Open Access

An Efficient Implementation of the Sign LMS Algorithm Using Block Floating Point Format

  • Mrityunjoy Chakraborty1Email author,
  • Rafiahamed Shaik1 and
  • Moon Ho Lee2
EURASIP Journal on Advances in Signal Processing20072007:057086

Received: 11 July 2005

Accepted: 24 November 2006

Published: 31 January 2007


An efficient scheme is presented for implementing the sign LMS algorithm in block floating point format, which permits processing of data over a wide dynamic range at a processor complexity and cost as low as that of a fixed point processor. The proposed scheme adopts appropriate formats for representing the filter coefficients and the data. It also employs a scaled representation for the step-size that has a time-varying mantissa and also a time-varying exponent. Using these and an upper bound on the step-size mantissa, update relations for the filter weight mantissas and exponent are developed, taking care so that neither overflow occurs, nor are quantities which are already very small multiplied directly. Separate update relations are also worked out for the step size mantissa. The proposed scheme employs mostly fixed-point-based operations, and thus achieves considerable speedup over its floating-point-based counterpart.


Authors’ Affiliations

Department of Electronics and Electrical Communication Engineering, Indian Institute of Technology
Department of Information and Communication, Chonbuk National University


  1. Ralev KR, Bauer PH: Realization of block floating-point digital filters and application to block implementations. IEEE Transactions on Signal Processing 1999,47(4):1076-1086. 10.1109/78.752605View ArticleMATHGoogle Scholar
  2. Sridharan S: Implementation of state-space digital filter structures using block floating-point arithmetic. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '87), April 1987, Dallas, Tex, USA 908-911.View ArticleGoogle Scholar
  3. Kalliojärvi K, Astola J: Roundoff errors in block-floating-point systems. IEEE Transactions on Signal Processing 1996,44(4):783-790. 10.1109/78.492531View ArticleGoogle Scholar
  4. Sridharan S, Dickman G: Block floating-point implementation of digital filters using the DSP56000. Microprocessors and Microsystems 1988,12(6):299-308. 10.1016/0141-9331(88)90186-XView ArticleGoogle Scholar
  5. Sridharan S, Williamson D: Implementation of high-order direct-form digital filter structures. IEEE Transactions on Circuits and Systems 1986,33(8):818-822. 10.1109/TCS.1986.1086002View ArticleGoogle Scholar
  6. Taylor FJ: Block floating-point distributed filters. IEEE Transactions on Circuits and Systems 1984,31(3):300-304. 10.1109/TCS.1984.1085491View ArticleGoogle Scholar
  7. Mitra A, Chakraborty M, Sakai H: A block floating-point treatment to the LMS algorithm: efficient realization and a roundoff error analysis. IEEE Transactions on Signal Processing 2005,53(12):4536-4544.MathSciNetView ArticleGoogle Scholar
  8. Mitra A, Chakraborty M: The NLMS algorithm in block floating-point format. IEEE Signal Processing Letters 2004,11(3):301-304. 10.1109/LSP.2003.822891View ArticleGoogle Scholar
  9. Erickson AC, Fagin BS: Calculating the FHT in hardware. IEEE Transactions on Signal Processing 1992,40(6):1341-1353. 10.1109/78.139240View ArticleMATHGoogle Scholar
  10. Elam D, Lovescu C: A block floating point implementation for an N-point FFT on the TMS320C55X DSP. In Application Report SPRA948. Texas Instruments, Dallas, Tex, USA; 2003.Google Scholar
  11. Bidet E, Castelain D, Joanblanq C, Senn P: A fast single-chip implementation of 8192 complex point FFT. IEEE Journal of Solid-State Circuits 1995,30(3):300-305. 10.1109/4.364445View ArticleGoogle Scholar
  12. Chakraborty M, Mitra A: A block floating-point realization of the gradient adaptive lattice filter. IEEE Signal Processing Letters 2005,12(4):265-268.View ArticleGoogle Scholar
  13. Farhang-Boroujeny B: Adaptive Filters—Theory and Application. John Wiley & Sons, Chichester, UK; 1998.Google Scholar


© Chakraborty et al. 2007