Translation invariance and sampling theorem of wavelet
Qiao Wang, Lenan Wu · IEEE Transactions on Signal Processing · 2000
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/spl isin/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/spl ges/3 are degenerate shiftable. Thus, we can recover approximately the waveform by double sampling without any information on shift offset a.