Design of High-Resolution Quadratic TFDs with Separable Kernels

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Design of High-Resolution Quadratic TFDs with Separable Kernels

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Title: Design of High-Resolution Quadratic TFDs with Separable Kernels
Author: Boashash, B; Putland, G.R.
Abstract: A separable kernel gives separate control of the frequency-smoothing and time- smoothing of the WVD: the lag-dependent factor causes a convolution in the fre- quency direction in the (t, f) plane, while the Doppler-dependent factor causes a convolution in the time direction. A Doppler-independent (DI) kernel smoothes the WVD in the frequency direction only, reducing the inner artifacts and preserving the time marginal. A lag-independent (LI) kernel smoothes the WVD in the time direction only, reducing the cross-terms and preserving the frequency marginal. For an LI kernel, slower variations in component frequencies allow easier sup- pression of cross-terms and higher frequency resolution in the TFD; such kernels should therefore be considered for representing multicomponent signals with slowly- varying instantaneous frequencies. For a multicomponent signal with at least one highly nonlinear IF law, a lag-dependent factor is also needed to suppress the inner artifacts. The separable-kernel approach allows a complete understanding and appraisal of the properties and behavior of the smoothed WVD [2], the B-distribution [5] and the modified B-distribution [3,4]. It also enables the construction of high-resolution quadratic TFDs using the classical smoothing functions commonly encountered in digital signal processing and spectral analysis.
Description: This Article presents the use of separable kernel TFDs for separate control of the frequency-smoothing and time-smoothing of the WVD as the lag-dependent factor causes a convolution in the fre- quency direction in the (t, f) plane, while the Doppler-dependent factor causes a convolution in the time direction. This separable-kernel approach the construction of high-resolution quadratic TFDs using the classical smoothing functions commonly encountered in digital signal processing and spectral analysis. (Additional details can be found in the comprehensive book on Time-Frequency Signal Analysis and Processing (see http://www.elsevier.com/locate/isbn/0080443354). In addition, the most recent upgrade of the original software package that calculates Time-Frequency Distributions and Instantaneous Frequency estimators can be downloaded from the web site: www.time-frequency.net. This was the first software developed in the field, and it was first released publicly in 1987 at the 1st ISSPA conference held in Brisbane, Australia, and then continuously updated).
URI: http://hdl.handle.net/10576/10791
Date: 2003

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