So, I've been working on a project to compare the Fourier Series of a Piano versus that of a Keyboard. I've computed the FFT on MATLAB using this code:
dt = 1/fs
t = (1:length(data))*dt
X=fft(data)
df=1/(length(data)*dt)
f=(1:length(X))*df
figure
plot(f,abs(X))
I plotted the FFT, and this is what I got:
Now, when I clicked GENERATE CODE, this is what I got:
function createfigure(X1, YMatrix1)
%CREATEFIGURE(X1, YMATRIX1)
% X1: vector of x data
% YMATRIX1: matrix of y data
% Auto-generated by MATLAB on 31-Aug-2016 19:32:43
% Create figure
figure1 = figure;
% Create axes
axes1 = axes('Parent',figure1);
hold(axes1,'on');
% Create multiple lines using matrix input to plot
plot(X1,YMatrix1);
box(axes1,'on');
NOW, My question is, how do I come up with the Fourier Series for this FFT? What I mean is, how do I include the Integration, Matrices, etc, essentially the mathematics behind this in my research paper? I can't just upload this graph, can I. I would appreciate it if somebody could explain how to do it and also support it with an example.
THANKS IN ADVANCE :-)