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Almost orthogonal functions

George Epstein, Raghavendra Rao Loka

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Abstract

Almost-orthogonal functions, which are obtained by perturbing orthogonal functions, do not exactly satisfy the orthogonality conditions. The notion of almost-orthogonal functions is explained with examples. An error analysis of expansion coefficients based on almost-orthogonal functions is given. Using examples derived from sinusoids, it is shown how computational advantage can be obtained by using almost-orthogonal functions in signal processing.>

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Almost-orthogonal functions, which are obtained by perturbing orthogonal functions, do not exactly satisfy the orthogonality conditions. The notion of almost-orthogonal functions is explained with examples. An error analysis of expansion coefficients based on almost-orthogonal functions is given. Using examples derived from sinusoids, it is shown how computational advantage can be obtained by using almost-orthogonal functions in signal processing.>

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Available abstract

Almost-orthogonal functions, which are obtained by perturbing orthogonal functions, do not exactly satisfy the orthogonality conditions. The notion of almost-orthogonal functions is explained with examples. An error analysis of expansion coefficients based on almost-orthogonal functions is given. Using examples derived from sinusoids, it is shown how computational advantage can be obtained by using almost-orthogonal functions in signal processing.>

Key concepts: Orthogonality, Orthogonal functions, Empirical orthogonal functions, Signal processing, Algorithm, Mathematics, Walsh function, SIGNAL (programming language)

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