A GENERAL SAMPLING THEOREM.
CRUFT LAB HARVARD UNIV CAMBRIDGE MASS
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The usual form of the sampling theorem states that a function at, whose Fourier Transform Af vanishes outside the interval -w, w may be reconstructed exactly from its values at equally spaced sampling points taken at the Nyquist Rate of 2w points per second. It is also known that at may be reconstructed from its sample values taken at half the Nyquist rate if in addition we use the same number of samples from certain functions derived from at e.g., its Hilbert Transform or its derivative. In this paper the authors derive necessary and sufficient conditions in order that at may be reconstructed from sample values of rather general functions b sub 1 t, b sub 2 t. . . b sub n t where the values of each b sub i t are taken at 1n times the Nyquist rate. In addition, the sampling functions necessary for reconstruction are exhibited directly as the solutions of a linear matrix equation. This result includes as special cases k-derivative sampling, irregular spacing sampling and Hilbert Transform sampling. Author
- Numerical Mathematics