This tutorial report describes how signals can be modeled as vectors in a Hilbert space, and highlights some of the geometric properties and interpretations that result. Two specific examples are highlighted: the space of square-integrable continuous-time signals, and the space of random variables with finite second moments. Some useful theorems from Hilbert space theory, such as the projection theorem, are shown to have useful application to optimization problems encountered in signal processing.
Geometric interpretation of signals: background
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