Applied Multidimensional Systems Theory by Nirmal K. Bose

Author:Nirmal K. Bose
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

2. Prove the reconstruction result in (3.15) by applying the steps indicated below. (a)For a fixed x 2 = x 20, expand g(x 1, x 2) as a function of x 1, since it is bandlimited to the interval by the 1-D WSK sampling theorem.

(b)Similarly, expand as follows the function in the variable x 2,

after realizing that g(x 1, x 2) as a function of x 2 for a fixed value of x 1 is bandlimited to the interval

(c)Combine the results in the previous two parts to get the result wanted.

3. Use the reproducing property in Problem 1 to arrive at its 2-D counterpart,

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