Plotting even and odd extensions of a function

What's an easy way of plotting odd or even extentions of a function on the whole real number line?

For instance, if you are given on , how can one plot the fourier series of this function for odd and even extentions.

Answer 1

[Star Strider]

I am not certain what you mean by ‘extensions’.

Fourier series are comprised of cosine functions (real coefficients) that are even, and sine functions (imaginary coefficients) that are odd. See the Wikipedia article on Even and odd functions (link) for an extended discussion.

[steven]

This example from Desmos visualizes what I mean by odd extention. I would like to plot a simliar piecewise function on all real number line.

[Star Strider]

I’m still not certain what you mean by ‘extension’.

That page illustrates the effect of adding more Fourier analysis ‘frequencies’ (with their associated coefficients) to the reconstruction of that waveform. The more terms you add, the more closely the reconstruction from the Fourier coefficients will approach the analysed waveform.

With respect to a square wave, that is very easy to demonstrate:

t = linspace(0, 3, 500);
f = sin(t(:) * [1 3 5 7 9] *2*pi) * 1./[1 3 5 7 9];

figure
plot(t, cumsum(f,2))
grid

Experiment to get the result you want.