Question

a. Show that the 2-D discrete Fourier Transform of an M × N digital image is periodic. That is, you must prove that F(u + M, v + N) = F(u, v). b. Suggest two methods to bring the frequency origin of a discrete Fourier Transform of an image to the center of the 2-D array of the frequency plane.

Name: a show that 2 d discrete fourier transform of a m n digital image is periodicthat is you must prove that fu m v n fu v b suggest two methods to bring the frequency origin of a discrete fouri 90915
Uploaded: 2023-06-15T07:12:11-08:00
Duration: 3 min 8 s
Channel: Sri K
Description: a show that 2 d discrete fourier transform of a m n digital image is periodicthat is you must prove that fu m v n fu v b suggest two methods to bring the frequency origin of a discrete fouri 90915

          a. Show that the 2-D discrete Fourier Transform of an M × N digital image is periodic. That is, you must prove that F(u + M, v + N) = F(u, v).
b. Suggest two methods to bring the frequency origin of a discrete Fourier Transform of an image to the center of the 2-D array of the frequency plane.

Added by Kari P.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

06/15/2023

Step 1

The 2-D discrete Fourier Transform (DFT) of a M × N digital image is given by: $$F(u, v) = \sum_{m=0}^{M-1} \sum_{n=0}^{N-1} f(m, n) e^{-j2\pi(um/M + vn/N)}$$ Now, let's consider the DFT of the shifted image coordinates: $$F(u + M, v + N) = \sum_{m=0}^{M-1} Show more…

Show all steps

Thanks for your feedback!

a. Show that the 2-D discrete Fourier Transform of an M × N digital image is periodic. That is, you must prove that F(u + M, v + N) = F(u, v). b. Suggest two methods to bring the frequency origin of a discrete Fourier Transform of an image to the center of the 2-D array of the frequency plane.