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Please answer all three parts. Please write down formulas that you use and write down explanations when needed! Will give you thumbs up and leave a great comment!!! Thank you!!!

4. (a) let x[n] be a finite duration signal of duration N. Let y[n] = DFT(DFT(a[n])). All DFTs are N point DFTs. Find vinl in termas of rinl Prove all the properties you use in arriving at your result (b) Let an] and yIn] be sequences of duration N with their corresponding N point DFTs denoted by Xk] and Y[k respectively. Show that N-1 N-1 (c) Let rn] be sequences of duration N with the corresponding N point DFTs denoted by Xk]. Let QlkX3k +2]. Find the sequence q/n], n 0,1,..1, whose DFT is Qkl. (Assume N is divisible by 3 for this problem.)

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