A synthesis of percussion musical instruments sounds is provided using a microprocessor (17) that implements an all pole lattice filter and applying either a single impulse signal to the filter or N samples of an excitation signal sequence to the filter by a memory (19). The coefficients of the filter are determined by storing digital samples (501) of desired musical note from a desired percussion instrument, generating a Fourier transform to get a spectrum (502), picking the peaks of the spectrum (503) to select the most prominent components in the spectrum and determining wanted frequencies for decaying sine waves and for the frequencies finding the time envelope and estimating therefrom the pole radius.