ELEN E6901 Time Encoding, Channels and Information

A fundametal question arising in information processing is how to represent a bandlimited signal as a discrete sequence. In digital signal processing the classical sampling theorem together with quantization of the discrete signal amplitude is the representation of choice. Due to the ever decreasing size of integrated circuits and the attendant low voltage, high precision quantizers are more and more difficult to build. These circuits provide increasing timing resolution, however, that a temporal code can take advantage of.

A Time Encoding Machine is a real-time asynchronous mechanism for encoding amplitude information into a time sequence. Inspired by models of the neuron, we introduce a Time Encoding Machine that is invertible. We show how to build an inverse Time Decoding Machine that recovers the original signal loss-free. The Time Decoding Machine suggests an alternative "spike processing" paradigm for information processing that incorporates the best properties of analog processing (impulse response) and digital processing (constant amplitude). This shift of paradigm will potentially revolutionize the fields of information processing and computation.

Research papers published in the neuroscience literature will be the object of our in class as well as project study. In the first part of the semester you are expected to create some of the common underlying building blocks of models of hearing, vision and olfactory systems. In the second half you will build a spike processing architecture that realizes one of these models. The midterm paper will describe the architecture of the biological system that you will focus on. A final exam presentation will be a live demonstration of the performance and capabilities of your architecture.

Course Benefits

Professor Lazar

Applicable Degree Programs

Most courses 4000-level and above can be credited to all degree programs. All courses are subject to advisor approval.
Lecturer/Manager Professor Aurel A. Lazar
Class location: 415 Shapiro
Office hours: Mondays and Wednesdays, 11:00 AM - 12:00 PM EST
Office phone: +1 212 854 1747
Email address: aurel "at" ee.columbia.edu
Class Web Site: Offered by the COMET Group
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Day and time: Mondays and Wednesdays, 9:35 - 10:50 AM
Credits for course: 3 points
Prerequisites: ELEN E4011 or ELEN E4810 or ELEN E6711 or the equivalent.
Description: Time Encoding and Decoding Machines, Time Encoding and Perfect Recovery of Bandlimited Signals, Asynchronous Sigma-Delta modulators, Neuro-modulators, Non-Uniform Sampling, Wavelets and Frames, Models of Hearing, Models of Vision, Models of Olfactory Systems.
Required text(s): research papers, sections of the reference texts.
Reference text(s): P. Dayan and L.F. Abbott, Theoretical Neuroscience, The MIT Press, Cambridge, MA, 2001.
S. Mallat, A Wavelet Tour of Signal Processing, Second edition, Academic Press, New York, 1998.
W. Gerstner and W. Kistler, Spiking Neuron Models Cambridge University Press, New York, NY, 2002.
F.M. Rieke, D. Warland, R. de Ruyter van Steveninck, W. Bialek, Spikes: Exploring the Neural Code, The MIT Press, Cambridge, MA, 1997.
G. Strang and T. Nguyen, Wavelets and Filter Banks, Wellesley-Cambridge Press, Wellesley, MA, 1997.
M. Vetterli and J. Kovacevic, Wavelets and Subband Coding, Prentice-Hall, Upper Saddle River, NJ, 1995.
H.R. Wilson, Spikes, Decisions and Actions, The Dynamical Foundations of Neuroscience, Oxford University Press, New York, 1999.

Homework(s): Reading research papers
Paper(s): Midterm paper
Project(s): 2 projects using Matlab or Mathematica
Midterm exam: Monday, March 10 (paper submission)
Final exam: Friday, May 16, 2003, 9:00 AM - 12:00 PM (final project presentation).
Grading: Projects 3/10, Midterm paper 1/5, final exam 1/2.
Hardware requirements: ---
Software requirements: Matlab or Mathematica
Homework submission: ---