Calculate area under FFT graph in MATLAB

Question

Currently I did a FFT of a set of data which gives me a plot with frequency at x axis and amplitude at y axis. I would like to calculate the area under the graph to give me the energy.

I am not sure how to determinate the area because I am without the equation and also I only want a certain area of the plot rather than whole area under the plot. Is there a way I can do it?

Answer 1

There are many ways to do numerical integration with Matlab. Here is an example:

%# create some data
x = linspace(0,pi/2,100); %# 100 equally spaced points between 0 and pi/2
y = sin(x);

%# integrate using trapz, which calculates the area in the trapezoid defined by 
%# x(k),x(k+1),y(k),y(k+1) for k=1:length(x)
integral = trapz(x,y);

%# if you only want to integrate part of the data, do
partialIntegral = trapz(x(10:20),y(10:20));

%# show the integrated area
figure, 
area(x,y); 
hold on, 
area(x(10:20),y(10:20),'FaceColor','red')

Answer 2

The FFT is discrete, not continuous - you just need to sum all the bin values. If you're looking at the power spectrum (magnitude squared) then the bin values are in W/Hz, so you would need to multiply each value (or alternatively just the sum), by the bin width in Hz to get power (and hence the total energy in your input sample).