# Wavelets and signal processing

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### "Wavelets and signal processing" refers background in this paper

...Such filters are called regular, and examples can be found in [DAU88, COHSOa , DAUSOb, RI090b, VETSOb]....

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### "Wavelets and signal processing" refers background or methods in this paper

...It may even happen that A=B (“tight frame”), in which case the wavelets behave exactly like an orthonormal basis, although they may not even be linearly independent [ DAUSOa ]! The reconstruction formula can also be made exact in the general case if one uses different synthesis functions h;.k(t) (which constitute the dualframe of the hjk(t)s [DAUSOal)....

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...This is in sharp contrast with the STET, where, according to the Balian-Low theorem [ DAUSOa ], it is impossible to have orthonormal bases with functions well localized in time and frequency (that is, for which the time-bandwidth product At Afis a finite number)....

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...For example, a signal may be reconstructed only with zero mean since h(t) dt = 0. In fact the type of convergence of (8) may be strengthened and is related to the numerical robustness of the reconstruction [ DAUSOa ]....

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...They may as well be discrete (DAU88, MAL89b, MEY89, DAUSOa ], leading to a Wavelet Series expansion....

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...Ftg. 8. Reconstruction SignallNoise Ratio (SNR) error afterframe decomposition for dtfferent sampling densities an = 2IfN [N = number of voices per octave), b = ad k bo [aBer [ DAUSOa ])....

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