(b) Write appropriate difference equations to implement the polyphase version of thesystem.
ECE 513 - Homework 66(a) LetX(k) be theN-point DFT of the sequencex(n), 0≤n≤N-1. We definea 2N-point sequencey(n) asy(n) =x(n+12),nodd0,neven(12)Express the 2N-point DFT ofy(n) in terms ofX(k).(b) Letx1[n] andx2[n] be twoN-point discrete-time sequences and letX1(k) andX2(k) be their respectiveN-point DFT sequences. It is known that multiplicationofX1(k) andX2(k) in frequency domain is equivalent to the circular convolutionofx1[n] andx2[n] in discrete-time domain.Prove the duality is true.That is,givenX3[k] =1NN-1Xl=0X1[l]X2[((k-l))N],(13)show thatx3[n] =x1[n]x2[n] forn= 0,1, . . . , N-1, where ((·))Nmeans moduloN.