Hilbert space array methods for finite rank process modeling and ladder form realizations

We present a Hilbert space array approach for deriving fast estimation and adaptive signal processing algorithms. These are obtained using, as a basic tool, projection operators and orthonormalizations, via the Gram-Schmidt procedure. The resultant algorithms are recursive in time and order, and are realized in ladder forms. The importance of this array method is that it can be applied to a large variety of signal processing problems. This paper deals with the application of our array approach to the class of fimte (shift) rank processes.