Multitaper marginal time–frequency distributions

Time–frequency distributions (TFDs) belonging to Cohen's class yield a frequency marginal that is equivalent to the periodogram of the signal. It is well-known that the periodogram is not a good spectral estimator since it is not a consistent estimate, i.e. its variance does not decrease with the sample size. Thomson addressed this issue by introducing a multitaper spectrum estimator with high resolution and statistical stability [D.J. Thomson, Spectrum estimation and harmonic analysis, Proc. IEEE 70 (9) (1982) 1055–1096]. In recent years, various approaches have been developed to extend such multitaper spectral estimators to the area of nonstationary signal analysis [F. Çakrak, P. Loughlin, Multiple window nonlinear time-varying spectral analysis, in: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 4, 1998, pp. 2409–2412; F. Çakrak, P. Loughlin, Multiple window nonlinear time-varying spectral analysis, IEEE Trans. Signal Process. 49 (2) (2001) 448–453; J.W. Pitton, Time–frequency spectrum estimation: an adaptive multitaper method, in: Proceedings of IEEE International Symposium on Time–frequency and Time-scale analysis, 1998, pp. 665–668; J.W. Pitton, Nonstationary spectrum estimation and time–frequency concentration, in: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 4, 1998, pp. 2425–2428; G. Frazer, B. Boashash, Multiple window spectrogram and time–frequency distributions, in: Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing, vol. 4, 1994, pp. 293–296; M. Bayram, R.G. Baraniuk, Multiple window time–frequency analysis, in: Proceedings of the IEEE International Symposium on Time–frequency and Time-scale analysis, 1996, pp. 173–176.]. In this paper, a new method that approaches the problem from the perspective of frequency marginals is introduced. A class of time–frequency distributions, multitaper marginal TFD (MTM-TFD), is constructed for analyzing time-varying signals in noise with statistically stable frequency marginals. A kernel design method yielding any desired frequency marginal, such as provided by Thomson's spectrum estimator, is derived for a given signal. The improvement in the performance of this new class of time–frequency distributions compared to the conventional time–frequency distributions is illustrated through examples.