Lecture 2 - Discrete Time System y n = f x n k ] y [ n ] =...

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Unformatted text preview: Discrete Time System y n = f x n k ] y [ n ] = f { x [ n-k ], y [ n-k ] } x [ n ] g214 y [ n ] x n n y Input x [ n ] Output y [ n ] IF x 1 n n y 1 Linear System Homogeneity Property x 1 [ n ] g214 y 1 [ n ] THEN a x 1 [ n ] g214 ____ Input x [ n ] Output y [ n ] ax 1 n n ay 1 Linear System x 1 n n y 1 x 2 n n y 2 IF x n g214 y n Additivity Property x [ n ] = x 1 + x 2 n n y [ n ] = y 1 + y 2 x 1 [ n ] g214 y 1 [ n ] x 2 [ n ] g214 y 2 [ n ] THEN x 1 [n] +x 2 [n] g214 ________ Input x [ n ] Output y [ n ] Linear System IF Additivity + Homogeneity g214 Linearity IF x 1 [ n ] g214 y 1 [ n ] x 2 [ n ] g214 y 2 [ n ] THEN ax 1 [n] +bx 2 [n] g214 _____________ Input x [ n ] Output y [ n ] Linear System Checking Difference Equation For Linearity: Nonlinear if Diff Equ. contains either: A constant term y [n] = Products of inputs or output terms y [n] = x 1 n n y 1 Time-Invariant System IF x 1 [ n ] g214 y 1 [ n ] Shift-Invariance Property n n x 2 [ n ] = x 1 [ n-3 ] y 2 [ n ] = y 1 [ n-3 ] x 2 [ n ] = x 1 [ n-k ] x 2 [ n ] g214 y 2 [ n ] Input x [ n ] Output y [ n ] THEN...
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Lecture 2 - Discrete Time System y n = f x n k ] y [ n ] =...

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