8. a) Define the convolution and correlation of two discrete functions x(t) and h(t) [4] b) Compute convolution product of y(t)=x(t)h(t) x(t)=2,1,2;h(t)=1,2,3,2,3 9. Prove that convolution product of two functions f(t) and h(t) is inverse Fourier Transform of product of F(u) and H(u) where F(u) and H(u) are the Fourier transforms of f(t) and h(t) respectively. [10] 5. Given four spatially adjacent points in an image be (x1,y1),(x1,y2),(x2,y1), and (x2,y2) and the corresponding intensities g1,g2,g3, and g4; find the intensity, g at point (x,y) which is inside the square formed by the four locations given above using bi-linear interpolation. [10] 6. Derive 33 Laplacian operators for sharpening images. [10] 7. Write a program to smoothen a given image using an averaging operator in 33 window [10]