Positive Time-frequency Distribution Research Articles

A New Approach for Estimation of Instantaneous Mean Frequency of a Time-Varying Signal

Analysis of nonstationary signals is a challenging task. True nonstationary signal analysis involves monitoring the frequency changes of the signal over time (i.e., monitoring the instantaneous frequency (IF) changes). The IF of a signal is traditionally obtained by taking the first derivative of the phase of the signal with respect to time. This poses some difficulties because the derivative of the phase of the signal may take negative values thus misleading the interpretation of instantaneous frequency. In this paper, a novel approach to extract the IF from its adaptive time-frequency distribution is proposed. The adaptive time-frequency distribution of a signal is obtained by decomposing the signal into components with good time-frequency localization and by combining the Wigner distribution of the components. The adaptive time-frequency distribution thus obtained is free of cross-terms and is a positive time-frequency distribution but it does not satisfy the marginal properties. The marginal properties are achieved by applying the minimum cross-entropy optimization to the time-frequency distribution. Then, IF may be obtained as the first central moment of this adaptive time-frequency distribution. The proposed method of IF estimation is very powerful for applications with low SNR. A set of real-world and synthetic signals of known IF dynamics is tested with the proposed method as well as with other common time-frequency distributions. The simulation shows that the method successfully extracted the IF of the signals.

Signal synthesis and positive time–frequency distributions

A method for obtaining a generalized transfer function (GTF) of a linear time-varying system based on evolutionary spectral theory is proposed. This GTF can be used to synthesize the signal, and its magnitude squared function results in the signal's positive time–frequency distribution that satisfies the marginals (i.e., a Cohen–Posch TFD). The procedure allows any prior estimate of the GTF to be modified such that the resulting posterior GTF is closest in the least square sense to the prior and satisfies the above-mentioned properties. Examples are presented to illustrate the performance of the method.

Feature sets for nonstationary signals derived from moments of the singular value decomposition of Cohen-Posch (positive time-frequency) distributions

This article presents a new method for determining the principal features of a nonstationary time series process based on the singular value decomposition (SVD) of the Cohen-Posch (1985) positive time-frequency distribution. This new method uses density functions derived from the SVD singular vectors to generate moments that are associated with the principal features of the nonstationary process. Since the SVD singular vectors are orthonormal, the vectors whose elements are composed of the squared elements of the SVD vectors are discrete density functions. Moments generated from these density functions are the principal features of the nonstationary time series process. The main reason for determining features of a time series process is to characterize it by a few simple descriptors.

The Analysis of Under Water Vehicle Non-Stationary AcousticTransient Signals Using a New Fast Algorithm for ConstructingPositive Time-Frequency Distributions

It is well know that under water vehicles emit many types of acoustic signals, including stationary as well as non-stationary. The non-stationary transient signals are receiving considerable attention, especially from the standpoint of detection and tracking of under water vehicles. Thus, modern methods for processing these non-stationary acoustic transient signals are required. This paper presents a very powerful method for analyzing acoustic transient signals, the positive time-frequency distribution. A fast algorithm that implements the minimum cross-entropy positive time-frequency distribution makes practical the processing of ’’real world data‘‘, like under water vehicle acoustic transient signals. An example of such a signal is presented, which is a generic acoustic transient signal from a under water vehicle. The signal is only representative, as it is normalized in time, in frequency, and in amplitude. The positive time-frequency distribution constructed for this generic transient signal is contrasted with the one-third octave method, which is currently the primary method being used by the under water vehicle community to analyze under water vehicle transients. The positive distribution is also contrasted with broad band and narrow band spectrograms.

Informative priors for minimum cross-entropy positive time-frequency distributions

A method for generating an informative prior when constructing a positive time-frequency distribution (TFD) by the method of the minimum cross-entropy (MCE) is developed. The prior is obtained from a combination of the Wigner distribution (WD) and the evolutionary periodogram, and results in a more informative MCE-TFD, as quantified via the mutual information of the distribution. The procedure allows any of the bilinear distributions to be used in the prior. Examples illustrate the performance of the new technique.

A note on "Positive time-frequency distributions"

We discuss the performance of certain recently proposed positive time-frequency distribution functions with correct marginals. It turns out that for signals of the FM type, satisfactory results can only be obtained with a strongly signal dependent choice of the parameters in these distribution functions.

Positive time-frequency distribution functions

We demonstrate the existence of positive joint distributions of time and frequency for arbitrary signals. A method is given to readily generate an infinite number of them for any signal. General properties of these distribution functions are derived and specific examples for some common signals are presented.

Positive time-frequency distribution functions [for formulating signal theory] : Cohen, Leon and T.E. Posch, 1985. IEEE Trans. Acoust. Speech Signal Process., ASSP-33(1):31–37. Dept. of Phys., Hunter Coll., CUNY, NY, NY, USA

Positive time-frequency distribution functions [for formulating signal theory] : Cohen, Leon and T.E. Posch, 1985. IEEE Trans. Acoust. Speech Signal Process., ASSP-33(1):31–37. Dept. of Phys., Hunter Coll., CUNY, NY, NY, USA