LIPIcs.TIME.2019.1.pdf
- Filesize: 412 kB
- 4 pages
Document
Computing the Fourier Transformation over Temporal Data Streams (Invited Talk)
Authors
Michael H. Böhlen 
,
-
Part of:
Volume:
26th International Symposium on Temporal Representation and Reasoning (TIME 2019)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Symposium on Temporal Representation and Reasoning (TIME) - License:
Creative Commons Attribution 3.0 Unported license
- Publication date: 2019-10-07
File
Document Identifiers
Author Details
Cite AsGet 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
https://doi.org/10.4230/LIPIcs.TIME.2019.1
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.
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
Metrics
- Access Statistics
-
Total Accesses (updated on a weekly basis)
0PDF Downloads
References
- W. Cochran, J. Cooley, D. Favin, H. Helms, R. Kaenel, W. Lang, G. Maling, D. Nelson, C. Rader, and P. Welch. What is the fast Fourier transform? IEEE Transactions on Audio and Electroacoustics, 15(2):45-55, June 1967. URL: https://doi.org/10.1109/TAU.1967.1161899.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.