Linear Operator Theory in Engineering and Science

Naylor, Arch W.; Sell, George R.

doi:10.1007/978-1-4612-5773-8

Cited by 512 publications

(301 citation statements)

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“…The second inequality proves that C * is bounded, and thus continuous (Naylor and Sell, 1982). Therefore, f is uniquely and continuously associated with { f , f k H } k∈Z , also known as the measurements of f (Eldar andWerther, 2005, Eldar, 2003).…”

Section: Appendix a An Overview Of Hilbert Spaces And Framesmentioning

confidence: 96%

“…PW Ω , which is equivalent to the fact that and Sell, 1982), also known as the harmonic Fourier basis (Aldroubi and Gröchenig, 2001), where…”

Section: Nonuniform Sampling and Reconstruction Of Bandlimited Functionsmentioning

confidence: 99%

“…More information on linear spaces, RKHSs or frames can be found in (Naylor and Sell, 1982), (Berlinet and Thomas-Agnan, 2004) or (Christensen, 2003), respectively.…”

Section: Appendix a An Overview Of Hilbert Spaces And Framesmentioning

confidence: 99%

“…The set of functions S = { f k } k∈Z where f k = Ω π · sinc(Ω(· − kT)), ∀k ∈ Z, T π/Ω forms an orthonormal basis in PW Ω (Naylor and Sell, 1982). Furthermore, the coefficients {c k } k∈Z of a function f ∈ PW Ω satisfy…”

Section: Appendix a An Overview Of Hilbert Spaces And Framesmentioning

confidence: 99%

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Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits

Florescu¹

2017

Springer Theses

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To my family iii The third problem addressed in this work is given by the need of developing neuromorphic engineering circuits that perform mathematical computations in the spike domain.In this respect, this thesis developed a new representation between the time encoded input and output of a linear filter, where the TEM is represented by an ideal IF neuron. A new practical algorithm is developed based on this representation. The proposed algorithm is significantly faster than the alternative approach, which involves reconstructing the input, simulating the linear filter, and subsequently encoding the resulting output into a spike train.

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Section: Appendix a An Overview Of Hilbert Spaces And Framesmentioning

confidence: 96%

“…PW Ω , which is equivalent to the fact that and Sell, 1982), also known as the harmonic Fourier basis (Aldroubi and Gröchenig, 2001), where…”

Section: Nonuniform Sampling and Reconstruction Of Bandlimited Functionsmentioning

confidence: 99%

“…More information on linear spaces, RKHSs or frames can be found in (Naylor and Sell, 1982), (Berlinet and Thomas-Agnan, 2004) or (Christensen, 2003), respectively.…”

Section: Appendix a An Overview Of Hilbert Spaces And Framesmentioning

confidence: 99%

Section: Appendix a An Overview Of Hilbert Spaces And Framesmentioning

confidence: 99%

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Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits

Florescu¹

2017

Springer Theses

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“…the nonlinearity, F M,N (·, ·, q) : H N × R s → H N , is given by and x 0,N = P N x 0 . We note that the operator inverse required in (4.2) is guaranteed to exist for all τ sufficiently small or all M sufficiently large by the well known theorem on Neumann Series (see [18]). …”

Section: Finite Dimensional Approximation Time Discretization and Comentioning

confidence: 99%

Deconvolving an estimate of breath measured blood alcohol concentration from biosensor collected transdermal ethanol data

Dumett¹,

Rosen²,

Sabat³

et al. 2008

Applied Mathematics and Computation

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Biosensor measurement of transdermal alcohol oncentration in perspiration exhibits significant variance from subject to subject and device to device. Short duration data collected in a controlled clinical setting is used to calibrate a forward model for ethanol transport from the blood to the sensor. The calibrated model is then used to invert transdermal signals collected in the field (short or long duration) to obtain an estimate for breath measured blood alcohol concentration. A distributed parameter model for the forward transport of ethanol from the blood through the skin and its processing by the sensor is developed. Model calibration is formulated as a nonlinear least squares fit to data. The fit model is then used as part of a spline based scheme in the form of a regularized, non-negatively constrained linear deconvolution. Fully discrete, steepest descent based schemes for solving the resulting optimization problems are developed. The adjoint method is used to accurately and efficiently compute requisite gradients. Efficacy is demonstrated on subject field data.

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Convolution

Paris

1999

Wiley Encyclopedia of Electrical and Electronics Engineering

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The sections in this article are Notation and Basic Definitions Linear, Time‐Invariant Systems Fundamental Properties Numerical Convolution Fast Algorithms for Convolution Applications and Extensions Summary

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Linear Operator Theory in Engineering and Science

Cited by 512 publications

References 0 publications

Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits

Reconstruction, Identification and Implementation Methods for Spiking Neural Circuits

Deconvolving an estimate of breath measured blood alcohol concentration from biosensor collected transdermal ethanol data

Convolution

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