## Simple real Fourier series approximation

Version 1.1 (3.37 KB) by
Computes coefficients for the real Fourier series approximation to a data set.

Updated Tue, 03 Mar 2020 21:45:39 +0000

Includes two functions: Fseries.m and Fseriesval.m
[a,b] = Fseries(X,Y,n) fits an nth-order Fourier expansion of the form
y = a_0/2 + Sum_k[ a_k cos(kx) + b_k sin(kx) ]
to the data in the vectors X & Y, using a least-squares fit.

Y = Fseriesval(a,b,X) evaluates the Fourier series defined by the coefficients a and b at the values in the vector X.

Extra arguments allow for rescaling of X data and sin-only or cosine-only expansions.

Example:
% Generate data
x = linspace(0,2,41)';
y = mod(2*x,1);
% Use FSERIES to fit
[a,b,yfit] = Fseries(x,y,10);
% Evaluate on finer grid
xfine = linspace(0,2)';
yfine = Fseriesval(a,b,xfine);
% Visualize results
plot(x,y,'x',x,yfit,'o',xfine,yfine)

This generates the attached image of a 10-term Fourier series approximation of a sawtooth wave.

### Cite As

Matt Tearle (2023). Simple real Fourier series approximation (https://www.mathworks.com/matlabcentral/fileexchange/31013-simple-real-fourier-series-approximation), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2010b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
1.1

Made a quick hack to the input-parsing utility to deal with the change in precedence rules. It should now work in 19b and in previous versions. Hasn't been really thoroughly tested, though, so please report any problems.

1.0.0.1