# Periodic Signal Processing

## General Description

This Project aims to successfully compress the extensive libraries of periodic sounds and tones that are contained in desktop music notation software suites to a size that is adequate for mobile devices with often less than 2 gigabytes of available space across the whole phone. This is accomplished through a mathematical approximation of the original files by means of a representative function.

Solutions to the wave equation with string like boundary conditions gives solutions in the form of a series of descrete functions. Due to this, The fourier spectra of the input signal can be well modeled as a fourier series with time dependent amplitudes.

- the program searches through the spectra to find an adequate root frequency. it does so by measuring the ratio of the 2 strongest frequency peaks, and rounding to the nearest fraction of digits.
- the time dependent fourier series is then taken. this is done by means of a window function integrated across the entire spectra.
- the output amplitudes and relative delta values it then curve fitted to a series of functions that represent a variety of effects such as : pitch bend, vibrato, decay attack and release.
- the function or combination of functions with the smallest sum of squared differences value is then output. Step 3 is repeated itoratively until all of the series terms are curve fitted to a desired accuracy.
- the final set of functions can be played back to verify accurate fitting has been produced and saved as an xml file to be loaded later.

This work was presented at the APS(American Physics Association) yearly conference.

You can find the Poster presented for this research here: