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

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

View Full Document Right Arrow Icon
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 .
Background image of page 1

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

View Full DocumentRight Arrow Icon
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 ) ( ,
Background image of page 2
-4 -3 -2 -1 0 1 0 0.5 1 2 ) 75 . 1 ( 2 )) ( 1 ( 2 ) 5 . 2 ( 2 )) ( 1 ( 2 75 . 0 1
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

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 Right Arrow Icon
Ask a homework question - tutors are online