Question

Is there a way to mathematically transform a piecewise function to make it cyclic so that the segment repeats itself again?

Answer 1

@mhchen

Answer 2

For instance if we have a function f(x) defined as

Answer 3

How can I add periodicity? Is there a way I can apply a Fourier transform? Any other transform?

Answer 4

(And yes this is without using any CAS)

Answer 5

you can use fourier transformation to do this

Answer 6

take the fourier transform of all the 'pieces' of your function with proper limits and add those transofmations together

Answer 7

Hey man thank you so much for responding I need it for a project quite badly.
If you have some extra time, can you show how to do it with this example on desmos (like maybe graph it on there)?

https://www.desmos.com/calculator/fbdbwmuhcr

Answer 8

really do appreciate it by the way

Answer 9

i'll be using fourier sine series for this

Answer 10

\[\huge{f(x) = \sum_{n=1}^{n=\infty}b_n}sin\left(\frac{n\pi x}{L}\right)\]

Answer 11

\[\large {b_n = \left(\int_{0}^{2}x^2sin\left( \frac{n\pi x}{5}\right)dx + \int_{2}^{4}(3.307 + lnx)sin\left( \frac{n\pi x}{5} + \right)dx + \\~~~~~~~~~~~~ \int_{4}^{5}(-4.693x+23.465)sin\left( \frac{n\pi x}{5}\right)dx\right)}\]

Answer 12

desmos can't digest this function, try MATLAB

Answer 13

Thank you so much for your help!!!! If I have any additional questions I'll refer back here. God Bless!

Answer 14

yw :-)