Linear combinations of B-splines as generating functions for signal approximation
Digital Signal Processing
On the aliasing error in wavelet subspaces
Journal of Computational and Applied Mathematics
Reconstruction of compressed samples in shift-invariant space base on matrix factorization
Computers and Electrical Engineering
Computation of wavelet coefficients from average samples
Journal of Computational and Applied Mathematics
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The authors first describe the general class of approximation spaces generated by translation of a function ψ(x), and provide a full characterization of their basis functions. They then present a general sampling theorem for computing the approximation of signals in these subspaces based on a simple consistency principle. The theory puts no restrictions on the system input which can be an arbitrary finite energy signal; bandlimitedness is not required. In contrast to previous approaches, this formulation allows for an independent specification of the sampling (analysis) and approximation (synthesis) spaces. In particular, when both spaces are identical, the theorem provides a simple procedure for obtaining the least squares approximation of a signal. They discuss the properties of this new sampling procedure and present some examples of applications involving bandlimited, and polynomial spline signal representations. They also define a spectral coherence function that measures the “similarity” between the sampling and approximation spaces, and derive a relative performance bound for the comparison with the least squares solution