# Harmonic1DMD:Background:Harmonic 1DMD Fourier Transform

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A powerful mathematical property discovered by Jean-Baptiste-Joseph Fourier, the Fourier Transform has numerous applications. Basically the idea behind it is that any continuous function can be represented as a sum of sin and cosine waves of varying amplitude and phases. The transform produces a new function of amplitudes with a frequency domain.

There are numerous applications for this property. Two notable ones include (1) a function can be re-characterized into series of more manageable (and perhaps actually solvable) equations; (2) an unknown wave made up of multiple frequencies (think sound waves) can be broken down to its component parts for comparison with other waves.

This simulation transforms the displacements to accomplish both previously said reasons, however more so the latter. Initial conditions are set up from a series of wave equations, and run concurrently on one set of atoms. The simulation can monitor the motion and break it down to its wave component parts. Also given an unknown equation or set of motion, the simulation can monitor the motion and describe it in a way that is easier to understand, interpret, and compare.