|
Signal Reconstruction in Event-driven Signal Processing
Project "SIREN - Signal Reconstruction in Event-driven Signal Processing" has been supported by the Norway Grants in the Polish-Norwegian Research Programme operated by the National Centre for Research and Development.
Principal Investigator Anna Gryboś.
Abstract
The project focuses on the event-driven signal processing, asynchronous analog-to-digital conversion and application of irregular sampling and frame theory to the signal reconstruction algorithms.
Conventional signal processing is based on uniform sampling requiring a synchronizing clock which is major energy consuming element of the architecture. Additionally, for slowly varying signals large amount of samples carry no relevant information. It becomes a main problem in wireless sensor devices with limited battery life or when the access to the battery is difficult like in the implantable biomedical devices.
The event-driven signal processing is forced by temporal changes of the signal, i.e. a sample is produced only when something significant occurs in the signal, for example the sampling is triggered if the signal deviates by delta from the value of the most recent sample. This sampling strategy is known as the event-based sampling, the level-crossing sampling or as the magnitude-driven sampling.
The event-driven approach allows for high energy efficiency but results in nonuniform sampling of the signal. The standard sampling framework is no longer applicable, because of the nonlinear behavior of the sampler, hence making space for the irregular systems. Reconstruction of such signal is possible, but requires advanced methods of frame theory and irregular sampling theory.
The mathematical results concern the reconstruction of a signal from the irregular samples and were applied in the situations where the irregularities in the sampling sets were caused at random (scattered data, perturbations or jitter, error of measurements, data loss due to channel erasures, etc.). Till now, the known mathematical results and methods were not applied to the reconstruction of the event-based sampled signals, i.e. in the situation when the irregularities in the sampling set are not random but they have their reason and meaning, they are caused by the sampling scheme itself ("event-driven").
Our contribution is to apply the mathematical results of the frame theory and irregular sampling theory to the problems of the event-driven sampling. The novelty of the approach consists of the application of the frame algorithm enhanced with adaptive weights method to the reconstruction of the signal from the irregular samples obtained by the send-on-delta sampling scheme. Basing on the theoretical research and analysis we elaborate the algorithms and implement them to the Matlab code. We provide the numerical simulations and the development of the numerical procedures set as toolbox and we set some perspectives for the further research.
Top of page
Publications and Conference Talks
Current list is available here.Conferences
14th Conference on Mathematics in technical and natural sciences (Talk)
Akademia Górniczo-Hutnicza w Krakowie,
Wrzesień 2015, Zakopane-Kościelisko, Polska
EBCCSP 2015 - "First International Conference on Event-based Control, Communication and Signal Processing" (Talk)
Akademia Górniczo-Hutnicza w Krakowie,
Czerwiec 2015, Kraków, Polska
SampTa 2015 - 11th International Conference on Sampling Theory and Applications (Poster)
American University, Washington
Maj 2015, Washington, USA
Czterdziesta trzecia ogólnopolska konferencja zastosowań matematyki (Talk)
Komitet Matematyki Polskiej Akademii Nauk
Zakopane-Kościelisko, 2-9.09.2014
Strobl 2014 "Modern Time-Frequency Analysis" (Poster),
Numerical Harmonic Analysis Group, EuCETIFA University of Vienna,
June 2-6, 2014, Strobl, Salzburg, AUSTRIA
Top of page
Seminary Talks
"Event-based sampling"
Seminarium Numerical Harmonic Analysis Group (NuHAG,)
Maj 2015 , Faculty of Mathematics, University of Vienna AUSTRIA
"Przybliżona rekonstrukcja sygnału próbkowanego metodą Integrate&Fire"
Seminarium Teorii falek, funkcji giętych i operatorowych metod aproksymacji
Maj 2015, WMS, AGH, Kraków, Poland
"Przetwarzenie sygnałów sterowane zdarzeniami"
Seminarium Katedry Matematyki Stosowanej
27.05.2014, Instytut Matematyki, UJ, Kraków, Poland
"Pewne własności krat (lokalizacja, kraty ważone)"
Seminarium Teorii falek, funkcji giętych i złożoności obliczeniowej
12.05.2014, WMS, AGH, Kraków, Poland
"O próbkowaniu nieregularnym czyli skąd się wzięły kraty?"
Seminarium Teorii falek, funkcji giętych i złożoności obliczeniowej
6.5, 13.5.2013, WMS, AGH, Kraków, Poland
Top of page