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 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 ...

Recently, Cohen has proposed a construction for joint distributions of arbitrary physical quantities, in direct generalization of joint time-frequency representations. Actually this method encompasses two approaches, one based on operator correspondences and one based on weighting kernels. The literature has emphasized the kernel method due to its ...

We introduce a new method for the time-scale analysis of non-stationary signals. Our work leverages the success of the "time-frequency distribution series / cross-term deleted representations" into the time-scale domain to match wide-band signals that are better modeled in terms of time shifts and scale changes than in terms of time and frequency ...

Given a unitary operator <i>A</i> representing a physical quantity of interest, we employ concepts from group representation theory to define two natural signal energy densities for <i>A</i>. The first is invariant to <i>A</i> and proves useful when the effect of <i>A</i> is to be ignored; the second is covariant to <i>A</i> and measures the "<i>A</i>" ...

In this paper, we introduce a new set of tools for time-varying spectral analysis: the pseudo affine Wigner distributions. Based on the affine Wigner distributions of J. and P. Bertrand, these new time-scale distributions support efficient online operation at the same computational cost as the continuous wavelet transform. Moreover, they take advantage ...

The authors describe the application of an adaptive optimal kernel (AOK) time-frequency representation to the processing of underwater acoustic data. The optimal kernel is a signal-dependent radially Gaussian function. Examples are given which demonstrate the effectiveness of the approach for simulated and real sonar data. The simulations indicate ...

In this paper, we propose a simple framework for studying certain distributions of variables beyond time-frequency and time-scale. When applicable, our results turn the theory of joint distributions of arbitrary variables into an easy exercise of coordinate transformation. While straightforward, the method can generate many distributions previously ...

A study of the phase and amplitude sensitivity of the recently proposed Renyi time-frequency information measure leads to the introduction of a new "Jensen-like" divergence measure. While this quantity promises to be a useful indicator of the distance between two time-frequency distributions, it is limited to the analysis of positive definite TFDs. ...

In this paper we propose a new class of signal analysis tools that generalizes the popular wavelet and short-time Fourier transforms. The class allows skews and rotations of the analyzing wavelet in the time-frequency plane, in addition to the time and frequency translations and scalings employed by conventional transforms. In addition to providing ...