Fractional Differential Equation-Based Instantaneous Frequency Estimation for Signal Reconstruction

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Yazgaç B. G. , Kırcı M.

Fractal and Fractional, vol.5, no.3, 2021 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 5 Issue: 3
  • Publication Date: 2021
  • Doi Number: 10.3390/fractalfract5030083
  • Title of Journal : Fractal and Fractional
  • Keywords: applied fractional calculus, signal reconstruction, instantaneous frequency estimation, phase estimation, memory parameter, PHASE, SOUNDS


© 2021 by the authors. Licensee MDPI, Basel, Switzerland.In this paper, we propose a fractional differential equation (FDE)-based approach for the estimation of instantaneous frequencies for windowed signals as a part of signal reconstruction. This approach is based on modeling bandpass filter results around the peaks of a windowed signal as fractional differential equations and linking differ-integrator parameters, thereby determining the long-range dependence on estimated instantaneous frequencies. We investigated the performance of the proposed approach with two evaluation measures and compared it to a benchmark noniterative signal reconstruction method (SPSI). The comparison was provided with different overlap parameters to investigate the performance of the proposed model concerning resolution. An additional comparison was provided by applying the proposed method and benchmark method outputs to iterative signal reconstruction algorithms. The proposed FDE method received better evaluation results in high resolution for the noniterative case and comparable results with SPSI with an increasing iteration number of iterative methods, regardless of the overlap parameter.