(a) Hand calculate to perform the linear convolution between these two matrices x(m,n) and h(m,n) given...

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(a) Hand calculate to perform the linear convolution between these two matrices x(m,n) and h(m,n) given below. Let the outside boundary pixels be zeros. You need to expand the boundary of x(m,n) to obtain all non-zero values in the result. Let the upper-left pixel of x(m,n) and h(m,n) be the origin. You need show step-by-step hand calculation process. (b) Similar to (a), but this time hand calculates to perform the linear correlation. (c) Using MATLAB functions, conv2 and xcorr2, to perform the linear convolution and correlation. Are the results the same as your calculated results in (a) and (b)? (d) Convolution in spatial domain is equal to multiplication in the frequency domain. That is given two images A and B, using Fourier Transform (F), we have F(A*B) = F(A)F(B). You can choose your own two images. Prove this by a MATLAB code. Show the code and resulting images. 1 2 3 x(m,n)= 4 5 6 7 8 9 h(m,n)=[3 4 5] (a) Hand calculate to perform the linear convolution between these two matrices x(m,n) and h(m,n) given below. Let the outside boundary pixels be zeros. You need to expand the boundary of x(m,n) to obtain all non-zero values in the result. Let the upper-left pixel of x(m,n) and h(m,n) be the origin. You need show step-by-step hand calculation process. (b) Similar to (a), but this time hand calculates to perform the linear correlation. (c) Using MATLAB functions, conv2 and xcorr2, to perform the linear convolution and correlation. Are the results the same as your calculated results in (a) and (b)? (d) Convolution in spatial domain is equal to multiplication in the frequency domain. That is given two images A and B, using Fourier Transform (F), we have F(A*B) = F(A)F(B). You can choose your own two images. Prove this by a MATLAB code. Show the code and resulting images. 1 2 3 x(m,n)= 4 5 6 7 8 9 h(m,n)=[3 4 5]

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