency spectrum of a simple sine wave signal sampled at 1000 Hz.

matlab

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

% Create a signal with a 50 Hz sine wave
x = 0.7*sin(2*pi*50*t);

% Compute the FFT
Y = fft(x);

% Compute the two-sided spectrum P2
P2 = abs(Y/L);

% Compute the single-sided spectrum P1 based on P2 and the even-valued signal length L
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);

% Define the frequency domain f
f = Fs*(0:(L/2))/L;

% Plot the single-sided amplitude spectrum
plot(f, P1)
title('Single-Sided Amplitude Spectrum of X(t)')
xlabel('Frequency (Hz)')
ylabel('|P1(f)|')
grid on;

Output

A plot window showing a peak at 50 Hz with amplitude about 0.7

Common Pitfalls

Common mistakes when plotting frequency spectrum in MATLAB include:

• Not normalizing the FFT output by the signal length, which leads to incorrect amplitude values.
• Plotting the two-sided spectrum instead of the single-sided spectrum for real signals, causing confusion.
• Incorrect frequency axis calculation, which mislabels the frequency peaks.
• Forgetting to multiply the single-sided spectrum values (except DC and Nyquist) by 2 to conserve signal energy.

matlab

%% Wrong way (no normalization and wrong frequency axis)
Y = fft(x);
plot(abs(Y));

%% Right way
P2 = abs(Y/L);
P1 = P2(1:L/2+1);
P1(2:end-1) = 2*P1(2:end-1);
f = Fs*(0:(L/2))/L;
plot(f, P1);

Quick Reference

Remember these key steps for plotting frequency spectrum in MATLAB:

• Use fft to get frequency components.
• Normalize by signal length L.
• Use single-sided spectrum for real signals.
• Calculate frequency axis with sampling rate Fs.
• Multiply amplitudes by 2 except for DC and Nyquist.

Key Takeaways

Use fft and normalize by signal length to get correct amplitude spectrum.

Plot the single-sided spectrum for real-valued signals to see meaningful frequencies.

Calculate the frequency axis using the sampling frequency and signal length.

Multiply amplitudes by 2 except for the first and last points to conserve energy.

Always label your plot axes clearly with frequency in Hz and amplitude.