Homework5

Homework5 - 4. An LTI system has an impulse response given...

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EE 200 – Fall 2009 (Weber) Homework 5 At the upper right corner on page 1 of all homeworks, show: Last name, First name Date EE 200, Homework # Show intermediate steps whenever possible. 1. For the following feedback ±lters, determine the system function and plot the location of the poles and zeros. a. y [ n ] = 1 2 y [ n - 1] - 1 3 y [ n - 2] - x [ n ] + 3 x [ n - 1] - 2 x [ n - 2] b. y [ n ] = - 0 . 9 y [ n - 6] + x [ n ] 2. An LTI ±lter is described by y [ n ] = 0 . 8 y [ n - 1] - 0 . 8 x [ n ] + x [ n - 1] a. What is the system function, H ( z )? b. Plot the poles and zeros of H ( z ). c. From H ( z ), determine an expression for the frequency response H ( e j ˆ ω ). d. Show that v v H ( e j ˆ ω ) v v 2 = 1 for all values of ˆ ω . e. Will this ±lter have any e²ect on signals going through it? If so, what does it do to the signals (brie³y.) 3. Problem P-8.16 from the textbook.
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Unformatted text preview: 4. An LTI system has an impulse response given by h ( t ) = b t t 1 otherwise a. For an input of x ( t ) = u ( t )-u ( t-2), use convolution to determine the output y ( t ) = x ( t ) * h ( t ). b. Draw graphs of x ( t ), h ( t ), and y ( t ). 5. An LTI system has the following impulse response and input. h ( t ) = 3 u ( t-5)-3 u ( t-1) x ( t ) = 2 u ( t )-2 u ( t-2) Find the system output y ( t ) = x ( t ) * h ( t ). You can nd the result by expanding the convolution into four terms and then use linearity and time-invariance and the results in Example 9-9 in the text. You dont have to use integration. 1...
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