Homework5

Homework5 - x ( n ). Then evaluate y ( n ) when the x ( n )...

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EE 200 Fall 2008 (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. A discrete-time system has an impulse response of h ( n ) = 7 s k =0 δ ( n - k ) a. Sketch h ( n ) b. If the input to the system is x ( n ) = cos( ωn ) where ω = π/ 4 radians/sample, what is the output y ( n )? Hint: Use convolution and make use of the sifting propery of the Kronecker delta function. c. What is the frequency response H ( ω ) of the sytsem? Use DTFT (equation 9.15 in the text) and example 9.12 to ±nd an expression for H ( ω ). d. What is the value of H ( ω ) for the frequency of the input in part b? The results of part b and d should be consistant. 2. Problem 4 in chapter 9 For parts b and c, ±rst use convolution to ±nd a expression for y ( n ) in terms of an input
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Unformatted text preview: x ( n ). Then evaluate y ( n ) when the x ( n ) = u ( n ) or x ( n ) = r ( n ). In part h, the phase response is given by n H ( ) = tan 1 p Im ( H ( )) Re ( H ( )) P In part i, since H ( ) is conjugate symmetric, you can use the expression at the bottom of page 297 to calculate y ( n ). 3. Problem 7 in chapter 9 4. Problem 10 in chapter 9 5. Find the the frequency response of a continuous-time system that has the impulse response below. Hint: Remember that if h ( t ) = h ( t- ) then the frequency response of h ( t ) is e i times the frequency response of h ( t ). Shift the signal around to make the integration easier and then multiply the result by a complex exponential. A 2T T t 1...
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