Chirp-like model and its parameter estimation

TL;DR

This paper introduces a chirp-like signal model that simplifies parameter estimation compared to traditional chirp models, with proven asymptotic properties and successful application to speech data.

Contribution

It proposes a new chirp-like model that approximates chirp signals more easily, along with estimation procedures and asymptotic analysis.

Findings

Estimation procedures are asymptotically consistent.

Simulation studies confirm theoretical results.

Application to speech data shows model effectiveness.

Abstract

We propose a chirp-like signal model as an alternative to a chirp model and a generalisation of the sinusoidal model, which is a fundamental model in the statistical signal processing literature. It is observed that the proposed model can be arbitrarily close to the chirp model. The propounded model is similar to a chirp model in the sense that here also the frequency changes linearly with time. However, the parameter estimation of a chirp-like model is simpler compared to a chirp model. In this paper, we consider the least squares and the sequential least squares estimation procedures and study the asymptotic properties of these proposed estimators. These asymptotic results are corroborated through simulation studies and analysis of four speech signal data sets have been performed to see the effectiveness of the proposed model, and the results are quite encouraging.