The Estimation and Tracking of Frequency

Many electronic and acoustic signals can be modelled as sums of sinusoids and noise. However, the amplitudes, phases and frequencies of the sinusoids are often unknown and must be estimated in order to characterise the periodicity or near-periodicity of a signal and consequently to identify its source. This book presents and analyses several practical techniques used for such estimation. The problem of tracking slow frequency changes over time of a very noisy sinusoid is also considered. Rigorous analyses are presented via asymptotic or large sample theory, together with physical insight. The book focuses on achieving extremely accurate estimates when the signal to noise ratio is low but the sample size is large. Each chapter begins with a detailed overview, and many applications are given. Matlab code for the estimation techniques is also included. The book will thus serve as an excellent introduction and reference for researchers analysing such signals.

Preface; 1. Introduction; 2. Statistical and probabilistic methods; 3. The estimation of a fixed frequency; 4. Techniques derived from ARMA modelling; 5. Estimation using Fourier coefficients; 6. Tracking frequency in low SNR conditions; 7. Other estimation techniques; References; Appendix. Matlab programs; Author index; Subject index.

This 2001 book presents and analyses practical techniques for estimating the frequencies and amplitudes of the sinusoids making up signals. Rigorous results and physical insight are both given, focusing on noisy signals and large sample sizes. Many applications are described and Matlab code is also included. An excellent introduction and reference for researchers.