A basic example of reconstructing FFT frequency axis

fft_reconstruct.m

% A simple example of how to reconstruct
% the frequency components from an FFT
%% Clean up the workspace
clear all;
close all;
clc;

%% Create the initial parameters
Window=5; %Set how long in time to sample + and -
Fs=100; %Set the sampling frequency
% Fs should be set atleast 2x max 
% frequency in the signal
% With the signal below, the max frequency is 
% 22Hz meaning we want to sample atleast at 44Hz

%% Generate the time domain signals
x=-Window:1/Fs:Window; %Create the time signal
y=5*sin(10*2*pi*x)+3*sin(22*2*pi*x)+cos(13*2*pi*x)+7;

% Plot the time domain signal
figure(1);
plot(x,y);

%% Compute and plot the frequency domain signal
figure(2);

% Extract the max frequency that the FFT
% can compute from the Fs we have specified
fmax=Fs/2; %Application of Nyquist Theorem

% Compute the magnitude of the fft of y
N=441;
FFTy=fftshift(abs(fft(y,N)));

% The frequency axis is generated using linspace
f_axix=linspace(-fmax,fmax,N-1);

% Plot the FFT using stem
stem(f_axix,FFTy(2:end)./length(FFTy));