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Computing the Fourier Transformation over Temporal Data Streams (Invited Talk)

Authors Michael H. Böhlen , Muhammad Saad

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Subject Classification

ACM Subject Classification
  • Information systems → Stream management
  • Theory of computation → Data structures and algorithms for data management
Keywords
  • Data streams
  • Fourier transform
  • time-varying data

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Abstract

In radio astronomy the sky is continuously scanned to collect frequency information about celestial objects. The inverse 2D Fourier transformation is used to generate images of the sky from the collected frequency information. We propose an algorithm that incrementally refines images by processing frequency information as it arrives in a temporal data stream. A direct implementation of the refinement with the discrete Fourier transformation requires O(N^2) complex multiplications to process an element of the stream. We propose a new algorithm that avoids recomputations and only requires O(N) complex multiplications.

Cite As Get BibTex

Michael H. Böhlen and Muhammad Saad. Computing the Fourier Transformation over Temporal Data Streams (Invited Talk). In 26th International Symposium on Temporal Representation and Reasoning (TIME 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 147, pp. 1:1-1:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019) https://doi.org/10.4230/LIPIcs.TIME.2019.1

Author Details

Michael H. Böhlen
  • University of Zürich, Switzerland
Muhammad Saad
  • University of Zürich, Switzerland

Funding

  • Saad, Muhammad: Partially supported by the Swiss National Science Foundation (SNSF) through project number 407550_167177.

References

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  2. K. Duda. Accurate, Guaranteed Stable, Sliding Discrete Fourier Transform [DSP Tips & Tricks]. IEEE Signal Processing Magazine, 27(6):124-127, November 2010. URL: https://doi.org/10.1109/MSP.2010.938088.
  3. E. Jacobsen and R. Lyons. The sliding DFT. IEEE Signal Processing Magazine, 20(2):74-80, March 2003. URL: https://doi.org/10.1109/MSP.2003.1184347.
  4. C. Park. Fast, Accurate, and Guaranteed Stable Sliding Discrete Fourier Transform [sp Tips & Tricks]. IEEE Signal Processing Magazine, 32(4):145-156, July 2015. URL: https://doi.org/10.1109/MSP.2015.2412144.
  5. C. Park and S. Ko. The Hopping Discrete Fourier Transform [sp Tips & Tricks]. IEEE Signal Processing Magazine, 31(2):135-139, March 2014. URL: https://doi.org/10.1109/MSP.2013.2292891.
  6. B. G. Sherlock and D. M. Monro. Moving discrete Fourier transform. IEE Proceedings F - Radar and Signal Processing, 139(4):279-282, August 1992. URL: https://doi.org/10.1049/ip-f-2.1992.0038.
  7. B.G Sherlock. Windowed discrete Fourier transform for shifting data. Signal Processing, 74(2):169-177, 1999. URL: https://doi.org/10.1016/S0165-1684(98)00209-6.
  8. A. Srivastava and V. Karwal. Windowed r-point update algorithm for Discrete Fourier Transform. In 2013 International Conference on Signal Processing and Communication (ICSC), pages 185-190, December 2013. URL: https://doi.org/10.1109/ICSPCom.2013.6719780.
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