Abstract
The Wigner bispectrum of multicomponent signals is studied, and its modified and reduced forms are introduced. A generalization of the presented forms to the Wigner higher-order spectra (WHOS), in the case of multicomponent signals, is provided. From our previous work it is known that cross terms removal (reduction) is possible for odd-order spectra with equal numbers of conjugated and nonconjugated terms. Here, we extend the analysis to even-order spectra. The theory is illustrated by examples.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
B. Boashash, Estimating and interpreting the instantaneous frequency of a signal: Part I-Fundamentals,IEEE Proceedings, vol. 80, no. 4, April 1992, pp. 519–538.
L. Carin and L. B. Felsen, Wave-oriented data processing for frequency-and time-domain scattering by nonuniform truncated arrays,IEEE Ant. and Propagation Mag., vol. 36, no. 3, June 1994, pp. 29–43.
J. R. Fonollosa and C. L. Nikias, Wigner higher order moment spectra: Definition, properties, computation and application to transient signal analysis,IEEE Trans. on Signal Processing, vol. 41, no. 1, January 1993, pp. 245–266.
N. L. Gerr, Introducing a third order Wigner distribution,Proc. IEEE, vol. 76, no. 3, March 1988, pp. 290–292.
N. Marinovic, L. Cohen, and S. Umesh, Joint representation in time and frequency scale for harmonic type signals, inProc. of IEEE-SP Int. Symp. on TF/TSA, Philadelphia, PA, October 1994, pp. 84–87.
N. Marinovic, L. Cohen, and S. Umesh, Scale and harmonic type signals, inProc. Int. Soc. Opt. Eng., vol. 2303, 1994.
J. M. Mendel, Tutorial on higher order statistics (spectra) in signal processing and system theory: Theoretical results and some applications,IEEE Proceedings, 79, March 1991, pp. 278–305.
C. L. Nikias and J. M. Mendel, Signal processing with higher order spectra,IEEE Signal Processing Magazine, July 1993, pp. 10–37.
L.J. Stankovic, A method for time-frequency analysis,IEEE Transactions on Signal Processing, vol. 42, no. 1, January 1994, pp. 225–229.
L.J. Stankovic, An analysis of the Wigner higher order spectra of multicomponent signals,Annales des Telecommunications, no. 3/4, March/April 1994, pp. 132–136.
L.J. Stankovic, A multi-time definition of the Wigner higher order distribution;L-Wigner distribution,IEEE Signal Processing Letters, vol. 1, no. 8, July 1994, pp. 106–109.
L.J. Stankovic, An analysis of some time-frequency and time-scale distribution,Annales des Telecommunications, no. 9/10, September/October 1994, pp. 505–517.
L.J. Stankovic and S. Jovicevic, Modified least squares method with application to diffraction and eigenvalue problems,IEEE Proc., vol. 135, part-H, no. 5, October 1988, pp. 339–343.
L.J. Stankovic and S. Jovicevic, Boundary condition expansion of basis functions method implemented by fast Fourier transform algorithms,IEEE Trans. on MTT, vol. 38, no. 3, March 1990, pp. 296–301.
L.J. Stankovic and S. Stankovic, Wigner distribution of noisy signals,IEEE Trans. on Signal Processing, vol. 41, no. 2, February 1993, pp. 956–960.
L.J. Stankovic and S. Stankovic, An analysis of instantaneous frequency presentation using time-frequency distributions—Generalized Wigner distribution,IEEE Trans. on Signal Processing, vol. 43, no. 2, February 1995.
L.J. Stankovic and S. Stankovic, On the Wigner distribution of discrete-time noisy signals with application to the study of quantization effects,IEEE Trans. on Signal Processing, vol. 40, no. 7, July 1994, pp. 1863–1867.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Stankovic, S., Stankovic, L.J. & Uskokovic, Z. Modified Wigner bispectrum and its generalizations. Circuits Systems and Signal Process 16, 27–40 (1997). https://doi.org/10.1007/BF01183173
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01183173