Some New Results on the Estimation of Sinusoids in Noise

Jesper Kjær Nielsen

Research output: Book/ReportPh.D. thesis

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Abstract

This thesis is concerned with the problem of estimating sinusoidal parameters from noisy observations. This field of research is applicable to solving problems in a large number of areas such as music and speech processing, electrocardiography, seismology, radar and sonar processing, astronomy, meteorology, and economics, and in this thesis a number of rather diverse contributions are made to this field of research. These contributions include new results and algorithms in relation to model comparison and selection, fundamental frequency estimation, inference in dynamic sinusoidal models, and filtering methods.

In the introductory part of this thesis, an overview over the modelling and inference problem is given, and the most important methods for solving these problems are briefly reviewed. During this introduction, the contributions are also stated and positioned in relation to these previously proposed methods. The second part of this thesis contains the contributions. First, the model comparison and selection problem is considered for a general non-linear model. In this connection, a few new model comparison methods are proposed and demonstrated to perform better than existing methods for both model selection and prediction. Second, the joint fundamental frequency estimation and model order detection problem is analysed within a Bayesian framework. A new method is also suggested and its accuracy is evaluated and demonstrated to perform better than a similar state-of-the-art method. Third, an efficient algorithm for performing inference and interpolation in a dynamic sinusoidal model is proposed. This method is applied to packet-loss concealment, and listening tests indicate that the proposed algorithm can be used for this purpose. Fourth, the Capon filtering method for amplitude estimation is extended in an interesting way by selecting the filter length of the Capon filter in a data-adaptive fashion. Finally, the recently proposed sampling scheme called compressed sensing is analysed in the context of estimating continuous parameter such as the frequency parameter and the direction-of-arrival, and it is shown that compressed sensing decreases the estimation accuracy of such parameters.

Although the estimation problems considered in this thesis are primarily analysed in the context of speech and audio applications, the results are useful in a wider range of applications. Along these lines, the main focus has not been on developing new algorithms for specific applications, but rather on understanding the underlying estimation problem and analysing it in a consistent fashion.
Original languageEnglish
Number of pages218
ISBN (Print)978-87-92328-91-5
ISBN (Electronic)978-87-92328-91-5
Publication statusPublished - 27 Sep 2012

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