hw3 - ECE 2200 Signals and Information Section 4(Week 5 Feb...

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Homework 3 ECE 220 Due: March 8, 2005 1. If the impulse response h [ n ] of a FIR filter is h [ n ] = 2 δ [ n - 1] + 4 δ [ n - 2] - δ [ n - 4] (a) Write the difference equation for the FIR filter. (b) Draw a direct-form implementation as a block diagram of this filter. (c) Draw a transposed direct form implementation of this filter. CD: Difference Block diagram of FIR filter CD: Difference & block diagram from impulse response 2. A LTI system is described the difference equation y [ n ] = x [ n ] + 4 x [ n ] - 3 x [ n - 2] (a) When the input to the system is x [ n ] = 0 n < 0 n 2 n = 0 , 1 , 2 n - 1 n = 3 , 4 1 n 5 Compute y [ n ] for 0 n 10. (b) Determine the impulse response of this system. (Hint: Use x [ n ] = δ [ n ] as an input to the system). CD: Determine the Output of a FIR Filter for a given input 3. Determine whether or not each system is linear, time invariant and causal: (a) y [ n ] = x [ n ] cos( . 4 πn ) (b) y [ n ] = 2 x [ n - 2] + 4 x [ n - 9] (c) y [ n ] = | x [ n ] | (d) y [ n ] = 5 l = - 10 x [ l ] h [ n - l ] for h [ n ] = 2 δ [ n ] + 3 δ [ n - 1] CD: Linearity, time-invariance, and causality of systems.
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