Polyspectral analysis of processes with mixed spectra is considered, and scaled polyperiodograms are introduced to clarify issues related to stalionarity, ergodicity, and suppression of additive stationary noise in harmonic retrieval problems. Spectral and polyspectral approaches are capable of retrieving (un)coupled harmonics, not only when the harmonics have constant amplitudes, but also when they are observed in nonzero mean multiplicative noise. Fourier series polyspectra and asymptotic properties of scaled polyperiodograms provide general tools for higher order analysis of time series with mixed spectra. A single record phase coupling detector is derived to obviate the assumption of independent multiple records required by existing methods. The novelties are illustrated by simulation examples.
Bibliographical noteFunding Information:
Manuscript received January 3, 1994; revised December 10, 1995. This work was supported by ONR under Grant N00014-93-1-0485. Some results of this paper were presented at the Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, November 1993. G. Zhou is with the School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332-0250 USA. G. B. Giannakis is with the Department of Electrical Engineering, University of Virginia, Charlottesville, VA 22903-2442 USA. Publisher Item Identifier S 0018-9448(96)02909-4.
- Asymptotic properties
- Frequency- and phase-coupled harmonics
- Multiplicative noise