Locally Optimized Adaptive Directional Time–Frequency Distributions

• DOI: 10.1007/s00034-018-0802-z
• Publication Date: 2018-03-19T12:47:29Z
• Authors: Mokhtar Mohammadi; Ali Akbar Pouyan; Nabeel Ali Khan; Vahid Abolghasemi
• Keywords: Smoothing; SIGNAL (programming language); Kernel (algebra); Basis (linear algebra)

This paper addresses the problem of estimating the parameters of adaptive directional time–frequency distributions (ADTFDs). ADTFDs locally optimize the direction of the smoothing kernel on the basis of directional Gaussian or double derivative directional Gaussian filter. Conventionally, the parameters of these techniques have to be tuned manually for each particular signal. Global optimization of the parameters fails to provide the desired results when the signal encompasses close or short-duration components. We propose a two-stage algorithm to resolve this issue. As part of the first stage, the length of the smoothing kernel is optimized globally. In the second stage, the parameters which control the shape of the selected smoothing window are optimized, locally. It is shown that the multistage algorithm can result in a time–frequency distribution that has both high resolution for close components and good concentration of signal energy for short-duration signal components. Experimental findings reveal the superiority of the proposed technique over the existing methods in the case of complete signals and its benefits in the case of signals with missing samples.