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.

Behaviour of dolomite, olivine and alumina as primary catalysts in air-steam gasification of sewage sludge

Sewage sludge gasification assays were performed in an atmospheric fluidised bed reactor using air and air–steam mixtures as the gasifying agents. Dolomite, olivine and alumina are three well known tar removal catalysts used in biomass gasification processing. However, little information is available regarding their performance in sewage sludge gasification. The aim of the current study was to learn about the influence of these three catalysts in the product distribution and tar production during sewage sludge gasification. To this end, a set of assays was performed in which the temperature (750–850 °C), the in-bed catalyst content (0, 10 and 15 wt.%) and the steam–biomass ratio (SB) in the range of 0–1 were varied with a constant equivalence ratio (ER) of 0.3. The results were compared to the results from gasification without a catalyst. We show that dolomite has the highest activity in tar elimination, followed by alumina and olivine. In addition to improving tar removal, the presence of water vapour and the catalysts increased the content of H2 in the gases by nearly 60%.