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Approximate Signal Processing

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Abstract

It is increasingly important to structure signal processing algorithms and systems to allow for trading off between the accuracy of results and the utilization of resources in their implementation. In any particular context, there are typically a variety of heuristic approaches to managing these tradeoffs. One of the objectives of this paper is to suggest that there is the potential for developing a more formal approach, including utilizing current research in Computer Science on Approximate Processing and one of its central concepts, Incremental Refinement. Toward this end, we first summarize a number of ideas and approaches to approximate processing as currently being formulated in the computer science community. We then present four examples of signal processing algorithms/systems that are structured with these goals in mind. These examples may be viewed as partial inroads toward the ultimate objective of developing, within the context of signal processing design and implementation, a more general and rigorous framework for utilizing and expanding upon approximate processing concepts and methodologies.

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References

  1. V.R. Lesser, J. Pavlin, and E. Durfee, “Approximate processing in real-time problem solving,” AI Magazine, pp. 49-61, Spring 1988.

  2. K.J. Lin, S. Natarajan, and J.W.S. Liu, “Imprecise results: Utilizing partial computations in real-time systems,” in Proc. Eighth Real-Time Sys. Symp., San Jose, CA, Dec. 1987, pp. 210-217.

  3. E.J. Horvitz, “Reasoning about beliefs and actions under computational resource constraints,” in Third Workhsop on Uncertainty in Artificial Intelligence, Seattle, WA, July 1987, pp. 429-439.

  4. N.S. Jayant and P. Noll, Digital Coding of Waveforms: Principles and Applications to Speech and Video, Englewood Cliffs, NJ, Prentice Hall, 1984.

    Google Scholar 

  5. K. Knowlton, “Progressive transmission of grey-scale and binary pictures by simple, efficient, and lossless encoding schemes,” Proc. IEEE, Vol. 68, pp. 885-896, July 1980.

    Google Scholar 

  6. T. Dean and M. Boddy, “An analysis of time-dependent planning,” in Proc. Seventh Nat'l. Conf. on Artificial Intelligence, St. Paul, MN, Aug. 1988, pp. 49-54.

  7. J. Pridmore, G. Buchanan, G. Caracciolo, and J. Wedgwood, ”Model-year architectures for rapid prototyping,” J. VLSI Sig. Proc., Vol. 15, pp. 83-96.

  8. J.W.S. Liu, S. Natarajan, and K.J. Lin, “Scheduling real-time periodic jobs using imprecise results,” in Proc. Eighth Real-Time Sys. Symp., San Jose, CA, Dec. 1987, pp. 252-260.

  9. K.J. Lin, S. Natarajan, and J.W.S. Liu, “Concord: A system of imprecise computations,” in Proc. 1987 IEEE Compsac, San Jose, CA, Dec. 1987, pp. 75-81.

  10. A. Garvey and V. Lesser, “A survey of research in deliberative real-time artificial intelligence,” Real-Time Systems, Vol. 6, pp. 317-347, May 1994.

  11. S.J. Russell and S. Zilberstein, “Composing real-time systems,” in Proc. 12th Int. Joint Conf. Artif. Intel., Sydney, Australia, 1992, pp. 212-217.

  12. S. Zilberstein and S. Russell, “Optimal composition of real-time systems,” Artificial Intelligence, Dec. 1995.

  13. S. Zilberstein, Operational Rationality through Compilation of Anytime Algorithms, Ph.D. Thesis, U.C. Berkeley, 1993.

  14. M. Boddy and T.L. Dean, “Solving time-dependent planning problems,” in Proc. Eleventh Int'l. Joint Conf. on Artificial Intelligence, Detroit, MI, 1989, pp. 979-984.

  15. J.A. Stankovic and K. Ramamritham, Hard Real-Time Systems, IEEE Computer Society Press, Washington, DC, 1988.

    Google Scholar 

  16. J.A. Stankovic and K. Ramamritham, Advances in Real-Time Systems, IEEE Computer Society Press, Washington, DC, 1993.

    Google Scholar 

  17. J.W.S. Liu, W.K. Shih, K.J. Lin, R. Bettati, and J.Y. Chung, ”Imprecise computations,” Proc. IEEE, Vol. 82, pp. 83-93, Jan. 1994.

  18. J.W.S. Liu, K.J. Lin, W.K. Shih, A.C. Yu, and J.Y. Chung, “Algorithms for scheduling imprecise computations,” Computer, Vol. 24, pp. 58-68, May 1991.

    Article  Google Scholar 

  19. E.L. Lawler and J.M. Moore, “A functional equation and its application to resource allocation and scheduling problems,” Management Science, Vol. 16, pp. 77-84, 1969.

    Article  MATH  Google Scholar 

  20. W.K. Shih and J.W.S. Liu, “On-line scheduling of imprecise computations to minimize total error,” in Proc. 13th Real-Time Sys. Symp., Pheonix, AZ, Dec. 1992, pp. 280-289.

  21. J.Y. Chung, W.K. Shih, J.W.S. Liu, and D.W. Gillies, “Scheduling imprecise computations to minimize total error,” Microprocessing and Microprogramming, Vol. 27, pp. 767-774, 1989.

    Article  Google Scholar 

  22. K.I.J. Ho, J.Y.T. Leung, and W.D. Wei, “Minimizing maximum weighted error of imprecise computation tasks,” Technical Report, Dept. of Computer Science and Engineering, University of Nebraska, 1992.

  23. J.Y. Chung and J.W.S. Liu, “Scheduling periodic jobs that allow imprecise results,” IEEE Trans. Computers, Vol. 39, pp. 1156-1173, Sept. 1990.

    Article  MATH  Google Scholar 

  24. I.K. Cheong, Scheduling Imprecise Hard Real-Time Jobs with Cumulative Error, Ph.D. Thesis, University of Illinois at Urbana-Champaign, 1992.

    Google Scholar 

  25. P. Henderson, Functional Programming: Application and Implementation, NJ, Prentice Hall, Englewood Cliffs, 1980.

    MATH  Google Scholar 

  26. E.J. Horvitz, G.F. Cooper, and D.E. Heckerman, “Reflection and action under scarce resources: Theoretical principles and empirical study,” in Proc. 11th Int. Joint Conf. Artif. Intel., Detroit, MI, 1989, pp. 1121-1127.

  27. E.J. Horvitz and G. Rutledge, “Time-dependent utility and action under uncertainty,” in Proc. 7th Conf. on Uncert. in Artif. Intel., Los Angeles, CA, July 1991, pp. 151-158.

  28. J. Pearl, “Fusion, propagation, and structuring in belief networks,” Artificial Intelligence, Vol. 29, pp. 241-288, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  29. E.J. Horvitz, Computation and Action Under Bounded Resources, Ph.D. Thesis, Stanford Univ., 1990.

  30. S. Russell and E. Wefald, “Principles of metareasoning,” Artificial Intelligence, May 1991.

  31. S.J. Russell and E. Wefald, Do the Right Thing: Studies in Limited Rationality, MIT Press, Cambridge, MA, 1991.

    Google Scholar 

  32. S. Zilberstein and S.J. Russell, “Anytime sensing, planning and action: A practical model for robot control,” in Proc. 13th Int. Joint Conf. Artif. Intel., Chambery, France, 1993, pp. 1402-1407.

  33. A.J. Garvey and V.R. Lesser, “Design-to-time real-time scheduling,”IEEE Trans. Sys., Man, and Cybernetics, Vol. 23, pp. 1491-1502, Nov. 1993.

    Article  Google Scholar 

  34. K. Decker, V. Lesser, and R.C. Whitehair, “Extending a blackboard architecture for approximate processing,” J. Real-Time Systems, Vol. 2, No. 1, pp. 47-79, 1990.

    Article  Google Scholar 

  35. N. Levinson, “The Wiener RMS error criterion in filter design and prediction,” J. Math. Phys., Vol. 25, pp. 261-278, Jan. 1947.

    MathSciNet  Google Scholar 

  36. M. Vetterli and C. Herley, “Wavelets and filter banks: Theory and design,” IEEE Trans. Signal Processing, Vol. 40, pp. 2207-2232, Sept. 1992.

    Article  MATH  Google Scholar 

  37. J.M. Winograd, S.H. Nawab, and A.V. Oppenheim, “FFT-based incremental refinement of suboptimal detection,” in Proc. IEEE Int. Conf. Acoust., Speech, and Signal Processing, Atlanta, GA, May 1996, pp. 2479-2482.

  38. H.L. Van Trees, Detection, Estimation, and Modulation Theory-Part I, John Wiley & Sons, New York, 1968.

    MATH  Google Scholar 

  39. R.J. Kenefic, “Generalized likelihood ratio detector performance for a tone with unknown parameters in Gaussian white noise,” IEEE Trans. Signal Processing, Vol. 39, pp. 978-980, April 1991.

    Article  Google Scholar 

  40. J.D. Markel, “FFT pruning,” IEEE Trans. Audio and Electroacoustics, Vol. AU-19, pp. 305-310, Dec. 1971.

    Article  Google Scholar 

  41. D.P. Skinner, “Pruning the decimation in-time FFT algorithm,” IEEE Trans. Acoust., Speech, and Signal Processing, pp. 193-194, April 1976.

  42. T.V. Sreenivas and P.V.S. Rao, “FFT algorithm for both input and output pruning,” IEEE Trans. Acoust., Speech, and Signal Processing, Vol. ASSP-27, pp. 291-292, June 1979.

    Article  Google Scholar 

  43. G. Goertzel, “An algorithm for the evaluation of finite trigonometric series,” Amer. Math. Monthly, Vol. 65, pp. 34-35, Jan.1958.

    Article  MathSciNet  MATH  Google Scholar 

  44. H.V. Sorensen and C.S. Burrus, “Efficient computation of the DFT with only a subset of input or output points,” IEEE Trans. Signal Processing, Vol. 41, pp. 1184-1200, March 1993.

    Article  MATH  Google Scholar 

  45. O.V. Shentov, S.K. Mitra, U. Heute, and A.N. Hossen, “Subband DFT-Part I: Definition, interpretation, and extensions,” Signal Processing, Vol. 41, pp. 261-277, Feb. 1995.

    Article  MATH  Google Scholar 

  46. G.F. Boudreaux-Bartels and T.W. Parks, “Discrete Fourier transform using summation by parts,” in Proc. IEEE Int. Conf. Acoust., Speech, and Signal Processing, Dallas, TX, 1987, Vol. 3, pp. 1827-1830.

    Google Scholar 

  47. M.P. Lamoureux, “The Poorman's transform: Approximating the Fourier transform without multiplication,” IEEE Trans. Signal Processing, Vol. 41, pp. 1413-1415, March 1993

    Article  MATH  Google Scholar 

  48. S.H. Nawab and E. Dorken, “Efficient STFT approximation using a quantization and differencing method,” in Proc. IEEE Int. Conf. Acoust., Speech, and Signal Processing, Minneapolis, MN, April 1993, pp. 587-590.

  49. J.M. Winograd and S.H. Nawab, “Incremental refinement of DFT and STFT approximations,” IEEE Signal Processing Letters, Vol. 2, pp. 25-28, Feb. 1995.

    Article  Google Scholar 

  50. S.H. Nawab and E. Dorken, “A framework for quality versus efficiency tradeoffs in STFT analysis,” IEEE Trans. Signal Processing, Vol. 43, pp. 998-1001, April 1995.

    Article  Google Scholar 

  51. A. Peled and B. Liu, “A new hardware realization of digital filters,” IEEE Trans. Acoust., Speech, and Signal Processing, Vol. ASSP-22, pp. 456-462, Dec. 1974.

    Article  Google Scholar 

  52. S.A. White, “Applications of distributed arithmetic to digital signal processing: A tutorial review,” IEEE ASSP Magazine, Vol. 6, pp. 4-19, July 1989.

    Article  Google Scholar 

  53. S. Chu and C.S. Burrus, “A prime factor FFT algorithm using distributed arithmetic,” IEEE Trans. Signal Processing, Vol. ASSP-30, pp. 217-226, April 1982.

    MathSciNet  Google Scholar 

  54. F.J. Taylor, “An RNS discrete fourier transform implementation,” IEEE Trans. Acoust., Speech, and Signal Processing, Vol. 38, pp. 1386-1394, Aug. 1990.

    Article  Google Scholar 

  55. J.M. Winograd and S.H. Nawab, “Probabilistic complexity analysis for a class of approximate DFT algorithms,” J. VLSI Sig. Proc., Vol. 14, pp. 193-205, 1996.

    Article  Google Scholar 

  56. S.H. Nawab and J.M. Winograd, “Approximate signal processing using incremental refinement and deadline-based algorithms,” in Proc. IEEE Int. Conf. Acoust., Speech, and Signal Processing, Detroit, MI, May 1995, Vol. 5, pp. 2857-2860.

    Google Scholar 

  57. M.-T. Sun, T.-C. Chen, and A.M. Gottlieb, “VLSI implementation of a 16 × 16 discrete cosine transform,” IEEE Trans. Circ. and Sys., Vol. 36, pp. 610-617, April 1989.

    Article  Google Scholar 

  58. S. Uramoto, Y. Inoue, A. Takabatake, J. Takeda, Y. Yamashita, H. Terane, and M. Yoshimoto, “A 100-MHz 2-D discrete cosine transform core processor,” IEEE J. Solid State Circuits, Vol. 27, pp. 492-498, April 1992.

    Article  Google Scholar 

  59. H. Fujiwara, M.L. Liou, M.-T. Sun, K.-M. Yang, M. Maruyama, K. Shomura, and K. Ohyama, “An all-ASIC implementation of a low bit-rate video codec,” IEEE Trans. Circ. and Sys. for Video Tech., Vol. 2, pp. 123-133, June 1992.

    Article  Google Scholar 

  60. J.T. Ludwig, S.H. Nawab, and A. Chandrakasan, “Low power filtering using approximate processing for DSP applications,” in Proc. Custom Integrated Circuits Conf., Santa Clara, CA, May 1995, pp. 185-188.

  61. J.T. Ludwig, S.H. Nawab, and A. Chandrakasan, “Low-power digital filtering using approximate processing,” IEEE J. Solid State Circ., Vol. 31, pp. 395-400, March 1996.

    Article  Google Scholar 

  62. J.T. Ludwig, S.H. Nawab, and A. Chandrakasan, “Convergence results on adaptive approximate filtering,” Advanced Signal Processing Algorithms, F.T. Luk (Ed.), Proc. SPIE 2846, Aug. 1996.

  63. J.T. Ludwig, S.H. Nawab, and A. Chandrakasan, “Approximate filtering using incremental refinement structures,” in preparation for submission to IEEE Trans. Sig. Proc., Summer 1996.

  64. A. Chandrakasan and R. Brodersen, Low Power Digital CMOS Design, Kluwer Academic Publishers, Norwell, MA, 1995.

    Book  Google Scholar 

  65. V. Gutnik and A. Chandrakasan, “An efficient controller for variable supply-voltage low power processing,” IEE Symposium on VLSI Circuits, June 1996.

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Authors and Affiliations

  1. ECE Department, Boston University, 44 Cummington St., Boston, MA, 02215

    S. Hamid Nawab & Joseph M. Winograd

  2. EECS Department, Massachusetts Institute of Technology, 77 Massachusetts Ave., Cambridge, MA, 02139

    Alan V. Oppenheim, Anantha P. Chandrakasan & Jeffrey T. Ludwig

Authors
  1. S. Hamid Nawab
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  2. Alan V. Oppenheim
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  3. Anantha P. Chandrakasan
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  4. Joseph M. Winograd
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  5. Jeffrey T. Ludwig
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Nawab, S.H., Oppenheim, A.V., Chandrakasan, A.P. et al. Approximate Signal Processing. The Journal of VLSI Signal Processing-Systems for Signal, Image, and Video Technology 15, 177–200 (1997). https://doi.org/10.1023/A:1007986707921

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