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A Low Computational Complexity Modified Complex Harmonic Wavelet Transform

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Abstract

Complex harmonic wavelet (CHW) is a time–frequency tool that directly computes the frequency content rather than scales with respect to time. The complex harmonic wavelet for discrete signal computes N coefficients for N input samples, with the computational complexity of \(O(N\log _2 N)\) by employing the FFT algorithm. However, this wavelet function for discrete signal is not conjugate symmetric for positive and negative half-planes. Therefore, this paper proposes a new basis function termed modified complex harmonic wavelet transform by multiplying a phase term with CHW. The novelty of this phase multiplication leads the modified CHW to complex conjugate that reduces its computational complexity compared to existing CHW, attaining a computational gain up to \(25 \%\) asymptotically for larger sample points. Like CHW, this proposed modified CHW retains the properties of orthogonality and compact support in the frequency domain.

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Acknowledgements

The authors would like to thank Deity, GOI, for partially using the utilities provided under SMDP-C2SD, Electrical Engineering Department (R &D/SP/EE/SMD/2015-16/126).

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  1. Electrical Engineering Department, Indian institute of Technology, Patna, Patna, 801103, India

    Pritiranjan Khatua & Kailash Chandra Ray

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  1. Pritiranjan Khatua
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  2. Kailash Chandra Ray
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Correspondence to Pritiranjan Khatua.

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Khatua, P., Ray, K.C. A Low Computational Complexity Modified Complex Harmonic Wavelet Transform. Circuits Syst Signal Process 41, 6462–6483 (2022). https://doi.org/10.1007/s00034-022-02095-3

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  • DOI: https://doi.org/10.1007/s00034-022-02095-3

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