Optimum filtering and multichannel receivers

We will examine the problem of optimum filtering when signals and noises are incoming on different channels. The filtering is defined by a rectangular matrix of filters and the non-linear operation in the signal processing is the general quadratic system. After the calculation of the output signal-to-noise ratio, we discuss the problem of optimum filtering. In this paper we consider only the solution in some particular cases as, for example, the correlator. In the second part, we discuss some properties of the optimum linear filters and we show in the third how the problem of directivity synthesis in omnidirectional noise is a particular case of optimum filtering.