Q.2 A filter given by the filter mask hrones (3,3) is applied to the input image 1 1 1 1 1 1 1 1 1 by using the convolution lout=conv2(h,I) in MATLAB which yields Iout 1 2 3 2 1 2 4 6 4 2 3 6 9 6 3 2 4 6 4 2 1 2 3 2 1 a) Apply the convolution operation by hand and verify lout. b) Let I(m, n) be a symmetric matrix with respect to the center element. Then we know that the 2-D Fourier transform of I(m, n) (image) is given by Fl(e)w, ejay ) = DSFT{I(m, n)} = MM MM 1(m, n)e-jmwx e-jnwy Compute the 2-D Fourier transform of [1(-1,-1) 1(-1,0) 1(-1,1)] [1 1 1 1(m, n) = 10,-1) 1(0,0) 1(0,1)= 1 1 1 I(1,-1) I(1,0) I(1,1) 1 1. L1 and prove that FI(elwx, ejwy) = 1 + 2cos wx + 2 cos w, + 4 cosa, cos Wy. Q.2 A filter given by the filter mask hrones (3,3) is applied to the input image 1 1 1 1 1 1 1 1 1 by using the convolution lout=conv2(h,I) in MATLAB which yields Iout 1 2 3 2 1 2 4 6 4 2 3 6 9 6 3 2 4 6 4 2 1 2 3 2 1 a) Apply the convolution operation by hand and verify lout. b) Let I(m, n) be a symmetric matrix with respect to the center element. Then we know that the 2-D Fourier transform of I(m, n) (image) is given by Fl(e)w, ejay ) = DSFT{I(m, n)} = MM MM 1(m, n)e-jmwx e-jnwy Compute the 2-D Fourier transform of [1(-1,-1) 1(-1,0) 1(-1,1)] [1 1 1 1(m, n) = 10,-1) 1(0,0) 1(0,1)= 1 1 1 I(1,-1) I(1,0) I(1,1) 1 1. L1 and prove that FI(elwx, ejwy) = 1 + 2cos wx + 2 cos w, + 4 cosa, cos Wy