Spectral Analysis of Signals

Abstract

The process of determining the frequency contents of a continuous-time signal in the discrete-time domain is known as spectral analysis. Most of the phenomena that occur in nature can be characterized statistically by random processes. Hence, the main objective of spectral analysis is the determination of the power spectrum density (PSD) of a random process. The power is the Fourier transform of the autocorrelation sequence of a stationary 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 the total power as a function of frequency. The power spectrum also plays an important role in detection, tracking, and classification of periodic or narrowband processes buried in noise. Other applications of spectrum estimation include harmonic analysis and prediction, time series extrapolation and interpolation, spectral smoothing, bandwidth compression, beam forming, and direction finding. The estimation of the PSD is based on a set of observed data samples from the process. Estimating the power spectrum is equivalent to estimating the autocorrelation. This chapter deals with the nonparametric methods, parametric methods, and subspace methods for power spectrum estimation. Further, the spectrogram computation of non-stationary signals using STFT is also briefly discussed in this chapter.