Introduction and Outline

Abstract

Linear signal spaces are of great importance in signal and system theory, communication theory, and modern signal processing. Traditionally, a linear signal space is considered to be a more or less abstract mathematical concept. In this work, however, a time-frequency (TF) analysis of linear signal spaces is proposed whereby linear signal spaces are represented as surfaces extending over a joint TF plane. This new viewpoint is based mathematically on specific TF representations of linear signal spaces that extend well-known TF representations of signals. Thus, this work provides an extension of the TF analysis of signals to linear signal spaces.