On first rahmonic amplitude in the analysis of synthesized aperiodic voice signals

Rahmonics comprise the prominent peaks in the cepstrum of voiced speech; their locations correspond to the fundamental period and its multiples. The amplitude of the first rahmonic, R1, has previously been used to indicate voice quality. Although a correspondence between R1 and the richness of the harmonic spectrum for voiced speech is well recognized, a formal description has remained absent. A theoretical description of rahmonic analysis of voiced speech containing aspiration noise is provided, leading to a characterization of R1. The theory suggests that R1 is directly proportional to the geometric mean harmonics-to-noise ratio (gmHNR), where the gmHNR is defined as the mean of the individual spectral (i.e., at specific frequency locations) harmonics-to-noise ratios in dB. This hypothesis is validated using synthetically generated voice signals. R1 is shown to be directly proportional to gmHNR (measured directly from the dB spectrum). It is shown that R1 (estimated from speech) is directly proportional to R1 taken from the glottal signal. R1 and gmHNR (measured spectrally) underestimate the actual gmHNR when (averaged) noise levels exceed harmonic levels. Limiting the number of harmonics in the analysis window overcomes this problem and also alleviates the (temporal) window length/f0 dependence of R1 when estimated period synchronously.