"Spectral Entropy Calculation Methods in Hardware, Targeting On-Board Applications"

N. Huber, T. Carozzi, E. Cabal-Yepez and P. Gough
University of Sussex


Scientifically interesting signals can be sparsely distributed amongst the vast datasets produced by spacecraft instrumentation. This data usually includes noise, inherent either in the measurement process, or in the nature of the studied phenomenon. It is common practice to apply compression techniques to maximize the data throughput of on-board instruments, but it is important to ensure that this data is still rich in scientific information.

In a recent work [1], it was shown how the use of the Shannon entropy measure [2] can be an effective tool in limiting the transmission to ground of data low in “information content”. In the same work, it was also demonstrated how it is feasible to implement “telemetry filtering” in FPGA hardware using spectral entropy applied to the specific case of data in the form of Auto-Correlation Functions.

This current work presents a set of new methods for calculating spectral entropy in hardware that are faster, more efficient, and more general in application than the previous work. These have been made possible by recent work [3] that identified a novel spectral transform, which involves only additions and subtractions. This transform has been shown to be directly adaptable to H/W with significant benefits [4]. Furthermore, newer and more accurate techniques [5] for the arithmetic calculations necessary during the entropy calculations have also been developed, minimizing the error of the entropy result.

We will be presenting our work based on a comparison between the existing entropy calculation methods and the newly created ones, both in terms of efficiency and accuracy. Furthermore, we will present the H/W implementation of the novel algorithms in an FPGA, along with their resource usage, performance and scalability. Finally, we present a case study where this modified entropy calculation method is applied as a telemetry filter in a forthcoming International Space Station instrument.


  1. HUBER, N. et. al.: “Filtering of Telemetry Using Entropy”, MAPLD Conference, Washington DC, Submission 132, 2005

  2. SHANNON, C. E. : “A Mathematical Theory of Communication”, Bell Syst. Tech. J., 27, 379-423, 623-656, 1948.

  3. CAROZZI, T. D., et. al.: “Detecting Periodicity Using Only Addition and Subtraction”, under review for publication in “ELSEVIER: Signal Processing”, 2006.

  4. CABAL-YEPEZ, E. et. al.: “A Hardware Implementation of the Discrete-Time FSWT for High-Speed Detection of Periodic Signals in Discrete-Time Data”, under review for publication in “IEEE Transactions on Computers”, 2006.

  5. HUBER, N. et. al.: Optimized Hybrid Algorithm for the Calculation of Base Two Logarithm of Integers in Hardware, under review for publication in “ELSEVIER Microprocessors and Microsystems”, 2006.


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