Homework5

# Homework5 - x n Then evaluate y n when the x n = u n or x n...

This preview shows page 1. Sign up to view the full content.

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 summationdisplay 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 find 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, first use convolution to find a expression for y ( n ) in terms of an input
This is the end of the preview. Sign up to access the rest of the document.

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 ( ω ) = tan − 1 p Im ( H ( ω )) Re ( H ( ω )) P In part i, since H ( ω ) 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-τ ) then the frequency response of h ′ ( t ) is e − iωτ 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...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern