—A sampling theorem for regular sampling in shift invariant subspaces is established. The sufficient-necessary condition for which it holds is found. Then, the theorem is modified to the shift sampling in shift-invariant subspaces by using the Zak transform. Finally, some examples are presented to show the generality of the theorem.
— In this paper, a necessary and sufficient condition for sampling in the general framework of shift invariant spaces is derived. Then this result is applied respectively to the regular sampling and the perturbation of regular sampling in shift invariant spaces. A simple necessary and sufficient condition for regular sampling in shift invariant spaces is… (More)
For finite energy 7-band continuous signal f (t) , t f E L 2 (R) and suppf(w) = [-7,-y], the classical Shannon Sampling Theorem gave the following reconstruction formula, where f (w) is the Fourier transform of f (t) defined by f (w) = J, f(t)e-* " *dt. Unfortunately it is not appropriate for non-band-limited signals. However if we let y = 2 m ~ , m € 2 ,… (More)
— From the Paley–Wiener 1/4-theorem, the finite energy signal f (t) can be reconstructed from its irregularly sampled values f (k + k) if f (t) is band-limited and sup k j k j < 1=4. We consider the signals in wavelet subspaces and wish to recover the signals from its irregular samples by using scaling functions. Then the way to estimate the upper bound of… (More)
SUMMARY Following our former works on regular sampling in wavelet subspaces, the paper provides two algorithms to estimate the truncation error and aliasing error respectively when the theorem is applied to calculate concrete signals. Furthermore the shift sampling case is also discussed. Finally some important examples are calculated to show the algorithm.
We propose a method of predicting the number of requests for video titles in an on-demand video delivery system considering their time dependency. To handle many heterogeneous video requests in a video streaming delivery network system using video servers, it is effective to introduce video caching systems in the network system. For the cache system design… (More)