Synthesis of percussion musical instrument sounds

A method of analyzing a percussion musical instrument sound comprising the steps of:

• storing digital samples of a musical note sound made by a percussion musical instrument;
• generating a Fourier transform of said samples to get a spectrum of said note sound;
• picking peaks of said spectrum of said note sound in said spectrum prominent components in said spectrum to determine wanted frequencies for decaying sine waves;
• for the wanted frequencies finding an amplitude envelope as a function of time for each picked peak;
• estimating pole radius by finding a correlation coefficient for said amplitude envelope;
• determining initial amplitude of each decaying exponential by determining amplitude that minimizes the squared error;
• and
• determining initial state such that modes of oscillation will have the proper amplitude relationship with each other.

An apparatus for providing synthesis of a percussion sound comprising:

• a microprocessor that implements an all pole lattice filter;
• and
• means for applying n samples of an excitation sequence to said microprocessor;
• said filter having filter coefficients optimized for a desired percussion sound when said excitation sequence is applied;
• said filter coefficients are provided by the steps of:
• storing digital samples of the sounds of a desired musical note from a desired percussion instrument;
• for that entire note generating a Fourier transform to get a spectrum of that note;
• picking the peaks of the spectrum to select most prominent components in the spectrum and determining wanted frequencies for decaying sine waves;
• and
• for the frequencies finding time envelope and estimating therefrom the pole radius.