Linear algorithms for recovering linear functionals from jittered information

Linear Signal Reconstruction from Jittered Sampling

This paper presents an accurate and simple method to evaluate the performance of AD/DA converters affected by clock jitter, which is based on the analysis of the mean square error (MSE) between the reconstructed signal and the original one. Using an approximation of the linear minimum MSE (LMMSE) filter as reconstruction technique, we derive analytic expressions of the MSE. Through asymptotic a...

Almost multiplicative linear functionals and approximate spectrum

We define a new type of spectrum, called δ-approximate spectrum, of an element a in a complex unital Banach algebra A and show that the δ-approximate spectrum σ_δ (a) of a is compact. The relation between the δ-approximate spectrum and the usual spectrum is investigated. Also an analogue of the classical Gleason-Kahane-Zelazko theorem is established: For each ε>0, there is δ>0 such that if ϕ is...

Symmetries of Linear Functionals

It is shown that a linear functional on a space of functions can be described by G, a group of its symmetries, together with the restriction of to certain G-invariant functions. This simple consequence of invariant theory has long been used, implicitly, in the construction of numerical integration rules. It is the author's hope that, by showing that these ideas have nothing to do with the origi...

Simultaneous Con dence Intervals for Linear Estimates of Linear Functionals

This note presents three ways of constructing simultaneous condence intervals for linear estimates of linear functionals in inverse problems, including \Backus-Gilbert" estimates. Simultaneous con dence intervals are needed to compare estimates, for example, to nd spatial variations in a distributed parameter. The notion of simultaneous con dence intervals is introduced using coin tossing as an...

Fuzzy Primal Simplex Algorithms for Solving Fuzzy Linear Programming Problems