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14 Spectrum Estimation and Modeling

The main objective of spectrumestimation is the determination of the power spectrumdensity (PSD) of a random process. | Djuric P.M. Kay S.M. Spectrum Estimation and Modeling Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC 14 Spectrum Estimation and Modeling Petar M. DjuriC State University of New York at Stony Brook Steven M. Kay University of Rhode Island 14.1 Introduction 14.2 Important Notions and Definitions Random Processes Spectra of Deterministic Signals Spectra of Random Processes 14.3 The Problem of Power Spectrum Estimation 14.4 Nonparametric Spectrum Estimation Periodogram The Bartlett Method The Welch Method Blackman-Tukey Method Minimum Variance Spectrum Estimator Multiwindow Spectrum Estimator 14.5 Parametric Spectrum Estimation Spectrum Estimation Based on Autoregressive Models Spectrum Estimation Based on Moving Average Models Spectrum Estimation Based on Autoregressive Moving Average Models Pisarenko Harmonic Decomposition Method Multiple Signal Classification MUSIC 14.6 Recent Developments References 14.1 Introduction The main objective of spectrum estimation is the determination of the power spectrum density PSD of a random process. The PSD is a function that plays a fundamental role in the analysis of stationary random processes in that it quantifies the distribution of total power as a function of frequency. The estimation of the PSD is based on a set of observed data samples from the process. A necessary assumption is that the random process is at least wide sense stationary that is its first and second order statistics do not change with time. The estimated PSD provides information about the structure of the random process which can then be used for refined modeling prediction or filtering of the observed process. Spectrum estimation has a long history with beginnings in ancient times 17 . The first significant discoveries that laid the grounds for later developments however were made in the early years of the eighteenth century. They include one of the most important .