Orthogonal functions are a set of functions that are mutually perpendicular in the context of an inner product space, meaning that the inner product of any two distinct functions in the set is zero. This concept is crucial because it allows for the expansion of functions in terms of a basis of orthogonal functions, which simplifies many analyses and calculations in harmonic analysis. Orthogonality ensures that the contribution from one function does not interfere with another, making it easier to study and decompose complex signals.
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