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

Answer 1

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).

Answer 2

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')