Question1) a) State and prove the convolution theorem. b) The process of sampling a function 𝑓 may be represented by multiplication of the function by a Dirac comb (an infinite set of regularly spaced Dirac distributions). Prove that in the Fourier domain the sampling in the object (time / space) domain is equivalent to replication in the Fourier domain of 𝐹 = ℱ(𝑓), the Fourier transform of 𝑓 (i.e. replication of the spectrum). c) What is the equivalent operation in the object space of sampling in the Fourier domain? d) Show the relationship between the sequences of samples transformed by the Discrete Fourier Transform (DFT) and the continuous Fourier transform with appropriate sampling in both object and Fourier domain. Question2) Question 3)