On the relationship between instantaneous frequency and pitch in speech signals

Authors: Zied Mnasri, Hamid Amiri

Abstract:

In this paper, a novel relationship between instantaneous frequency (IF) and fundamental frequency (F0) in voiced parts of speech signals is presented. IF is calculated as the time-derivative of the phase of the analytic signal, yielding from Hilbert transform. Whereas F0 can be extracted using any classical pitch tracking technique (e.g. autocorrelation, cepstrum, subharmonic-to-harmonic ratio (SHR) ...ect.) this relashionship has been verified independently of the tool used to extract F0. This relationship states that the envelope of the residual of the instantaneous frequency, defined as the difference between IF and the maximum of harmonics tends to F0. Such a direct relationship may be useful for further developments of F0 extraction directly from the speech signal, avoiding the approximation that exists in most pitch extraction techniques.