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SIGNAL PROCESSING

Revisiting signal analysis in the big data era

Nature Computational Science volume 2, pages 70–71 (2022)Cite this article

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A fast and accurate time–frequency analysis is challenging for many applications, especially in the current big data era. A recent work introduces a fast continuous wavelet transform that effectively boosts the analysis speed without sacrificing the resolution of the result.

In the first decade of the 1900s, when Albert Einstein was making breakthroughs in physics, there was a silent revolution happening in the yet-to-be-born field of signal processing: the invention of varying time–frequency analysis that later became popular as wavelet transforms1. Wavelet transforms simultaneously probe signal data based on its index location and its variation in magnitude, and allow multiresolution analysis of the signal by customizing time and frequency resolutions (that is, by providing flexibility in zooming in and out). With the advent of computers and digital applications, the multiresolution property of wavelet transforms has seen applications in different fields, such as medicine, image and video processing, telecommunication, industrial processing, and fundamental science. This wavelet transform revolution was spearheaded by the discrete wavelet transform2 (DWT), a relatively fast transform to compute as it reduces the number of data points to a necessary minimum to reconstruct the original signal, which was a boon to computers in the 1980s and 1990s owing to their limited computing and data-storage capabilities. Moreover, fewer data points were necessary because signals needed to be compressed, stored and transmitted with a small bandwidth. However, DWT has low resolution, which limits its application in advanced signal analysis and processing that require high accuracy. Continuous wavelet transform3 (CWT) was developed as an alternative that improves resolution when compared with DWT, but at the same time substantially increases the computational cost. This trade-off between computational cost and resolution limits the application of wavelet transforms for real-time and accurate signal processing. Writing for Nature Computational Science, Arts and van den Broek overcome this problem by introducing fast CWT (fCWT)4.

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Fig. 1: The fast continuous wavelet transform process and its comparison with the standard continuous wavelet transform.

References

  1. Daubechies, I. Ten Lectures on Wavelets (USA Society for Industrial and Applied Mathematics, 1992).

  2. Shena, M. J. IEEE Trans. Signal Process. 40, 2464–2482 (1992).

    Article  Google Scholar 

  3. Addison, P. S. Phil. Trans. R. Soc. A 376, 20170258 (2018).

    Article  Google Scholar 

  4. Arts, L. P. A. & van den Broek, E. L. Nat. Comput. Sci. https://doi.org/10.1038/s43588-021-00183-z (2022).

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  1. National Biomedical Center for Advanced ESR Technology, Cornell University, Ithaca, NY, USA

    Madhur Srivastava

  2. Department of Chemistry and Chemical Biology, Ithaca, NY, USA

    Madhur Srivastava

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  1. Madhur Srivastava
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Correspondence to Madhur Srivastava.

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Srivastava, M. Revisiting signal analysis in the big data era. Nat Comput Sci 2, 70–71 (2022). https://doi.org/10.1038/s43588-022-00210-7

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  • DOI: https://doi.org/10.1038/s43588-022-00210-7

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