By Martin J. Bastiaans (auth.), Robert J. Marks II (eds.)
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 signs and photographs. Sampling and reconstruction are basic difficulties in any box that deals with real-time indications or pictures, together with communication engineering, photograph processing, seismology, speech acceptance, and electronic sign processing. This second quantity contains contributions from best researchers within the box on such themes as Gabor's sign expansion, sampling in optical picture 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 concept to optics and to time-frequency representations. The exhaustive bibliography on Shannon sampling idea will make this an invaluable learn software in addition to a very good textual content for students making plans extra examine within the box.
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Example text
Light proceeds toward the image plane. This step can be described as an inverse FT if the coordinates axes in the object and image planes are opposedly oriented. 1 ) 44 Franco Gori where the integration region is (possibly) the whole y-axis. In equivalent terms, the spectra g(p) and j(p) of the image and the object. respectively, are related by g(p) = j(p)S(p). 2) The venerable concept of resolving power can be introduced in a simple manner. A single object point gives rise to a light patch in the image.
First, we have assumed that the only non-negligible samples are those falling within the geometrical image. This is based more on physical intuition than on mathematically sound arguments. As a matter of fact, it is not difficult to find examples in which many relevant samples are outside the geometrical image [715J. This may be seen. , in Fig. 5 that gives the image produced by the following object. 1/2PM' The condition 4XMPM » 1 is satisfied and yet significant parts of the image are outside the interval [-XM' XMJ.
This implies again Eq. 13) or, more properly, its complex conjugate. The final result is the attenuated version of n. 1/2] and make an inverse FT of both sides of Eq. 13). Interchanging order of integration on the left and changing variables on the right, we obtain j C/2 -c/2 n(Y} dy = en j1/2 -1/2 e27rip (x-y) dp {ii:; jC/2 nCu}e27rivx/c dv. 17) 53 2. 9). We shall now use the PSWF to give a formal solution of Eq. 9). ,}. 19) 00 I(x) = L n=O 00 n=O -c/2 -c/2 On inserting from Eq. 19) into Eq.
