On the Parameter Estimation of Sinusoidal Models for Speech and Audio Signals

TL;DR

This paper compares three sinusoidal models for speech and audio signal parameter estimation, analyzing their accuracy and robustness across synthetic and real signals, and suggests combining their strengths for improved audio analysis.

Contribution

It provides a comparative analysis of the standard SM, EDSM, and eaQHM models, highlighting their respective advantages and proposing a hybrid approach for better audio signal processing.

Findings

eaQHM outperforms EDS in medium-to-large window analysis

EDSM yields higher reconstruction for small window sizes

Future work may combine adaptivity and robustness of the models

Abstract

In this paper, we examine the parameter estimation performance of three well-known sinusoidal models for speech and audio. The first one is the standard Sinusoidal Model (SM), which is based on the Fast Fourier Transform (FFT). The second is the Exponentially Damped Sinusoidal Model (EDSM) which has been proposed in the last decade, and utilizes a subspace method for parameter estimation, and finally the extended adaptive Quasi-Harmonic Model (eaQHM), which has been recently proposed for AM-FM decomposition, and estimates the signal parameters using Least Squares on a set of basis function that are adaptive to the local characteristics of the signal. The parameter estimation of each model is briefly described and its performance is compared to the others in terms of signal reconstruction accuracy versus window size on a variety of synthetic signals and versus the number of sinusoids on real signals. The latter include highly non stationary signals, such as singing voices and guitar solos. The advantages and disadvantages of each model are presented via synthetic signals and then the application on real signals is discussed. Conclusively, eaQHM outperforms EDS in medium-to-large window size analysis, whereas EDSM yields higher reconstruction values for smaller analysis window sizes. Thus, a future research direction appears to be the merge of adaptivity of the eaQHM and parameter estimation robustness of the EDSM in a new paradigm for high-quality analysis and resynthesis of general audio signals.