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Two-channel perfect reconstruction (PR) quadrature mirror filter (QMF) bank design using logarithmic window function and spline function

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Abstract

In this work, two-channel perfect reconstruction quadrature mirror filter (QMF) bank has been proposed based on the prototype filter using windowing method. A novel window function based on logarithmic function along with the spline function is utilized for the design of prototype filter. The proposed window has a variable parameter ‘\(\alpha \)’, which varies the peak side lobe level and rate of fall-off side lobe level which in turn affects the peak reconstruction error (PRE) and amplitude distortion (\(e_{am}\)) of the QMF bank . The transition width of the prototype is controlled by the spline function using the parameter ‘\(\mu \)’. The perfect reconstruction condition is satisfied by setting the cutoff frequency (\(\omega _{c}\)) of the prototype low-pass filter at ‘\(\pi /2\)’. The performance of the proposed design method has been evaluated in terms of mean square error in the pass band, mean square error in the stop band, first side lobe attenuation (\(A_{1}\)), peak reconstruction error (PRE) and amplitude error (\(e_{am}\)) for different values of ‘\(\alpha \)’ and ‘\(\mu \)’. The results are provided and compared with the existing methods.

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Acknowledgments

The authors are grateful to Ministry of Human Resource and Development, Government of India and Medical Imaging and Computational Modeling of Physiological Systems Research Laboratory, Department of Electronics and Communication Engineering, Dr. B.R.Ambedkar National Institute of Technology, Jalandhar, Punjab (India) for providing every type of financial, technical and administrative help to present this work.

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  1. Department of Electronics and Communication Engineering, Dr. B. R. Ambedkar National Institute of Technology Jalandhar, Jalandhar, India

    Aman Kumar & Ramesh K. Sunkaria

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  1. Aman Kumar
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  2. Ramesh K. Sunkaria
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Correspondence to Aman Kumar.

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Kumar, A., Sunkaria, R.K. Two-channel perfect reconstruction (PR) quadrature mirror filter (QMF) bank design using logarithmic window function and spline function. SIViP 10, 1473–1480 (2016). https://doi.org/10.1007/s11760-016-0958-6

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  • DOI: https://doi.org/10.1007/s11760-016-0958-6

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