ABSTRACT
This chapter discusses a set of delay operators that generalize the ideal delay operator almost exclusively utilized in digital signal processing. The theory of optimal signal processing has a long history that began with the seminal work of Norbert Wiener and was later made practical by many advances, from which Bernard Widrow’s least mean squares algorithm. The problem concerning the choice of bases is the least addressed in the signal processing literature. Under the linear signal model, affine transforms of the input space axes are normally appropriate. Optimal linear filtering was originally developed by Wiener in continuous time for stochastic processes. The digital counterpart of Wiener’s theory using the finite impulse response filter utilizes the same mathematical tools of least squares. The chapter shows that the focused time delay neural network are, in fact, universal approximators in functional spaces for the class of functions with approximately finite memory, which is important in engineering practice.
