Analysis of phase derivatives of speech signals

Abstract

This paper examines the phase derivatives of speech signals. The instantaneous complex spectra obtained in the single frequency filtering (SFF) analysis of signals is used to derive the phase function. The problem of phase wrapping is avoided by using the proposed modification to SFF analysis to derive a scaled down version of the phase function. We consider the derivatives of the exponent (i.e., logarithm) of the complex SFF spectra, with respect to frequency, time, and both frequency and time. The imaginary part of the exponent is the phase function, and the real part is the log magnitude function. The negative derivative of phase with respect to frequency is the group delay (GD) function, and the derivative of the phase with respect to time is the instantaneous frequency (IF) function. The features of speech production displayed through the GD function are compared with the features displayed through the derivative with respect to frequency of the corresponding log magnitude function. Likewise, the features of production displayed through the IF function are compared with the features displayed through the derivative with respect to time of the corresponding log magnitude function. The speech production characteristics reflected in these representations of phase derivatives are examined for different types of utterances.