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**Unformatted text preview: **Homework #Set 1 Signals, Systems, and Fourier Transforms 1. (a) y [ n ] = x [2 n ] stable, non-causal, linear, time-variant, memory. (b) y [ n ] = min{ x [ n –1], x [ n ], x [ n +1]} stable, non-causal(causal) , non-linear, time-invariant, memory. (c) y [ n ] = 2 y [ n – 1] +3 x [ n ] with y [-1] = 0 unstable, causal, linear, time-invariant, memory (d) y [ n ] = n x [ n – 2] + 3 x [ n + 2] + 5 unstable, non-causal, non-linear, time-variant, memory (e) h [ n ] = 2-n u [ n – 1] stable, causal, linear, time-invariant, memory. (f) y [ n ] = 3 x [ n ] + 2 x [ n – 1]+ n unstable, casual, nonlinear, time-variant, memory (g) h [ n ] = 3 ( n – 2) δ [ n ]+2 δ [ n-1] stable, casual, linear, time-invariant, memory (h) ⎩ ⎨ ⎧ = = = odd n even n n x n y if if ] 2 / [ ] [ stable, casual, linear, time-variant, memory 2. (a) ]. 5 [ 6 ] 4 [ ] 3 [ 6 ] 2 [ 6 ] 1 [ 4 ] [ ] [ 1 − + − + − + − + − + = n n n n n n n y δ δ δ δ δ δ (b) ]. 5 [ 2 ] 4 [ 3 ] 3 [ 2 ] 2 [ 6 ] [ ] [ 2...

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