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

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

ISBN-10: 146139757X

ISBN-13: 9781461397571

ISBN-10: 1461397596

ISBN-13: 9781461397595

Advanced subject matters 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 signs and photographs. Sampling and reconstruction are primary difficulties in any box that deals with real-time signs or photos, together with communication engineering, photograph processing, seismology, speech acceptance, and electronic sign processing. This second quantity comprises contributions from top researchers within the box on such issues as Gabor's sign expansion, sampling in optical photo formation, linear prediction idea, polar and spiral sampling concept, interpolation from nonuniform samples, an extension of Papoulis's generalized sampling enlargement to better dimensions, and functions of sampling thought to optics and to time-frequency representations. The exhaustive bibliography on Shannon sampling thought will make this an invaluable learn instrument in addition to a very good textual content for students making plans additional examine within the box.

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This is exactly what happens as soon as c exceeds a few units. As an example, the eigenvalues versus n are represented in Fig. 7 for c = 32/7r [833]. The eigenvalues lin are almost unity for index values less than c and then become extremely small. The transition from high to low eigenvalues occurs in a range of indices that grows proportionally to In(c). Such a step function behavior is no longer valid when c approaches 1. , from Fig. 8 referring to c = 4/pi. As we shall see, this has important consequences.

T. w) -_ e jwt/2 e _11"1(1 2 /20'(2[(0(*) 2f{0(. 19) 25 1. Gabor's Signal Expansion In the case of a Gaussian elementary signal get), its associated function g(t,w) has a simple zero for (t = ~T. w = ~n). 20) [cf. 3), Zmk = (_1)m+k. 21) DISCRETE-TIME SIGNALS We consider the symmetrical, three-point elementary signal g[n] g[n] = { for n = 0 for n = ±1 (0 elsewhere. 22) which we considered already in section 4 as a window sequence. cf. Fig. 6. For the maximum-overlap case (N = 1), we find ejn19 U:,(n.

7 for c = 32/7r [833]. The eigenvalues lin are almost unity for index values less than c and then become extremely small. The transition from high to low eigenvalues occurs in a range of indices that grows proportionally to In(c). Such a step function behavior is no longer valid when c approaches 1. , from Fig. 8 referring to c = 4/pi. As we shall see, this has important consequences. In optical terms, we would explain the small values of the /In by saying that the energy conveyed by the corresponding n goes mostly outside the pupil.

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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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