Time Encoding and Decoding in Bandlimited and Shift-Invariant Spaces

2017 ◽  
pp. 7-29
Author(s):  
Dorian Florescu
Keyword(s):  
Time Encoding ◽  
Shift Invariant Spaces ◽  
Invariant Spaces

A Novel Reconstruction Framework for Time-Encoded Signals with Integrate-and-Fire Neurons

2015 ◽  
Vol 27 (9) ◽  
pp. 1872-1898 ◽  
Author(s):  
Dorian Florescu ◽  
Daniel Coca
Keyword(s):  
Reconstruction Algorithm ◽  
Spike Time ◽  
Reconstruction Algorithms ◽  
Real Time Processing ◽  
Integrate And Fire ◽  
Time Encoding ◽  
Shift Invariant Spaces ◽  
Band Limited ◽  
Invariant Spaces ◽  
Time Sequences

Integrate-and-fire neurons are time encoding machines that convert the amplitude of an analog signal into a nonuniform, strictly increasing sequence of spike times. Under certain conditions, the encoded signals can be reconstructed from the nonuniform spike time sequences using a time decoding machine. Time encoding and time decoding methods have been studied using the nonuniform sampling theory for band-limited spaces, as well as for generic shift-invariant spaces. This letter proposes a new framework for studying IF time encoding and decoding by reformulating the IF time encoding problem as a uniform sampling problem. This framework forms the basis for two new algorithms for reconstructing signals from spike time sequences. We demonstrate that the proposed reconstruction algorithms are faster, and thus better suited for real-time processing, while providing a similar level of accuracy, compared to the standard reconstruction algorithm.

scholarly journals Shift-invariant spaces from rotation-covariant functions

2008 ◽  
Vol 25 (2) ◽  
pp. 240-265 ◽  
Author(s):  
Brigitte Forster ◽  
Thierry Blu ◽  
Dimitri Van De Ville ◽  
Michael Unser
Keyword(s):  
Shift Invariant Spaces ◽  
Invariant Spaces

Backward Continued Fractions and their Invariant Measures

1996 ◽  
Vol 39 (2) ◽  
pp. 186-198 ◽  
Author(s):  
Karlheinz Gröchenig ◽  
Andrew Haas
Keyword(s):  
Nonnegative Integer ◽  
Continued Fractions ◽  
Invariant Measures ◽  
Specific Class ◽  
Integer Sequences ◽  
New Family ◽  
Shift Map ◽  
Shift Invariant Spaces ◽  
Invariant Spaces

AbstractThis paper continues our investigation of backward continued fractions, associated with the generalized Renyi maps on [0,1). We first show that the dynamics of the shift map on a specific class of shift invariant spaces of nonnegative integer sequences exactly models the maps Tu for u € (0,4). In the second part we construct a new family of explicit invariant measures for certain values of the parameter u.

Sign in / Sign up

Export Citation Format

Share Document