### Abstract

Time encoding is a novel real-time asynchronous mechanism for encoding amplitude information into a time sequence. The analog bandlimited input is fed into a simple nonlinear neuron-like circuit that generates a strictly increasing time sequence based on which the signal can be reconstructed. The heart of the reconstruction is solving a system of ill-conditioned linear equations. This contribution shows that the equations can be manipulated so that the reconstruction becomes feasible using a Cellular Neural Network (CNN) with a banded system matrix. In particular, the system is first transformed into a well-conditioned smaller system; and then, the Lanczos process is used to lay it out into a set of even smaller systems characterized by a set of tridiagonal matrices. Each of these systems can directly be solved by CNNs, whereas the preprocessing (transformation and Lanczos algorithm) and simple postprocessing phases can be partly or fully implemented by using the digital capabilities of the CNN Universal Machine (CNN-UM). Each step of the proposed formulation is confirmed by numerical (digital) simulations.

Original language | English |
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Title of host publication | 2004 Seventh Seminar on Neural Network Applications in Electrical Engineering - Proceedings, NEUREL 2004 |

Editors | B. Reljin, S. Stankovic |

Pages | 97-102 |

Number of pages | 6 |

Publication status | Published - 2004 |

Event | 2004 Seventh Seminar on Neural Network Applications in Elecrtical Engineering, NEUREL 2004 - Belgrade Duration: Sep 23 2004 → Sep 25 2004 |

### Other

Other | 2004 Seventh Seminar on Neural Network Applications in Elecrtical Engineering, NEUREL 2004 |
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City | Belgrade |

Period | 9/23/04 → 9/25/04 |

### Fingerprint

### ASJC Scopus subject areas

- Engineering(all)

### Cite this

*2004 Seventh Seminar on Neural Network Applications in Electrical Engineering - Proceedings, NEUREL 2004*(pp. 97-102)

**A time decoding realization with a CNN.** / Lazar, Aurel A.; Roska, T.; Simonyi, Erno K.; Tóth, L.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*2004 Seventh Seminar on Neural Network Applications in Electrical Engineering - Proceedings, NEUREL 2004.*pp. 97-102, 2004 Seventh Seminar on Neural Network Applications in Elecrtical Engineering, NEUREL 2004, Belgrade, 9/23/04.

}

TY - GEN

T1 - A time decoding realization with a CNN

AU - Lazar, Aurel A.

AU - Roska, T.

AU - Simonyi, Erno K.

AU - Tóth, L.

PY - 2004

Y1 - 2004

N2 - Time encoding is a novel real-time asynchronous mechanism for encoding amplitude information into a time sequence. The analog bandlimited input is fed into a simple nonlinear neuron-like circuit that generates a strictly increasing time sequence based on which the signal can be reconstructed. The heart of the reconstruction is solving a system of ill-conditioned linear equations. This contribution shows that the equations can be manipulated so that the reconstruction becomes feasible using a Cellular Neural Network (CNN) with a banded system matrix. In particular, the system is first transformed into a well-conditioned smaller system; and then, the Lanczos process is used to lay it out into a set of even smaller systems characterized by a set of tridiagonal matrices. Each of these systems can directly be solved by CNNs, whereas the preprocessing (transformation and Lanczos algorithm) and simple postprocessing phases can be partly or fully implemented by using the digital capabilities of the CNN Universal Machine (CNN-UM). Each step of the proposed formulation is confirmed by numerical (digital) simulations.

AB - Time encoding is a novel real-time asynchronous mechanism for encoding amplitude information into a time sequence. The analog bandlimited input is fed into a simple nonlinear neuron-like circuit that generates a strictly increasing time sequence based on which the signal can be reconstructed. The heart of the reconstruction is solving a system of ill-conditioned linear equations. This contribution shows that the equations can be manipulated so that the reconstruction becomes feasible using a Cellular Neural Network (CNN) with a banded system matrix. In particular, the system is first transformed into a well-conditioned smaller system; and then, the Lanczos process is used to lay it out into a set of even smaller systems characterized by a set of tridiagonal matrices. Each of these systems can directly be solved by CNNs, whereas the preprocessing (transformation and Lanczos algorithm) and simple postprocessing phases can be partly or fully implemented by using the digital capabilities of the CNN Universal Machine (CNN-UM). Each step of the proposed formulation is confirmed by numerical (digital) simulations.

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M3 - Conference contribution

AN - SCOPUS:20844438029

SN - 0780385470

SP - 97

EP - 102

BT - 2004 Seventh Seminar on Neural Network Applications in Electrical Engineering - Proceedings, NEUREL 2004

A2 - Reljin, B.

A2 - Stankovic, S.

ER -