{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

EL 611 HW 6

# EL 611 HW 6 - sin n n x o = results in the output sin o o o...

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

EL611 3 Homework 5 1) Given an LTI system with real impulse response (i.e. the impulse response ) ( n h has no imaginary part), show that a) Any real input gives rise to a real output. Use the convolution sum to show this. b) If the response to a complex input, ) ( n x , is ) ( n y , then the response to the input ) ( * n x is ) ( * n y . Use the convolution integral again to show this. c) If the response to a complex input, ) ( n x , is ) ( n y , then the response to the input { } ) ( Re n x is { } ) ( Re n y , and the response to the input { } ) ( Im n x is { } ) ( Im n y . 2) Given an LTI system with transfer function ) ( z H , we know that the input n j o e n x ! = ) ( results in the output )) ( ( ) ( ) ( ) ( ) ( ) ( o o o o o o n j o n j j o n j j e A e e A e e H n y ! " ! ! ! " ! ! ! ! + = = = . a) Using the results of problem (1), part (c) above, show that the input ) cos( ) ( n n x o ! = results in the output )) ( cos( ) ( ) ( o o o n A n y ! " ! ! + = . b) Using the results of problem (1), part (c) above, show that the input

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ) sin( ) ( n n x o = results in the output )) ( sin( ) ( ) ( o o o n A n y + = . 3) Given the function ) cos 8 17 )( cos 6 10 ( cos 4 5 ) (cos " + + = V . a) Is this the magnitude function of any rational ) ( z H ? b) If the answer to part (a) is yes, find any ) ( z H that has the magnitude function given. 4) Let x[n] be a causal, N-point sequence that is zero outside the range 0 <= n <= N-1. When this x[n] is the input to the causal LTI system described by: ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! a. Is y[n] also a causal N point sequence? b. Show that this system describes an all-pass filter....
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