Finite word length effects of the Leroux-Gueguen algorithm in computing reflection coefficients

An experiment to study the effects of finite word length computation of reflection coefficients using the Leroux-Gueguen algorithm(1) is described. The word lengths specified are the number of bits (in two's complement) for the reflection coefficients, and the residuals. The effects studied are the number of instabilities and statistics of Itakura's likelihood ratio(6) for a data set consisting of one utterance each by three male, three female and three child speakers at three different sampling rates: 12.5kHz, 10 kHz and 8 kHz. The results are classified according to voiced and unvoiced frames. The statistics obtained are valuable in the design considerations of special hardware for LPC analysis circuits and speech recognition systems. Spectrograms of a sample utterance demonstrate word length effects. A tape of synthesized speech demonstrates word length effects.