%taken from e80 course at Harvey Mudd College

function [X,freq]=centeredFFT(x,Fs)
%x is the signal that is to be transformed
%Fs is the sampling rate


N=length(x);

%this part of the code generates that frequency axis
if mod(N,2)==0
    k=-N/2:N/2-1; % N even
else
    k=-(N-1)/2:(N-1)/2; % N odd
end
T=N/Fs;
freq=k/T;  %the frequency axis

%takes the fft of the signal, and adjusts the amplitude accordingly
X=fft(x)/N; % make up for the lack of 1/N in Matlab FFT
X=fftshift(X); %shifts the fft data so that it is centered