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.
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References
A. Schuster, On the investigation of hidden periodicities with application to a supposed 26 day period of meteorological phenomena. Terr. Magn. Atmos. Electr. 3, 13–41 (1898)
M.S. Bartlett, Smoothing periodograms from time series with continuous spectra. Nature 161, 686–687 (1948)
P.D. Welch, The use of fast Fourier transform for the estimation of power spectra: A method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. 15, 70–83 (1967)
R.B. Blackman, J.W. Tukey, The Measurement of Power Spectra from the Point of View of Communication Engineering (Dover Publications, USA, 1958)
J.G. Proakis, D.G. Manolakis, Digital Signal Processing Principles, Algorithms and Applications (Printice-Hall, India, 2004)
J.P. Burg, A new Analysis technique for time series data. Paper presented at the NATO Advanced Study Institute on Signal Processing, Enschede, 1968
H. Akaike, Power spectrum estimation through autoregressive model fitting. Ann. Inst. Stat. Math. 21, 407–420 (1969)
H. Akaike, A new look at the statistical model identification. IEEE Trans. Autom. Control 19(6), 716–723 (1974)
S.L. Marple, in Digital Spectral Analysis. (Prentice-Hall, Englewood Cliffs, NJ, 1987), pp. 373–378, 686–687
R.O. Schmidt, Multiple emitter location and signal parameter estimation. IEEE Trans. Antennas Propag. AP-34, 276–280 (1986)
D.H. Johnson, The application of spectral estimation methods to bearing estimation problems. Proc. IEEE 70(9), 126–139 (1982)
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Rao, K., Swamy, M. (2018). Spectral Analysis of Signals. In: Digital Signal Processing. Springer, Singapore. https://doi.org/10.1007/978-981-10-8081-4_12
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DOI: https://doi.org/10.1007/978-981-10-8081-4_12
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