Strömberg wavelet
mathematic orthonornal wavelet
In mathematics, the Strömberg wavelet is a certain orthonormal wavelet discovered by Jan-Olov Strömberg and presented in a paper published in 1983. Even though the Haar wavelet was earlier known to be an orthonormal wavelet, Strömberg wavelet was the first smooth orthonormal wavelet to be discovered. The term wavelet had not been coined at the time of publishing the discovery of Strömberg wavelet and Strömberg's motivation was to find an orthonormal basis for the Hardy spaces.
Definition
Let m be any non-negative integer. Let V be any discrete subset of the set R of real numbers. Then V splits R into non-overlapping intervals. For any r in V, let Ir denote the interval determined by V with r as the left endpoint. Let P(m)(V) denote the set of all functions f(t) over R satisfying the following conditions:
f(t) is square integrable.
f(t) has continuous derivatives of all orders up to m.
f(t) is a polynomial of degree m + 1 in each of the intervals Ir.
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