Wavelet Sampling Theorems for Irregularly Sampled Signals
نویسندگان
چکیده
In digital signal and image processing, digital communications, and so forth, a continuous signal is usually represented and processed by using its discrete samples. How, then, are we to reconstruct the original signal from its discrete samples? The classical Shannon sampling theorem gives the following formula for band-limited finite energy signals. For a finite energy s-band continuous signal f(t), t Î R, that is, supp f̂(w) Ì [-s, s] and f Î L (R), it can be recovered by the formula where f̂ is the Fourier transform of f(t) defined by
منابع مشابه
Irregular Sampling Theorems for Wavelet Subspaces - Information Theory, IEEE Transactions on
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 supk j kj < 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 sup k j kj such that the irregularly sampled s...
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