A matrix pencil approach to the existence of compactly supported reconstruction functions in average sampling

The aim of this work is to solve a question raised for average sampling in shift-invariant spaces by using the well-known matrix pencil theory. In many common situations in sampling theory, the available data are samples of some convolution operator acting on the function itself: this leads to the problem of average sampling, also known as generalized sampling. In this paper we deal with the existence of a sampling formula involving these samples and having reconstruction functions with compact support. Thus, low computational complexity is involved and truncation errors are avoided. In practice, it is accomplished by means of a FIR filter bank. An answer is given in the light of the generalized sampling theory by using the oversampling technique: more samples than strictly necessary are used. The original problem reduces to finding a polynomial left inverse of a polynomial matrix intimately related to the sampling problem which, for a suitable choice of the sampling period, becomes a matrix pencil. This matrix pencil approach allows us to obtain a practical method for computing the compactly supported reconstruction functions for the important case where the oversampling rate is minimum. Moreover, the optimality of the obtained solution is established.

Computing the Hessenberg matrix associated with a self-similar measure

We introduce in this paper a method to calculate the Hessenberg matrix of a sum of measures from the Hessenberg matrices of the component measures. Our method extends the spectral techniques used by G. Mantica to calculate the Jacobi matrix associated with a sum of measures from the Jacobi matrices of each of the measures. We apply this method to approximate the Hessenberg matrix associated with a self-similar measure and compare it with the result obtained by a former method for self-similar measures which uses a fixed point theorem for moment matrices. Results are given for a series of classical examples of self-similar measures. Finally, we also apply the method introduced in this paper to some examples of sums of (not self-similar) measures obtaining the exact value of the sections of the Hessenberg matrix.

Simultaneous determination of multiclass emerging contaminants in aquatic plants by ultrasound assisted matrix solid phase dispersion and GC-MS

A multiresidue method was developed for the simultaneous determination of 31 emerging contaminants (pharmaceutical compounds, hormones, personal care products, biocides and flame retardants) in aquatic plants. Analytes were extracted by ultrasound assisted-matrix solid phase dispersion (UA-MSPD) and determined by gas chromatography-mass spectrometry after sylilation. The method was validated for different aquatic plants (Typha angustifolia, Arundo donax and Lemna minor) and a semiaquatic cultivated plant (Oryza sativa) with good recoveries at concentrations of 100 and 25 ng g-1 wet weight, ranging from 70 to 120 %, and low method detection limits (0.3 to 2.2 ng g-1 wet weight). A significant difference of the chromatographic response was observed for some compounds in neat solvent versus matrix extracts and therefore quantification was carried out using matrix-matched standards in order to overcome this matrix effect. Aquatic plants taken from rivers located at three Spanish regions were analyzed and the compounds detected were parabens, bisphenol A, benzophenone-3, cyfluthrin and cypermethrin. The levels found ranged from 6 to 25 ng g-1 wet weight except for cypermethrin that was detected at 235 ng g-1 wet weight in Oryza sativa samples.