Weight Functions for Signal Reconstruction Based On Level Crossings

Authors: Nagesha, G. Hemantha Kumar

Abstract:

Although the level crossing concept has been the subject of intensive investigation over the last few years, certain problems of great interest remain unsolved. One of these concern is distribution of threshold levels. This paper presents a new threshold level allocation schemes for level crossing based on nonuniform sampling. Intuitively, it is more reasonable if the information rich regions of the signal are sampled finer and those with sparse information are sampled coarser. To achieve this objective, we propose non-linear quantization functions which dynamically assign the number of quantization levels depending on the importance of the given amplitude range. Two new approaches to determine the importance of the given amplitude segment are presented. The proposed methods are based on exponential and logarithmic functions. Various aspects of proposed techniques are discussed and experimentally validated. Its efficacy is investigated by comparison with uniform sampling.

Keywords: speech signals, sampling, signal reconstruction, asynchronousdelta modulation, non-linear quantization.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1075677

References:

[1] R. J. Mitchell and R. C Gonzalez, Multilevel crossing rates for automated signal classification, Proc. of ICASSP-78, Volume 3, Apr 1978 Page(s):218 222.
[2] H. Inose, T. Aoki and K. Wantanable, Asynchronous delta modulation systems, Electron. Commun., Japan, pp.34-42, Mar. 1966.
[3] N. Sayiner, H. V. Sorensen and T. R. Viswanathan, A level crossing sampling scheme for A/D conversion, IEEE Transactions on Circuits and Systems II 43, April-1996, pp. 335-339.
[4] E. Allier, G. Sicard, L. Fesquet and M. Renaudin, Asynchronous level crossing analog to digital converters, Measurement Journal, April, 2005,Vol. 37, pp.296-309.
[5] Karen Guan and Andrew C. Singer, A Level Crossing Sampling Scheme for Non-Bandlimited Signals, Proc. of ICASSP 2006, May 2006, Volume: 3,pp: III-381-383.
[6] Marek Miskowicz, Efficiency of Level-Crossing Sampling for Bandlimited Gaussian Random Processes, Proc. of IEEE International Workshop on Factory Communication Systems-2006, June 2006, pp: 137- 142
[7] William H. Press, Saul A. Teukolsky, T. V William and P. F Brian, Numerical Recipes in C++, Cambridge university press, Second Edition, 2002.
[8] M. Lim and C. Saloma, Direct signal recovery from threshold crossings Phys. Rev. E 58, pp:6759 - 6765 (1998).
[9] G. Tapang and C. Saloma, Dynamic range enhancement of an optimized 1-bit AD converter, IEEE Trans. Circuits Syst II, Vol. 49, pp. 42-47 (2002).
[10] I. F. Blake and W. C. Lindsey, Level-crossing problems for random processes, IEEE Transactions on Information Theory, no:3, pp. 295-315, 1973.
[11] F. Akopyan, R. Manohar and A. B. Apsel, A level-crossing flash asynchronous analog-to-digital converter, Proc. of IEEE International Symposium on Asynchronous Circuits and Systems 2006,pp.12-22.
[12] Layer 7 LonMark Interoperability Guidelines, Ver. 3.2; LonMark Interoperability Association,2002.
[13] S. C. Gupta, Increasing the sampling efficiency for a control system. IEEE Transactions on Automatic Control 1963, 8 (3), 263-264.
[14] M. Miskowicz, Send-on-delta concept: an event-based data reporting strategy, Sensors, Special Issue: Wireless Sensor Networks and Platforms vol. 6, no 1, pp. 49-63, 2006.
[15] K. J. Astrom and B. Bernhardsson, Comparison of periodic and event based sampling for first-order stochastic systems, Proc. of IFAC World Congress 1999, pp. 301-306.
[16] P. Otanez, J. Moyne and D. Tilbury, Using deadbands to reduce communication in networked control systems, Proc. of American Control Conference 2002, pp. 3015-3020.
[17] M. Miskowicz, Asymptotic Effectiveness of the Event-Based Sampling according to the Integral Criterion, Sensors, Special Issue: Wireless Sensor Networks and Platforms vol. 6, no 1, pp. 49-63, 2006.
[18] B. Bernhardsson,Event triggered sampling, Research problem formulations in the DICOSMOS project 1998, Lund Institute of Technology.
[19] K. J. Astrom and B. Bernhardsson, Comparison of Riemann and Lebesgue Sampling for First Order Stochastic Systems, Proc. of the 41st IEEE Conference on Decision and Control, Vol 2, pp. 2011- 2016, 2002.
[20] V. Daria and C. Saloma, High-Accuracy Fourier Transform Interferometry, Without Oversampling, with a 1-Bit Analog-to-Digital Converter, Appl. Opt. 39 108-113 (2000)
[21] M. A. Nazario and C. Saloma, Signal Recovery in Sinusoid-Crossing Sampling by use of the Minimum-Negativity Constraint, Appl. Opt. 37, 2953-2963 (1998)
[22] J. S. Garofolo and L. F. Lamel, DARPA TIMIT Acoustic-phonetic Continuous Speech Corpus, U.S.Department of Commerce, 1993
[23] G. Lu, Communication and Computing for Distributed Multimedia Systems, Artech House, ISBN: 0-89006-884-4, 1996.