A STUDY OF TIME‐SHIFTED SIGNALS AND THEIR EXPANSIONS Available to Purchase

A simple extension of the concept of the inner product leads to orthonormal expansions of time‐shifted signals with coefficients dependent on the shift variable. It is shown that such expansions have their counterparts of Parseval's identity and Bessel inequality. The Projection Theorem holds, and a version of Mercer's theorem and Karhumen—Loeve's expansion are also shown to hold, in a non‐stochastic regime. The approach leads to new interpretations of time correlation functions and Fourier Series expansions.