The integrate-and-fire sampler: A special type of asynchronous Σ - Δ modulator

We present the integrate-and-fire (IF) model as a time encoding scheme and show that it corresponds to a special case of the asynchronous Σ-Δ modulator (ASDM). We depart from typical rate based encoding used by conventional ASDM towards time based encoding. We show that for certain families of signals, such as neural recordings, the IF sampler accurately encodes the regions of interest at sub-Nyquist data rates. Nevertheless, the encoder requires nonlinear recovery algorithms, instead of the typical low pass filter.

[1]  László Tóth,et al.  Time encoding and perfect recovery of bandlimited signals , 2003, 2003 IEEE International Conference on Acoustics, Speech, and Signal Processing, 2003. Proceedings. (ICASSP '03)..

[2]  Hossein Sameti,et al.  Likelihood-Maximizing-Based Multiband Spectral Subtraction for Robust Speech Recognition , 2009, EURASIP J. Adv. Signal Process..

[3]  E. Roza,et al.  Analog-to-digital conversion via duty-cycle modulation , 1997 .

[4]  Arthur H. M. van Roermund,et al.  Sigma-delta modulators operating at a limit cycle , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[5]  Saeed Mian Qaisar,et al.  Adaptive Rate Sampling and Filtering Based on Level Crossing Sampling , 2009, EURASIP J. Adv. Signal Process..

[6]  Wulfram Gerstner,et al.  Spiking Neuron Models: An Introduction , 2002 .

[7]  A.H.M. van Roermund,et al.  Analysis and design of high-performance asynchronous sigma-delta Modulators with a binary quantizer , 2006, IEEE Journal of Solid-State Circuits.

[8]  Thierry Blu,et al.  Sampling signals with finite rate of innovation , 2002, IEEE Trans. Signal Process..

[9]  E. W. Williams,et al.  Integrated converters : D to A and D architectures, analysis and simulation , 2001 .

[10]  José Carlos Príncipe,et al.  Approximate reconstruction of bandlimited functions for the integrate and fire sampler , 2009, Advances in Computational Mathematics.

[11]  Vaibhav Garg,et al.  An asynchronous delta-sigma converter implementation , 2006, 2006 IEEE International Symposium on Circuits and Systems.

[12]  Ivars Bilinskis.  Digital alias-free signal processing , 2007 .

[13]  Emmanuel J. Candès,et al.  Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information , 2004, IEEE Transactions on Information Theory.

[14]  John G. Harris,et al.  Signal reconstruction from spiking neuron models , 2004, 2004 IEEE International Symposium on Circuits and Systems (IEEE Cat. No.04CH37512).

[15]  Marek Miśkowicz,et al.  Asynchronous Sigma-Delta analog-to digital converter based on the charge pump integrator , 2008 .

[16]  John G. Harris,et al.  Stimulus reconstruction from the biphasic integrate-and-fire sampler , 2009, 2009 4th International IEEE/EMBS Conference on Neural Engineering.

[17]  José Carlos Príncipe,et al.  Florida Wireless Implantable Recording Electrodes (FWIRE) for Brain Machine Interfaces , 2007, 2007 IEEE International Symposium on Circuits and Systems.

[18]  H. Inose,et al.  A Telemetering System by Code Modulation - Δ- ΣModulation , 1962, IRE Transactions on Space Electronics and Telemetry.

[19]  Hiroshi Inose,et al.  Asynchronous delta-modulation system , 1966 .

[20]  José Carlos Príncipe,et al.  Integrate and fire circuit as an ADC replacement , 2011, 2011 IEEE International Symposium of Circuits and Systems (ISCAS).

[21]  José Carlos Príncipe,et al.  Brain-Machine Interface Engineering , 2006, Brain-Machine Interface Engineering.

[22]  E. Roza,et al.  Poly-phase sigma-delta modulation , 1997 .

[23]  Aurel A. Lazar,et al.  Time encoding with an integrate-and-fire neuron with a refractory period , 2004, Neurocomputing.

[24]  Vaibhav Garg,et al.  Low power integrate and fire circuit for data conversion , 2009, 2009 IEEE International Symposium on Circuits and Systems.