Assignment 5_ Convolution.pdf - ECE 301 Homework 5 Convolution 1 Find and sketch c=(t f1(t \u2217 f 2(t for the pairs in Figure.1 Figure 1 2(a If 1 \u2217 2 =

# Assignment 5_ Convolution.pdf - ECE 301 Homework 5...

This preview shows page 1 - 2 out of 2 pages.

ECE 301 Homework 5 Convolution 1. Find and sketch 1 2 ( ) ( ) ( ) c t f t f t = for the pairs in Figure.1 Figure 1 2. (a) If 𝑓𝑓 1 ( 𝑡𝑡 ) 𝑓𝑓 2 ( 𝑡𝑡 ) = 𝑐𝑐 ( 𝑡𝑡 ) , prove (i) 𝑓𝑓 1 ( 𝑡𝑡 − 𝑇𝑇 ) 𝑓𝑓 2 ( 𝑡𝑡 ) = 𝑐𝑐 ( 𝑡𝑡 − 𝑇𝑇 ) (ii) 𝑓𝑓 1 ( 𝑡𝑡 ) 𝑓𝑓 2 ( 𝑡𝑡 − 𝑇𝑇 ) = 𝑐𝑐 ( 𝑡𝑡 − 𝑇𝑇 ) (b) Find the answer to (i) 𝑓𝑓 ( 𝑡𝑡 ) ∗ 𝛿𝛿 ( 𝑡𝑡 ) (ii) 𝑓𝑓 ( 𝑡𝑡 ) ∗ 𝛿𝛿 ( 𝑡𝑡 − 𝑇𝑇 ) (c) Using direct integration, find 𝑒𝑒 −𝑎𝑎𝑎𝑎 𝑢𝑢 ( 𝑡𝑡 ) 𝑒𝑒 −𝑏𝑏𝑎𝑎 𝑢𝑢 ( 𝑡𝑡 ) . Note in the above question, T is a constant and t is the signal/time variable. 3. (a) Using direct integration, find sin( 𝑡𝑡 ) 𝑢𝑢 ( 𝑡𝑡 ) 𝑢𝑢 ( 𝑡𝑡 ) . (b) Using direct integration, find t ∙ 𝑢𝑢 ( 𝑡𝑡 ) 𝑢𝑢 ( 𝑡𝑡 ) . 4. Let
𝑥𝑥 [ 𝑛𝑛

#### You've reached the end of your free preview.

• Spring '20
• Impulse response, Sketch C

### 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