Recovery of the optimal approximation from samples in wavelet subspace
Digital Signal Processing
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The sampling theorem for wavelet spaces built by Walter (1992) lacks the translation invariance except for Walter's weak translation invariant wavelet, i.e., Meyer's wavelet. Indeed, we must know a priori the shift offset a in the samples {f(n+a);n∈Z}; otherwise, the waveform cannot be recovered since the interpolation function is dependent on this offset. In this correspondence, we generalize our metric functional to metrize weak shiftability and find a somewhat surprising result that the B spline wavelets of order n⩾3 are degenerate shiftable. Thus, we can recover approximately the waveform by double sampling without any information on shift offset a