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**Unformatted text preview: **Homework #Set 1 Signals, Systems, and Fourier Transforms 1. For each of the following systems, determine whether the system is (1) stable, (2) causal, (3) linear (4) time invariant, and (5) memoryless . (a) y [ n ]= x [2 n ]; (b) h [ n ] = min{ x [ n − 1], x [ n ], x [ n-1]}; (c) y [n] = 2 y [ n − 1] + 3 x [ n ] with y [ − 1] = 0; (d) y [ n ] = nx [ n − 2] + 3 x [ n + 2] + 5; (e) h [ n ] = 2 − n u [ n − 1]; (f) y [ n ] = 3 x [ n ] + 2x [ n − 1] + n ; (g) h [ n ] = 3 ( n − 2) δ [ n ]+ 2 δ [ n − 1]; (h) y [ n ] = odd n even n n x = = ⎩ ⎨ ⎧ if if ] 2 / [ 2. The impulse responses of two linear time-invariant system are shown below. Determine and sketch the responses of these two systems when they use the same input as x [ n ] = δ [ n ] + 2 δ [ n − 1] − δ [ n − 2] + 2 δ [ n − 3]. 3 . Let x [ n ] and X ( e j ω ) represent a sequence and its Fourier transform, respectively. Determine, in terms of X (e j ω ) the Fourier transforms of y s [ n ], y d [ n ],...

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