Spectral Analysis of Nonuniformly Sampled Data: A New Approach Versus the Periodogram

• Published in: IEEE transactions on signal processing Vol. 57; no. 3; pp. 843 - 858
• Main Authors: Stoica, P., Jian Li, Hao He
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.03.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Applied sciences; BIC; Councils; Estimates; Exact sciences and technology; Fourier analysis; Frequency; Information technology; Information, signal and communications theory; Informationsteknik; iterative adaptive approach; Iterative methods; Least squares method; Miscellaneous; nonuniformly; nonuniformly sampled data; periodogram; Sampled data; Signal and communications theory; Signal processing; Signal representation. Spectral analysis; Signal, noise; Spectra; Spectral analysis; Studies; TECHNOLOGY; TEKNIKVETENSKAP; Telecommunications and information theory; Virtual reality; Weighting; iterative adaptive approach; periodogram; Harmonic analysis; Iterative method; spectral analysis; nonuniformly sampled data; Adaptive method; Complex variable method; Weighting; Least squares method; Spectrum analysis; Signal processing; least-squares method; Curve fitting; Signal analysis; BIC
• ISSN: 1053-587X; 1941-0476; 1941-0476
• DOI: 10.1109/TSP.2008.2008973

We begin by revisiting the periodogram to explain why arguably the plain least-squares periodogram (LSP) is preferable to the ldquoclassicalrdquo Fourier periodogram, from a data-fitting viewpoint, as well as to the frequently-used form of LSP due to Lomb and Scargle, from a computational standpoint. Then we go on to introduce a new enhanced method for spectral analysis of nonuniformly sampled data sequences. The new method can be interpreted as an iteratively weighted LSP that makes use of a data-dependent weighting matrix built from the most recent spectral estimate. Because this method is derived for the case of real-valued data (which is typically more complicated to deal with in spectral analysis than the complex-valued data case), it is iterative and it makes use of an adaptive (i.e., data-dependent) weighting, we refer to it as the real-valued iterative adaptive approach (RIAA). LSP and RIAA are nonparametric methods that can be used for the spectral analysis of general data sequences with both continuous and discrete spectra. However, they are most suitable for data sequences with discrete spectra (i.e., sinusoidal data), which is the case we emphasize in this paper.