Estimating the parameters of multiple chirp signals

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.This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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“…Using Lemma 2 of Lahiri [35], it is easy to see that: to get the desired result. To show this, we proceed as follows.…”

Section: Consistency Of the Lsesmentioning

confidence: 98%

Estimation of parameters of a harmonic chirp model

Grover

Kundu

Mitra

2021

IET Signal Processing

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“…The Hessian is defined in (24), and the approximate expression is derived using the following two assumptions. a) Asymptotic assumption: We assume that the data size N is large enough so that we can use the asymptotic result [37,App. A] lim…”

Section: Appendix a Approximate Hessianmentioning

confidence: 99%

A Fast Algorithm for Maximum-Likelihood Estimation of Harmonic Chirp Parameters

Jensen

Nielsen

Jensen

et al. 2017

IEEE Trans. Signal Process.

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The analysis of (approximately) periodic signals is an important element in numerous applications. One generalization of standard periodic signals often occurring in practice are harmonic chirp signals where the instantaneous frequency increases/decreases linearly as a function of time. A statistically efficient estimator for extracting the parameters of the harmonic chirp model in additive white Gaussian noise is the maximum likelihood (ML) estimator which recently has been demonstrated to be robust to noise and accurate-even when the model order is unknown. The main drawback of the ML estimator is that only very computationally demanding algorithms for computing an estimate are known. In this paper, we give an algorithm for computing an estimate to the ML estimator for a number of candidate model orders with a much lower computational complexity than previously reported in the literature. The lower computational complexity is achieved by exploiting recursive matrix structures, including a block Toeplitz-plus-Hankel structure, the fast Fourier transform, and using a two-step approach composed of a grid and refinement step to reduce the number of required function evaluations. The proposed algorithms are assessed via Monte Carlo and timing studies. The timing studies show that the proposed algorithm is orders of magnitude faster than a recently proposed algorithm for practical sizes of the number of harmonics and the length of the signal.

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“…In the harmonic chirp summation (HCS) method, this inversion is avoided by replacing the matrix with its asymptotic expression (in N ). Specifically, we have from the results in [14] that…”

Section: Harmonic Chirp Summationmentioning

confidence: 99%

Fast harmonic chirp summation

Nielsen

Jensen

et al. 2017

2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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The harmonic chirp signal model has only very recently been introduced for modelling approximately periodic signals with a timevarying fundamental frequency. A number of estimators for the parameters of this model have already been proposed, but they are either inaccurate, non-robust to noise, or very computationally intensive. In this paper, we propose a fast algorithm for the harmonic chirp summation method which has been demonstrated in the literature to be accurate and robust to noise. The proposed algorithm is orders of magnitudes faster than previous algorithms which is also demonstrated via timing studies.

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Estimating the parameters of multiple chirp signals

Cited by 28 publications

References 9 publications

Estimation of parameters of a harmonic chirp model

Estimation of parameters of a harmonic chirp model

A Fast Algorithm for Maximum-Likelihood Estimation of Harmonic Chirp Parameters

Fast harmonic chirp summation

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