Zero Quefrency in Speech Analysis
John I. Makhoul · The Journal of the Acoustical Society of America · 1973
The zero component of the cepstrum (transform of the log spectrum) is also known as the zero quefrency c0. c0 contains information about R0 (the total energy in the signal), as well as the shape of the signal power spectrum. The energy information can be removed by subtracting R0 from c0. If that difference is exponentiated, one obtains a normalized parameter V = ec0/R0. V can be interpreted as the ratio of the geometric mean to the arithmetic mean of the spectrum. For any spectrum, it can be shown that 0⩽V⩽1. The value of V depends only on the spectral shape. By taking advantage of the fact that most voiced sounds have the energy concentrated at low frequencies, while most unvoiced sounds have the energy relatively spread out across the spectrum, the parameter V can be used as a voicing detector. A detailed analysis of the behavior of V as a function of different spectral shapes can be found in Makhoul and Wolf [BBN Rep. No. 2304 (1972)]. Conditions under which V can be used as a voicing detector will be discussed.