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

February 23, 2017 | Theory | By admin | 0 Comments

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

Advanced themes 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 pictures. Sampling and reconstruction are basic difficulties in any box that deals with real-time signs or photos, together with communication engineering, snapshot processing, seismology, speech attractiveness, and electronic sign processing. This second quantity contains contributions from major researchers within the box on such issues as Gabor's sign expansion, sampling in optical photograph formation, linear prediction idea, polar and spiral sampling thought, interpolation from nonuniform samples, an extension of Papoulis's generalized sampling enlargement to raised 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 study instrument in addition to an outstanding textual content for students making plans additional learn within the box.

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J. 1) J = 2~ J = 2~ J

20) Hence. on dividing the image coefficients 9n by the corresponding eigenvalues /In. we obtain the object coefficients In. • the solution of our problem (see Eq. 18». What about the number of DOF of the image? In the noiseless case considered so far. all of the (infinitely many) DOF of the object represented by the set of coefficients In are transferred to the image in the set of the gn' However, in the passage from the object to the image each coefficient is multiplied by the corresponding eigenvalue.

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.

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