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The canonical and alternate duals of a wavelet frame

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Online Research Database In Technology
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Abstract

We show that there exists a frame wavelet ψ with fast decay in the time domain and compact support in the frequency domain generating a wavelet system whose canonical dual frame cannot be generated by an arbitrary number of generators. On the other hand, there exists infinitely many alternate duals of ψ generated by a single function. Our argument closes a gap in the original proof of this fact by Daubechies and Han [Appl. Comp. Harmonic Anal. 12 (2002), no. 3, 269 –285].

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