function [X_AXIS, FFT_OUTPUT] = fft_analysis(x,T)
%
%[X_AXIS, FFT_OUTPUT] = FFT_ANALYSIS(x,T)
%
%This function gives the fft of a time domain signal.
%x is the time domain signal and T is the sampling period.
%If the sampling period isn't specified, it is set to 125 us (1/8kHz)
%The input x must be a column matrix in order for the x-axis to be
%computed correctly.
%This function computes the fft; centers the spectral
%information around 0 Hz; and computes the x-axis frequency
%points for each fft output sample. This function returns 
%the fft centered output and the x-axis.

if nargin == 1
   T = 1/8e3;
end

FFT_OUTPUT = fft(x); %compute the FFT of x
FFT_OUTPUT = fftshift(FFT_OUTPUT); %center the spectrum of the FFT output
X_AXIS = -(size(FFT_OUTPUT,2)/2):(size(FFT_OUTPUT,2)/2)-1; %set axis to -NUM_OF_SAMPLES/2 < SAMPLE < (NUM_OF_SAMPLES/2)-1
X_AXIS  = X_AXIS*(1/(size(FFT_OUTPUT,2)*T));  %set frequency axis to -Fs/2 < F < (Fs/2)-1  axis (Hz) = K(1/NT); axis (radians) = K(2pi/NT)
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