A decade of piecewise constant orthogonal functions in systems and control

The systems of Haar function (HF), Rademacher functions (RF), Walsh functions (WF), and block pulse functions (BPF) have played a significant role in the fields of applied mathematics and engineering applications so far in the 20th century. Some of these systems of piecewise constant basis functions (PCBF) have, particularly in the last ten years (l973–1983), been extensively applied in the fields of systems and control. In this paper we summarize and discuss the developments. An attempt is made here to outline the course of the developments. Some desirable directions for future research are also indicated.