Fourier Analysis and Compression of String based Instrument Signals

Fourier analysis provides many possibilities in the study of periodic signals’ compression. Previous modeling of the normal modes of three weakly coupled strings under small oscillations has provided functions with decaying amplitudes for each of the normal modes. Outside of the small oscillation regime, the periodicity of each mode is found to be dependent on the amplitude. Comparing this model to the instrument's signal can aid in the compression of these signals via a representative output function instead of a representative raw signal. Implementing Fourier synthesis, with a sine cardinal function as a window and linear regression techniques, we simplified the signals into simple functions containing amplitude decay and time dependent periodicity. This was achieved through independent linear regression of the amplitude and the phase. The resulting output functions resulted in a compression ratio of 300 or greater than 95% space savings when deflated. It is the goal of this investigation to provide a proof of concept for future compression techniques.