Linear prediction using homomorphic deconvolution in the autocorrelation domain

The conventional model of the linear prediction analysis suffers from difficulties in estimating vocal tract characteristics of high-pitched speakers. This paper shows that for voiced speech the vocal tract characteristics can be estimated accurately by homomorphic deconvolution in the autocorrelation domain. The speech autocorrelation function used by linear prediction is actually an 'aliased' version of that of the vocal tract system impulse response. This aliasing occurs due to the periodic nature of voiced speech. By using cepstrum analysis, the effect of this periodicity is eliminated from the autocorrelation function which is also periodic with the same periodicity as speech itself. The formant frequencies estimated using the deconvolved autocorrelation sequences of the system impulse response are found to be accurate by more than an order of magnitude when compared with the conventional linear prediction. The accuracy of formant estimation is verified on synthetic vowels for a wide range of pitch periods. The validity of the proposed method is also examined by inspecting the estimated spectral envelopes of real speech spoken by a female child.