Tuto4_Conv - EE3210 Tutorial 4: Convolution 1. Let x[ n] =...

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Unformatted text preview: EE3210 Tutorial 4: Convolution 1. Let x[ n] = 4δ [ n] + 2δ [ n − 1] and h[ n] = 3δ [n] + δ [ n − 1]. Use the graphical method to find their convolution sum. Repeat using the superposition method. 2. (Problem 2.1) Let x[ n] = δ [ n] + 2δ [ n − 1] − δ [ n − 3] and h[ n] = 2δ [ n + 1] + 2δ [ n − 1]. Compute and plot each of the following convolutions: a) y1 [n] = x[n] ∗ h[n] b) y 2 [n] = x[n + 2] ∗ h[n] (Express your answer in terms of y1[n].) c) y 3 [n] = x[n] ∗ h[n + 2] (Express your answer in terms of y2[n].) 3. (Problem 2.21) Compute the convolution y[ n] = x[n] ∗ h[ n] of the following pairs of signals: x[n] = α n u[n], h[n] = β n u[n], α ≠ β . 4. (Example 2.8) Let y(t) denote the convolution of the following two signals: x(t ) = e 2t u (−t ) h(t ) = u (t − 3) Find y(t). 5. (Problem 2.14) Consider a continuous-time LTI system whose impulse response is h(t ) = e − (1− 2 j ) t u (t ) . Is the system stable? ...
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