# hmw5 - x [ n ] and h [ n ], compute the response oF this...

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Due February 17, 2010 BME 171, Spring 2010 - HOMEWORK 5 FIR/IIR Filters and Discrete Convolution 1. Consider a flter is described by the Following di±erence equation: y [ n ] = x [ n ] 3 x [ n 1] + 2 x [ n 3] . (a) Determine and sketch the impulse response h [ n ] oF this flter. (b) Draw a block diagram oF this flter. (c) Is this a ²IR or an IIR flter? Is this flter causal? Determine its order and length. 2. Consider input x [ n ] illustrated in the fgure below: n 6 4 2 0 2 4 -2 x[n] (a) Determine the support oF x [ n ], i.e., the range oF n where x [ n ] n = 0. (b) Signal x [ n ] is an input to the flter considered in Problem 1. Determine the support oF the response y [ n ]. 3. Use discrete convolution to compute the response y [ n ] oF the flter From Problem 1 to input oF Problem 2. Do it by hand, showing all excruciating details. Sketch your response. 4. Now write a Matlab script that will display

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Unformatted text preview: x [ n ] and h [ n ], compute the response oF this flter to input x [ n ], and then display y [ n ]. Use Matlab Function conv to compute convolution. Turn in plots oF x [ n ] , h [ n ] and y [ n ]. All three signals should be plotted as subplots on the same page and all horizontal axes should be aligned in index number and have the same scale. 5. Compare y [ n ] computed by hand and by Matlab. What do you have to do in your Matlab program to make these two answers agree? verte 6. An IIR flter is given by a block diagram shown below: z-1 z-1 z-1 1/3 1/3 y[n] 1/3 x[n] (a) IdentiFy on the block diagram the Feed-Forward and the Feed-back parts oF this flter. (b) Write the di±erence equation governing this flter. (c) What is the order oF this flter? JustiFy. 2...
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## This note was uploaded on 05/25/2010 for the course BME 171 taught by Professor Izatt during the Spring '08 term at Duke.

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hmw5 - x [ n ] and h [ n ], compute the response oF this...

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