An introduction to wavelets
Fast Reconstruction Methods for Bandlimited Functions from Periodic Nonuniform Sampling
SIAM Journal on Numerical Analysis
Sampling theorem for wavelet subspaces: error estimate andirregular sampling
IEEE Transactions on Signal Processing
Translation invariance and sampling theorem of wavelet
IEEE Transactions on Signal Processing
Spectral analysis of randomly sampled signals: suppression of aliasing and sampler jitter
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing - Part I
Multiresolution representations using the autocorrelation functionsof compactly supported wavelets
IEEE Transactions on Signal Processing
A Theory for Sampling Signals From a Union of Subspaces
IEEE Transactions on Signal Processing
Irregular sampling for spline wavelet subspaces
IEEE Transactions on Information Theory
Irregular sampling theorems for wavelet subspaces
IEEE Transactions on Information Theory
A sampling theorem for wavelet subspaces
IEEE Transactions on Information Theory - Part 2
Objective evaluation of speech dysfluencies using wavelet packet transform with sample entropy
Digital Signal Processing
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The success of the typical sampling theories for a wavelet subspace mostly benefits from the fact that the sampling operation is an isomorphism of a wavelet subspace onto l^2(R). However, this operation is not an isometry of a general wavelet subspace onto l^2(R). As a result, many sampling theories only concentrate on the recovery of a signal in a single wavelet subspace. In this paper, some theorems are proposed to discuss the isometric isomorphism of a wavelet subspace and a convolved l^2(R) space. We show that the sampling operation is an isometric isomorphism of a wavelet subspace onto a convolved l^2(R) space only if the sampling operation is an isomorphism of a wavelet subspace onto l^2(R). Based on the isometric isomorphism, we further verify the existence of the mapping from the samples to the projection of a signal on an approximation space. At last, we propose the corresponding algorithm to construct this mapping so that the optimal approximations of a signal at the different resolution can be recovered from the samples. The simulation shows that our algorithm is more suitable to recover the projection of a signal than Shannon sampling theorem in a general multiresolution analysis.