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.

Methods for noise reduction in far-field patterns obtained from cylindrical near-field antenna measurements

Two different methods to reduce the noise power in the far-field pattern of an antenna as measured in cylindrical near-field (CNF) are proposed. Both methods are based on the same principle: the data recorded in the CNF measurement, assumed to be corrupted by white Gaussian and space-stationary noise, are transformed into a new domain where it is possible to filter out a portion of noise. Those filtered data are then used to calculate a far-field pattern with less noise power than that one obtained from the measured data without applying any filtering. Statistical analyses are carried out to deduce the expressions of the signal-to-noise ratio improvement achieved with each method. Although the idea of the two alternatives is the same, there are important differences between them. The first one applies a modal filtering, requires an oversampling and improves the far-field pattern in all directions. The second method employs a spatial filtering on the antenna plane, does not require oversampling and the far-field pattern is only improved in the forward hemisphere. Several examples are presented using both simulated and measured near-field data to verify the effectiveness of the methods.