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6 Properties of Convolution Transference between Input & Output Suppose xn * hn = yn If L is a linear system, x1n = L{xn}, y1n = L{yn} Then x1n ∗ hn= y1n5S Compute the convolution yn = xn * hn of the following pairs of signals a) α β β α ≠ = = when h n u n x n u n n n b) x n = h n = αn u n c) 4 2) 4 2 1 (h n u n x n u n n n = − = − − d) xn and hn are as in following figure Hint first draw x(t)ELG 31 Signals and Systems Chapter 2 3/2 Yao Example Consider the LTI system with impulse responsehn and input xn, as illustrated in Fig 2 2 n hn 1 0 1 2 1 1 n xn 05 0 1 2 (a) The output response based on Eq (25) can be expressed Amea High Resolution Stock Photography And Images Alamy ƒ‚ƒ"ƒXƒ^[ƒnƒ"ƒ^[ƒ[ƒ‹ƒh •ÇŽ†