Open AccessEstimation of parameters of a harmonic chirp model
Author(s) -
Grover Rhythm,
Kundu Debasis,
Mitra Amit
Publication year - 2021
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
eISSN - 1751-9683
pISSN - 1751-9675
DOI - 10.1049/sil2.12038
Subject(s) - estimator , least squares function approximation , chirp , mathematics , harmonic , estimation theory , generalized least squares , algorithm , estimation , mathematical optimization , computer science , statistics , laser , physics , management , quantum mechanics , optics , economics
Here, we address the problem of estimation of the parameters of a harmonic chirp model, often encountered in speech and music applications. This model was introduced recently by Christensen and Jensen [1] as an extension of a standard harmonic model. We propose two methods of estimation: the least squares estimation method and the approximate least squares estimation method. We establish the asymptotic properties of the least squares estimators as well as the approximate least squares estimators of the parameters of this model under the assumption of stationary errors. These asymptotic properties are proved analytically as well as corroborated through simulation experiments. We present two speech signal data sets and their analysis using both the estimation methods. The results show that the proposed methods perform reasonably well for estimating the unknown model parameters.