3 2 1 -2-01 2 -1 Figure 10.7: Length 4 signal x[n] for Problem 10.1. Problem 10.1 Consider the length 4 signal x[n] shown in Figure 10.7. Let X[k], k = 0, 1, 2, 3, denote the 4-point DFT of x[n]. For k = 0, 1, 2, 3, define X₁[k] = X*[k], X2[k] = Re(X[k]), X3[k] = (−j)*X[k] Using only time domain operations, derive and sketch, for n = 0, 1, 2, 3, the corresponding inverse DFTS: (a) x1[n] (b) x2n (c) x3[n]. Problem 10.3 Redo Problem 10.1, considering the same signal, but now defining X[k], k = 0, 1, ..., 7 as the 8-point DFT. Using time domain operations alone, derive and sketch the inverse DFTs (a) x1[n], (b) x2[n], and (c) x3[n] for n = 0, 1, ..., 7. =