# A6_SOL - Signals and Systems Fall 2013 Solution to Homework...

• Homework Help
• 3

This preview shows pages 1–2. Sign up to view the full content.

Signals and Systems Fall 2013 Solution to Homework Assignment #6 1. Find the z transform of each of the following sequences. (a) f ( k ) = 2 δ ( k ) δ ( k 2) = = = otherwise 0 2 , 1 0 , 2 k k We then obtain the z -transform as follows 2 2 2 1 2 1 ( ) 2 for 0 z F z z z z = − = (b) f ( k ) = < 5 , 2 5 0 , 1 0 , 0 5 k k k k . 5 ( ) ( ) ( 5) 2 ( 5) k s s s f k u k u k u k = + The z -transform can then be obtained as, 6 5 5 5 4 1 1 2 1 ( ) for 2 1 1 2 ( 1)( 2) z z z z z F z z z z z z z z z z + = × + × = > . (c) f ( k ) = {2,2,0, 1, 1, 1,2,2,0, 1, 1, 1,2,2,0, 1, 1, 1, ⋅⋅⋅ }. [Hint: Express f ( k ) as the sum of shifted, identical, finite sequences.] Let g ( k ) = {2,2,0, 1, 1, 1, 0,0,0, 0 , 0 ,0,0,0,0, 0 , 0 ,0 ⋅⋅⋅ }. Then, 6 12 18 1 1 1 ( ) ( ) { ( )} { ( )} { ( )} f k g k g k g k g k E E E =+ + + + It then follows that, 6 12 18 6 6 0 0 6 1 1 1 ( ) ( ) ( ) ( ) ( ) 1 1 1 ( ) ( ) ( ) ( ) 1 ( ) 1 m m m m F z G z G z G z G z z z z G z G z G z G z z z z = = = + + + + = = = = 6 6 ( ) ( ) 1 z F z G z z = where 5 4 2 3 4 5 5 2 1 1 1 2 2 1 ( ) 2 for 0 z z z z G z z z z z z z +

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.
• Fall '09
• MALIKELBULUK
• SIGNALS

{[ 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