Example of an FFT computation and plotting.

fast_fourier.m

function [frequency, amplitude] = fast_fourier(time, signal, sample_rate, varargin)
% function [frequency, amplitude] = fast_fourier(time, signal, sample_rate, varargin)
%
% Parameter
% =========
% time : double, size: 1 x n
%     The time vector.
% signal : double, size: 1 x n
%     The signal as a function of time.
% sample_rate : double, size 1 x 1
%     The sample rate of the signal.
% plot : boolean, optional
%     If true a plot of the results will appear.
%
% Returns
% =======
% frequency : double, size: 1 x m
%    The FFT frequencies.
% amplitude : double, size: 1 x m
%    The amplitude as a function of frequency.

n = length(time);       % Signal length
NFFT = 2 ^ nextpow2(n); % Next power of 2 from length of y

amplitude = fft(signal, NFFT) / n;
frequency = sample_rate / 2 * linspace(0, 1, NFFT / 2);

if length(varargin) > 0 && varargin{1}
    fig = figure();
    plot(frequency, 2 * abs(amplitude(1:NFFT / 2 )));
    title('Single-Sided Amplitude Spectrum of the Signal');
    xlabel('Frequency (Hz)');
    ylabel('|Amplitude(Frequency)|');
end

matlab_fft_example.m

% fft Fourier transform, get the right amlitude and frequency
Fs = 1000;                    % Sampling frequency
T = 1/Fs;                     % Sample time
L = 1000;                     % Length of signal
t = (0:L-1)*T;                % Time vector
% Sum of a 50 Hz sinusoid and a 120 Hz sinusoid
x = 0.7*sin(2*pi*50*t) + sin(2*pi*120*t);⋅
y = x + 1*randn(size(t));     % Sinusoids plus noise
figure
plot(Fs*t(1:50),y(1:50))
title('Signal Corrupted with Zero-Mean Random Noise')
xlabel('time (milliseconds)')
NFFT = 2^nextpow2(L); % Next power of 2 from length of y
Y = fft(y,NFFT)/L;
f = Fs/2*linspace(0,1,NFFT/2);

% Plot single-sided amplitude spectrum.
figure
plot(f,2*abs(Y(1:NFFT/2)))⋅
title('Single-Sided Amplitude Spectrum of y(t)')
xlabel('Frequency (Hz)')
ylabel('|Y(f)|')⋅