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Mathieu Windows for Signal Processing

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Abstract

Two new windows for signal processing are introduced in this work. The windows are based on radial Mathieu functions and their performance is compared with well-known ones such as Kaiser, cosh, exponential, Hamming, prolate, and other windows. Most of the results are focused on 1D systems (or windows) and extensions to 2D and multidimensional cases are straightforward. These new Mathieu windows have three adjusting parameters and, by a proper choice of them, it is possible to have a wide span of window shapes that cover most of the existing ones and they might be more appropriate for some applications. An example dealing with the identification of three tones plus normal noise is studied, and the performance of these Mathieu windows is among the best ones. So, they are highly recommended for spectral or harmonic analysis applications. Moreover, due to the high flexibility in adjusting Mathieu windows shapes, these new proposed windows may be applicable for smoothing finite response filters, and related applications as well.

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Acknowledgements

The author would like to thank Tecnologico de Monterrey and Conacyt (Grant No. CB 2015-256237-Y) for the partial support provided to do this work.

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  1. School of Engineering and Sciences, Tecnológico de Monterrey, Av. Eugenio Garza Sada 2501 Sur, C.P. 64849, Monterrey, NL, Mexico

    Ramón M. Rodríguez-Dagnino

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Correspondence to Ramón M. Rodríguez-Dagnino.

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Rodríguez-Dagnino, R.M. Mathieu Windows for Signal Processing. Circuits Syst Signal Process 38, 2736–2766 (2019). https://doi.org/10.1007/s00034-018-0989-z

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