A Novel Fractional-Order Time–Frequency Framework for Modeling and Analysis of Non-Stationary Signals

Abstract

The problem of non-stationary signal analysis is a cornerstone in the contemporary signal processing as conventional time-frequency (TF) applications like the short-time Fourier transform and wavelet transform are associated with various limitations in that they have a limited resolution and inadequate localization of energy. In order to overcome these problems, this paper offers a new fractional-order time-frequency framework that uses the versatility of fractional transforms to offer greater flexibility in signal representation of complex and time-varying signals. The presented approach presents an evolvable fractional parameter, which allows optimizing the time-frequency resolution and enhancing signal energy concentration in the joint domain. An effective algorithmic implementation is created, with effective computational methods and parameter optimization processes. Quantitative analysis of the proposed framework is performed with the help of common measures, such as Rényi entropy, signal-to-noise ratio (SNR) and reconstruction error, which shows a significant improvement compared to traditional methods. The experimental findings on synthetic and realistic data sets prove the high-quality time frequency localization, less cross-term interference, and robustness in noisy situations. The suggested framework has a high potential of application across diverse applications such as biomedical signal analysis, radar signal processing and speech analysis where the examination of non-stationary behavior is important.