Question 1 Let U be a two-dimensional image with N^2 pixels; that is, U element of R^NxN. Furthermore, let V be the two-dimensional unity DFT of V. Hence, V element of RNxN. The vectors u and v are defined to be the row-ordered mapping of U and V respectively. Hence, u element of R^N^2x1 and v element of R^N^2x1. Define F = F F In words, F is the Komecker product of the unity Fourier matrix F with itself. Jain states v = Fu (2) Implement the two-dimensional DFT using the above matrix multication. Demostrate that your implementation is correct by showing that FF* = 1 (3) Take care that you don\'t crash your system by taking N too large. If you source code is excessively large, then email me the code. Question 2 Part A. Derive a method, which could be used as a bases for a computer algorithm, for calculating Fi. the ith row of F without calculating all N^4 entries in F. The below equation may be of help. where ei = In words, the vector ei contains all zeros except for the ith element. Part B. Implement the above on Wrangler and/or a Hadoop computer system. Solution what is this matrix mulication .

1. Question 1 Let U be a two-dimensional image with N^2 pixels; that is, U element of R^NxN.
Furthermore, let V be the two-dimensional unity DFT of V. Hence, V element of RNxN. The
vectors u and v are defined to be the row-ordered mapping of U and V respectively. Hence, u
element of R^N^2x1 and v element of R^N^2x1. Define F = F F In words, F is the Komecker
product of the unity Fourier matrix F with itself. Jain states v = Fu (2) Implement the two-
dimensional DFT using the above matrix multication. Demostrate that your implementation is
correct by showing that FF* = 1 (3) Take care that you don't crash your system by taking N too
large. If you source code is excessively large, then email me the code. Question 2 Part A. Derive
a method, which could be used as a bases for a computer algorithm, for calculating Fi. the ith
row of F without calculating all N^4 entries in F. The below equation may be of help. where ei =
In words, the vector ei contains all zeros except for the ith element. Part B. Implement the above
on Wrangler and/or a Hadoop computer system.
Solution
what is this matrix mulication