{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# HW3 - w F − =(d 2 2 5 1 w jw jw w F − = Hint complete...

This preview shows page 1. Sign up to view the full content.

ECE 45 Fall 2007 Homework #3 Due Tuesday, Nov. 13, 2007 Note : You should be able to solve each of these problems without a calculator. Problem 1 : Kudeki 7.3. Write your final answer in terms of the sinc function. Problem 2 : Using the Fourier transform definition, find F(w) given (a) ) ( ) cos( ) ( t u t w e t f o at = , where a > 0. Hint: write cosine as a sum of complex exponentials. (b) ) 5 cos( ) ( ) ( t t g t f = given that = , 0 , 2 ) ( w G otherwise w 1 1 < < For (b) only, sketch G(w) and F(w). Problem 3 : Kudeki 7.6 Problem 4 : Kudeki 7.7 Problem 5 : Find f(t) given the following Fourier transform F(w). Hint: use partial fraction expansion (for some problems) and Table 7.2 from the text to solve for f(t). (a) 2 3 2 2 6 ) ( w jw jw w F + + = (b) 2 2 5 2 2 ) ( w jw jw w F + + = (c) 2 4 2 1 ) ( w jw
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: w F + − = (d) 2 2 5 1 ) ( w jw jw w F − + + = . Hint: complete the square for the expression in the denominator. Problem 6 : An LTI system is described by the following differential equation ) ( 5 ) ( ) ( 6 ) ( 5 ) ( 2 2 t x dt t dx t y dt t dy dt t y d + = + + find the response of the system y(t) when the input is ) ( ) ( 4 t u e t x t − = . Problem 7 : Kudeki 7.12 Problem 8 : Using the same circuit in (7), solve for y(t) if the input is the following (a) ) 60 cos( 37 ) ( ° + = t t x (b) x(t) is a periodic signal and is defined below over one period: + = , , 2 , ) ( t x 2 1 1 1 1 2 < < < < − − < < − t t t...
View Full Document

{[ snackBarMessage ]}