hmw12 - y n = 0 5 y n-1 x n Using z-transform determine the...

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Due April 28, 2010 BME 171, Spring 2010 - HOMEWORK #12 Z Transform 1. Consider two systems given by their impulse responses: h 1 [ n ] = 2 n u [ n ] h 2 [ n ] = 1 - 1 3 n u [ n ] (a) Find the transfer functions H ( z ) and the difference equations governing these systems. (b) Determine the stability of these systems. (c) Draw block diagrams of these systems. 2. Consider a system given by its governing difference equation: y [ n ] = 2 x [ n ] + 3 x [ n - 1] - 3 y [ n - 1] - 2 y [ n - 2] . Find the transfer function H ( z ) and impulse response h [ n ] of this system. 3. Consider the system
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Unformatted text preview: y [ n ] = 0 . 5 y [ n-1] + x [ n ] . Using z-transform, determine the formula for the response of this system to input x [ n ] = u [ n ]. 4. The input to a digital filter is x [ n ] = { ⇓ 1 , . 5 } and the response is described by y [ n ] = δ [ n + 1]-2 δ [ n ]-δ [ n-1]. (a) Determine the transfer function of this filter. (b) Is this a FIR filter or an IIR filter? Justify. (c) Is this filter stable? Is it causal? Justify....
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