A Sampling Theorem for Fractional Wavelet Transform With Error Estimates

As a generalization of the ordinary wavelet transform, the fractional wavelet transform (FRWT) is a very promising tool for signal analysis and processing. Many of its fundamental properties are already known; however, little attention has been paid to its sampling theory. In this paper, we first in...

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Veröffentlicht in:	IEEE transactions on signal processing 2017-09, Vol.65 (18), p.4797-4811
Hauptverfasser:	Shi, Jun, Liu, Xiaoping, Sha, Xuejun, Zhang, Qinyu, Zhang, Naitong
Format:	Artikel
Sprache:	eng
Schlagworte:	Aliasing Chirp Fractional Fourier transform fractional wavelet transform Frequencies Multiresolution analysis Sampling Sampling error sampling theorem Signal analysis Signal processing Subspaces Time-frequency analysis Wavelet analysis Wavelet transforms
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description	As a generalization of the ordinary wavelet transform, the fractional wavelet transform (FRWT) is a very promising tool for signal analysis and processing. Many of its fundamental properties are already known; however, little attention has been paid to its sampling theory. In this paper, we first introduce the concept of multiresolution analysis associated with the FRWT, and then propose a sampling theorem for signals in FRWT-based multiresolution subspaces. The necessary and sufficient condition for the sampling theorem is derived. Moreover, sampling errors due to truncation and aliasing are discussed. The validity of the theoretical derivations is demonstrated via simulations.
doi_str_mv	10.1109/TSP.2017.2715009
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subjects	Aliasing Chirp Fractional Fourier transform fractional wavelet transform Frequencies Multiresolution analysis Sampling Sampling error sampling theorem Signal analysis Signal processing Subspaces Time-frequency analysis Wavelet analysis Wavelet transforms
title	A Sampling Theorem for Fractional Wavelet Transform With Error Estimates
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