Read e-book online Advanced Topics in Shannon Sampling and Interpolation Theory PDF

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 Theoryis the second one quantity of a textbook on sign research solelydevoted 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.

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


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