# Digital Signal Processing Handbook P9

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## Digital Signal Processing Handbook P9

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Complexity theory of computation attempts to determine how “inherently” difﬁcult are certain tasks. For example, how inherently complex is the task of computing an inner product of two vectors of length N? Certainly one can compute the inner product N=1 xj yj by computing the j N products xj yj and then summing them. But can one compute this inner product with fewer than N multiplications? The answer is no, but the proof of this assertion is no trivial matter. One ﬁrst abstracts

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