To compute the 2D-DFT one can use 1D-DFT by separating the equation for the 2D-DFT as

(a) Using the one-dimensional MATLAB function fft to implement the above result, and for the signal

with values M = N = 10. compute X(m, ℓ) for every value of m and then find X(k, ℓ), the two-dimensional DFT of x[m, n]. Verify your result is the same as when you directly use the function fft2 to compute X(k, ℓ).

(b) Is the MATLAB expression fft(fft(x)!0)!0 equivalent to fft2(x) ? Try it and then explain.

(c) Use different values of M₁ and N₁ to verify that the support of x[m, n] in the space domain is inversely proportional to the support of X(k, ℓ).

Transcribed Image Text:

N-1 — )2т km M-1 м- — )2тёn' E [m, n] exp ( en X (k, €) |exp Σ т-0 м п-0 X(т,0) - )2лkm I X(m, 0)ехp (—M m=0 1 0< m< (M1 – 1), 0