Unlike synchronous processing, asynchronous processing is more efficient in biomedical and sensing networks applications as it is free from aliasing constraints and quantization error in the amplitude, it allows continuous–time processing and more importantly data is only acquired in significant parts of the signal. We consider signal decomposers based on the asynchronous sigma delta modulator (ASDM), a non-linear feedback system that maps the signal amplitude into the zero-crossings of a binary output signal. The input, the zero-crossings and the ASDM parameters are related by an integral equation making the signal reconstruction difficult to implement. Modifying the model for the ASDM, we obtain a recursive equation that permits to obtain the non-uniform samples from the zero-time crossing values. Latticing the joint time-frequency space into defined frequency bands, and time windows depending on the scale parameter different decompositions are possible. We present two cascade low- and high-frequency decomposers, and a bank-of-filters parallel decomposer. This last decomposer using the modified ASDM behaves like a asynchronous analog to digital converter, and using an interpolator based on Prolate Spheroidal Wave functions allows reconstruction of the original signal. The asynchronous approaches proposed here are well suited for processing signals sparse in time, and for low-power applications.

References

1. 1)
  - 21. Senay, S., Oh, J., Chaparro, L.F.: ‘Regularized signal reconstruction for level-crossing sampling using Slepian functions’, Signal Process., 2012, 92, (4), pp. 1157–1165 (doi: 10.1016/j.sigpro.2011.11.017).
2. 2)
  - 22. Neumaier, A.: ‘Solving ill-conditioned and singular linear systems: a tutorial on regularization’, SIAM Rev., 1998, 40, pp. 636–666 (doi: 10.1137/S0036144597321909).
3. 3)
  - E. Roza . Analog-to-digital conversion via duty-cycle modulation. IEEE Trans. Circuit Syst. Part II , 11 , 907 - 914
4. 4)
  - 18. Hansen, P.C.: ‘Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion texte imprimé. SIAM monographs on mathematical modeling and computation’ (SIAM, Philadelphia, 1998).
5. 5)
  - 12. Kaldy, C., Lazar, A., Simonyi, E., Toth, L.: ‘Time encoded communications for human area network biomonitoring’. Technical Report 2-07, Department of Electrical Engineering, Columbia University, New York, NY, June 2007.
6. 6)
  - 16. Eldar, Y., Michaeli, T.: ‘Beyond bandlimited sampling’, IEEE Signal Process. Mag., 2009, 26, (3), pp. 48–68 (doi: 10.1109/MSP.2009.932125).
7. 7)
  - 19. Slepian, D.: ‘Prolate spheroidal wave functions, Fourier analysis and uncertainty’, Bell Syst. Tech. J., 1978, 57, (5), pp. 1371–1429 (doi: 10.1002/j.1538-7305.1978.tb02104.x).
8. 8)
  - 17. Can, A., Sejdic, E., Chaparro, L.F.: ‘Asynchronous sampling and reconstruction of sparse signals’. Proc. 20th European Signal Processing Conference (EUSIPCO), August 2012, pp. 854–858.
9. 9)
  - 20. Choi, H., Munson, D.C.Jr.: ‘Analysis and design of minimax-optimal interpolators’, IEEE Trans. Signal Process., 1998, 46, (6), pp. 1571–1579 (doi: 10.1109/78.678470).
10. 10)
  - 23. Sejdic, E., Can, A., Chaparro, L.F., Steele, C.M., Chau, T.: ‘Compressive sampling of swallowing accelerometry signals using time–frequency dictionaries based on modulated discrete Prolate spheroidal sequences’, EURASIP J. Adv. Signal Process., 2012, 2012, (1), pp. 1–14 (doi: 10.1186/1687-6180-2012-101).
11. 11)
  - 9. Kurchuk, M., Tsividis, Y.: ‘Signal-dependent variable-resolution clockless A/D conversion with application to continuous-time digital signal processing’, IEEE Trans. Circuits Syst. I: Reg. Pap., 2010, 57, (5), pp. 982–991 (doi: 10.1109/TCSI.2010.2043987).
12. 12)
  - 2. Renaudin, M.: ‘Asynchronous circuits and systems: a promising design alternative’, Microelectron. Eng., 2000, 54, (12), pp. 133–149 (doi: 10.1016/S0167-9317(00)80065-9).
13. 13)
  - 14. Can, A., Sejdic, E., Alkishriwo, O., Chaparro, L.F.: ‘Compressive asynchronous decomposition of heart sounds’. IEEE Statistical Signal Processing Workshop (SSP), August 2012, pp. 736–739.
14. 14)
  - 4. Hawkes, T., Simonpieri, P.: ‘Signal coding using asynchronous delta modulation’, IEEE Trans. Commun., 1974, 22, (5), pp. 729–731 (doi: 10.1109/TCOM.1974.1092255).
15. 15)
  - 5. Tsividis, Y.: ‘Digital signal processing in continuous time: a possibility for avoiding aliasing and reducing quantization error’. IEEE Int. Conf. Acoustics, Speech, and Signal Processing (ICASSP ‘04), 2004, vol. 2, pp. ii-589–592.
16. 16)
  - 8. Tsividis, Y.: ‘Mixed-domain systems and signal processing based on input decomposition’, IEEE Trans. Circuits Syst. I: Reg. Pap., 2006, 53, (10), pp. 2145–2156 (doi: 10.1109/TCSI.2006.882822).
17. 17)
  - 1. Aeschlimann, F., Allier, E., Fesquet, L., Renaudin, M.: ‘Asynchronous FIR filters: towards a new digital processing chain’. Proc. 10th Int. Symp. Asynchronous Circuits and Systems, 2004, pp. 198–206 (doi: 10.1109/ASYNC.2004.1299303).
18. 18)
  - 13. Lazar, A., Simonyi, E., Toth, L.: ‘Time encoding of bandlimited signals, an overview’. Proc. Conf. Telecommunication Systems, Modeling and Analysis, November 2005.
19. 19)
  - 6. Guan, K., Singer, A.C.: ‘A level-crossing sampling scheme for non-bandlimited signals’. Proc. IEEE Int. Conf. Acoustics, Speech and Signal Processing (ICASSP), May 2006, vol. 3, p. III.
20. 20)
  - 15. Lazar, A.A., Simonyi, E.K., Toth, L.T.: ‘An overcomplete stitching algorithm for time decoding machines’, IEEE Trans. Circuits Syst. I: Reg. Pap., 2008, 55, (9), pp. 2619–2630.
21. 21)
  - 11. Aksenov, E.V., Ljashenko, Y.M., Plotnikov, A.V., Prilutskiy, D.A., Selishchev, S.V., Vetvetskiy, E.V.: ‘Biomedical data acquisition systems based on sigma-delta analogue-to-digital converters’. Engineering in Medicine and Biology Society, 2001. Proc. 23rd Annual Int. Conf. IEEE, 2001, vol. 4, pp. 3336–3337.
22. 22)
  - 7. Senay, S., Chaparro, L.F., Sun, M., Sclabassi, R.: ‘Adaptive level-crossing sampling and reconstruction’. Proc. 18th European Signal Processing Conference (EUSIPCO), August 2010.
23. 23)
  - 3. Kinniment, D., Yakovlev, A., Gao, B.: ‘Synchronous and asynchronous a-d conversion’, IEEE Trans. Very Large Scale Integr. (VLSI) Syst., 2000, 8, (2), pp. 217–220 (doi: 10.1109/92.831441).
24. 24)
  - 24. Sejdic, E., Jiang, J.: ‘Selective regional correlation for pattern recognition’, IEEE Trans. Syst. Man Cybern. Part A: Syst. Hum., 2007, 37, (1), pp. 82–93 (doi: 10.1109/TSMCA.2006.886333).

Asynchronous processing of sparse signals

References

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