Many functions have been proposed for estimating signal information content and complexity on the time-frequency plane, including moment-based measures such as the time-bandwidth product and the Shannon and Renyi entropies. When applied to a time-frequency representation from Cohen's class, the Renyi entropy conforms closely to the visually based ...

We consider the design of kernels for time-frequency distributions through the phase, rather than amplitude, response. While phase kernels do not attenuate troublesome cross-components, they can translate them in the time-frequency plane. In contrast to previous work on phase kernels that concentrated on placing the cross-components on top of the ...

Time-frequency analysis has recently undergone significant advances in two main directions: statistically optimized methods that extend the scope of time-frequency-based techniques from merely exploratory data analysis to more quantitative application, and generalized joint signal representations that extend time-frequency-based methods to a richer ...

This paper deals with the problem of classification of nonstationary signals using signatures which are essentially independent of the signal length. We develop the notion of a separable approximation to the Continuous Wavelet Transform (CWT) and use it to define a power signature. We present a simple technique which uses the Singular Value Decomposition ...

Bilinear time-frequency representations (TFRs) and time-scale representations (TSRs) are potentially very useful for detecting a nonstationary signal in the presence of nonstationary noise or interference. As quadratic signal representations, they are promising for situations in which the optimal detector is a quadratic function of the observations. ...

In many practical detection and classification problems, the signals of interest exhibit some uncertain nuisance parameters, such as the unknown delay and Doppler in radar. For optimal performance, the form of such parameters must be known and exploited as is done in the generalized likelihood ratio test (GLRT). In practice, the statistics required ...

Time-frequency representations (TFRs) provide a powerful and flexible structure for designing optimal detectors in a variety of nonstationary scenarios. In this paper, we describe a TFR-based framework for optimal detection of arbitrary second-order stochastic signals, with certain unknown or random nuisance parameters, in the presence of Gaussian ...

We propose a robust method for estimating the time-varying spectrum of a non-stationary random process. Our approach extends Thomson's powerful multiple window spectrum estimation scheme to the time-frequency and time-scale planes. The method refines previous extensions of Thomson's method through optimally concentrated window and wavelet functions ...

The classification of nonstationary signals of unknown duration is of great importance in areas like oil exploration, moving target detection, and pattern recognition. In an earlier work, we provided a solution to this problem, based on the wavelet transform, by defining representations called <i>pseudo power signatures</i> for signal classes which ...

Generalized joint signal representations (JSRs) extend the scope of joint time-frequency representations (TFRs) to a richer class of nonstationary signals, but their use, just as in the case of TFRs, has been primarily limited to qualitative, exploratory data analysis. To exploit their potential more fully, JSR-based statistical signal processing ...