Circuits, Systems, and Signal Processing

, Volume 37, Issue 8, pp 3154–3174 | Cite as

Locally Optimized Adaptive Directional Time–Frequency Distributions

  • Mokhtar Mohammadi
  • Ali Akbar PouyanEmail author
  • Nabeel Ali Khan
  • Vahid Abolghasemi


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.


Quadratic time–frequency distributions Adaptive directional kernels Complete signals Sparse signal Parameter optimization 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Mokhtar Mohammadi
    • 1
    • 2
  • Ali Akbar Pouyan
    • 1
    Email author
  • Nabeel Ali Khan
    • 3
  • Vahid Abolghasemi
    • 1
  1. 1.Laboratory of Advanced Industrial Signal Processing and AIShahrood University of TechnologyShahroodIran
  2. 2.Department of Computer ScienceUniversity of Human DevelopmentSlemaniIraq
  3. 3.Electrical EngineeringFoundation UniversityIslamabadPakistan

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