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Dual Window Fourier Transform (DWFT): A Tool to Analyze Non-stationary Signals

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Abstract

Time–frequency representation plays a significant role in the analysis of non-stationary signals. A number of such representations have been reported in the literature with each having its own strengths. In this paper, an alternative time–frequency analysis method, Dual Window Fourier Transform (DWFT) has been suggested which enables compact localization of the signal components in joint time–frequency plane. The method utilizes two windows of optimal length for improving the resolution of the analyzed signal. The main contribution of this work is in the algorithm developed to find the optimal window length. This method, requiring no prior information, is applicable for multi-component and non-stationary signals. Moreover, a smoothed version of DWFT, that uses thresholding for removing interferences or reflections, has also been developed for signals which are closely localized in frequency domain. Both real world and simulated signals have been used to test the efficacy of the given method. Measures such as Hoyer’s measure, normalized Renyi entropy, ratio of norm-based measure and modified energy concentration have been used for performance evaluation. A comparative analysis of suggested method with other linear Time–Frequency Distribution methods has also been carried out.

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The funding was provided by Ministry of Human Resource Development.

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  1. National Institute of Technology Hamirpur, Hamirpur, India

    Akhil Walia & Amit Kaul

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  1. Akhil Walia
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Walia, A., Kaul, A. Dual Window Fourier Transform (DWFT): A Tool to Analyze Non-stationary Signals. Circuits Syst Signal Process 41, 6075–6097 (2022). https://doi.org/10.1007/s00034-022-02061-z

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  • DOI: https://doi.org/10.1007/s00034-022-02061-z

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