# ps1soln - MIT OpenCourseWare http/ocw.mit.edu 2.161 Signal...

This preview shows pages 1–4. Sign up to view the full content.

MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal Processing: Continuous and Discrete Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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

View Full Document
MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing – Continuous and Discrete Fall Term 2008 Problem Set 1 Solution: Convolution and Fourier Transforms Problem 1: Use the convolution definition ! " " # # = \$ = % d t h f h f t y ) ( ) ( ) ( (a) ) 75 . 0 ( ) ( ) 5 . 1 ( ) ( ! + + + = t t t t f " ! " # \$ \$ % % = otherwise t t t h , 0 1 1 |, | 1 ) ( ( ) , ) ( ) 75 . 0 ( ) ( ) ( ) ( ) 5 . 1 ( ) ( ) 75 . 0 ( ) ( ) 5 . 1 ( ) ( ! ! ! ! " " # " " # " " # " " # # # + # + # + = # # + + + = \$ d t h d t h d t h d t h t y and using the sifting property of the impulse function, ) 75 . 0 ( ) ( ) 5 . 1 ( ) ( ! + + + = t h t h t h t y -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 0 0.2 0.4 0.6 0.8 1 1.2 1.4 (b) h(t) is the as same used in part (a) ! " # \$ \$ % = otherwise t t f , 0 75 . 0 5 . 1 , 1 ) ( ,
-4 -3 -2 -1 0 1 0 0.5 1 2 ) 75 . 1 ( 2 )) ( 1 ( 2 ) 5 . 2 ( 2 )) ( 1 ( 2 75 . 0 1

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.

{[ snackBarMessage ]}

### Page1 / 7

ps1soln - MIT OpenCourseWare http/ocw.mit.edu 2.161 Signal...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online