By Martin J. Bastiaans (auth.), Robert J. Marks II (eds.)

ISBN-10: 146139757X

ISBN-13: 9781461397571

ISBN-10: 1461397596

ISBN-13: 9781461397595

**Advanced issues in Shannon Sampling and Interpolation Theory****is the second one quantity of a textbook on sign research solely****devoted to the subject of sampling and recovery of ****continuous time indications and photographs. Sampling and ****reconstruction are basic difficulties in any box that ****deals with real-time indications or pictures, together with ****communication engineering, picture processing, seismology, ****speech reputation, and electronic sign processing. This ****second quantity contains contributions from major ****researchers within the box on such themes as Gabor's sign ****expansion, sampling in optical picture formation, linear ****prediction concept, polar and spiral sampling concept, ****interpolation from nonuniform samples, an extension of ****Papoulis's generalized sampling enlargement to better ****dimensions, and purposes of sampling idea to optics ****and to time-frequency representations. The exhaustive ****bibliography on Shannon sampling conception will make this an ****invaluable examine device in addition to a very good textual content for ****students making plans extra learn within the box. **

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29) inside the basic interval. The corresponding window sequence tu[n] then reads (see Fig. 12) win] ~{ for -(N -1)::; n::; 0 for 1 ::; n ::; N elsewhere. 30) 1. 12: The window function corresponding to the one-sided exponential elementary signal, cf. Eq. 30). We use this example to show once more the possible non-uniqueness of Gabor's signal expansion. In the limiting case a = 0, the function g(n, '19) has zeros for '19 = r(27r /N} (r = ... , -1,0,1, ... uted in Gabor's signal representation. 7 Degrees of Freedom of a Signal Gabor's signal expansion as introduced in section 5 is related to the degrees of freedom of a signal: each expansion coefficient amk represents one complex degree of freedom.

1, ... ). 22) /In It is seen that the error term is amplified 1/ /In times by this process. To give a feeling of this effect, we consider an example. Let c = 32/tr and suppose we want to evaluate In up to n ::;:: 20 (which corresponds to twice the number of DOF furnished by Eq. 5». From the tables of [833J it turns out that when we try to recover 120, the error term is multiplied by the frightening figure of 10 12 . Unless the errors on the image coefficients decrease as fast as the /l'n, this would induce a disaster.

B - .. I 0 . 11: The window function corresponding to the symmetrical, three-point elementary signal, in the case of partial overlap, cf. Eq. 26). In the basic interval -(N - 1) ::; n ::; O. 17). The function w(n, '19) now takes the form '1b(n. 29) inside the basic interval. The corresponding window sequence tu[n] then reads (see Fig. 12) win] ~{ for -(N -1)::; n::; 0 for 1 ::; n ::; N elsewhere. 30) 1. 12: The window function corresponding to the one-sided exponential elementary signal, cf. Eq.

### Advanced Topics in Shannon Sampling and Interpolation Theory by Martin J. Bastiaans (auth.), Robert J. Marks II (eds.)

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