# A2 - Signals and Systems Fall 2015 Issued 2 September 2015...

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Signals and Systems Fall 2015 Issued: 2 September 2015 Due: 9 September 2015 Homework Assignment #2 1. Make a sketch of each of the following discrete-time signals. (a) ) 5 ( ) 2 ( ) ( 2 ) ( = k u k u k u k x s s s (b) ) 5 ( ) ( ) 1 ( ) ( ) ( + + = k u k u k k k x s s δ δ (c) )] 5 ( ) 2 ( [ )] 2 ( ) ( [ 2 ) ( + = k u k u k u k u k x s s s s (d) )] 12 ( ) 3 ( [ ) 3 / sin( ) ( = k u k u k k k x s s π (e) )} ( ) 6 . 0 4 . 0 Re{( ) ( k u j k x s k + = 2. For each of the input-output relations, determine whether the system is linear or nonlinear, time-invariant or time-varying, causal or non-causal. (a) + = t d x t x t y τ τ ) ( 5 ) ( 2 ) ( (b) + = t d x t tx t y τ τ ) ( 5 ) ( 2 ) ( (c) + = 2 2 ) ( 5 ) ( t t d x t y τ τ (d) < = 2 , 0 2 , ) ( 5 ) ( 2 t t d x t y t τ τ (e) = t d x t y τ τ τ | ) ( | ) ( 3. Use fixed-point iterations of the form x ( k + 1) = f ( x ( k )). to find both real solutions of the nonlinear equation 0 1 2 4 = x x .

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Signals and Systems Fall 2015 Solution to Homework Assignment #2 1. Sketch of the following discrete-time signals.
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