POWER SPECTRUM AND CORRELATION Power Spectrum and Correlation Fourier Series: Representation of Periodic Signals Fourier Transform: Representation of Aperiodic Signals Non-Parametric Power Spectral Estimation Model-Based Power Spectral Estimation High Resolution Spectral Estimation Based on Subspace Eigen-Analysis Summary T he power spectrum reveals the existence, or the absence, of repetitive patterns and correlation structures in a signal process. These structural patterns are important in a wide range of applications such as data forecasting, signal coding, signal detection, radar, pattern recognition, and decision-making systems. The most common method of spectral estimation is based on the fast Fourier transform (FFT). For many. | Advanced Digital Signal Processing and Noise Reduction Second Edition. Saeed V. Vaseghi Copyright 2000 John Wiley Sons Ltd ISBNs 0-471-62692-9 Hardback 0-470-84162-1 Electronic 9 POWER SPECTRUM AND CORRELATION Power Spectrum and Correlation Fourier Series Representation of Periodic Signals Fourier Transform Representation of Aperiodic Signals Non-Parametric Power Spectral Estimation Model-Based Power Spectral Estimation High Resolution Spectral Estimation Based on Subspace Eigen-Analysis Summary The power spectrum reveals the existence or the absence of repetitive patterns and correlation structures in a signal process. These structural patterns are important in a wide range of applications such as data forecasting signal coding signal detection radar pattern recognition and decision-making systems. The most common method of spectral estimation is based on the fast Fourier transform FFT . For many applications FFT-based methods produce sufficiently good results. However more advanced methods of spectral estimation can offer better frequency resolution and less variance. This chapter begins with an introduction to the Fourier series and transform and the basic principles of spectral estimation. The classical methods for power spectrum estimation are based on periodograms. Various methods of averaging periodograms and their effects on the variance of spectral estimates are considered. We then study the maximum entropy and the model-based spectral estimation methods. We also consider several high-resolution spectral estimation methods based on eigen-analysis for the estimation of sinusoids observed in additive white noise. 264 Power Spectrum and Correlation Power Spectrum and Correlation The power spectrum of a signal gives the distribution of the signal power among various frequencies. The power spectrum is the Fourier transform of the correlation function and reveals information on the correlation structure of the signal. The strength
