Dual Wavelet
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a dual wavelet is the dual to a wavelet. In general, the wavelet series generated by a square integrable function will have a dual series, in the sense of the Riesz representation theorem. However, the dual series is not in general representable by a square integral function itself.An example of an R-function without a dual is easy to construct. Let be an orthogonal wavelet. Then define (x) = (x) + z (2x) for some complex number z. It is straightforward to show that this does not have a wavelet dual.…mehr

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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a dual wavelet is the dual to a wavelet. In general, the wavelet series generated by a square integrable function will have a dual series, in the sense of the Riesz representation theorem. However, the dual series is not in general representable by a square integral function itself.An example of an R-function without a dual is easy to construct. Let be an orthogonal wavelet. Then define (x) = (x) + z (2x) for some complex number z. It is straightforward to show that this does not have a wavelet dual.