{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Homework2

# Homework2 - EE 200 Fall 2009(Weber Homework 2 At the upper...

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

EE 200 – Fall 2009 (Weber) Homework 2 At the upper right corner on page 1 of all homeworks, show: Last name, First name Date EE 200, Homework # Show intermediate steps whenever possible. 1. Define x ( t ) as x ( t ) = 5 cos( ωt + 3 2 π ) + 4 cos( ωt + 2 3 π ) + 4 cos( ωt + 1 3 π ) a. Express x ( t ) in the form x ( t ) = A cos( ωt + φ ) by finding the numerical values of A and φ . b. Plot all the phasors used to solve part (a) in the complex plane. 2. If a function is periodic with period T 0 , then x ( t ) = x ( t + kT 0 ) for integer values of k . For each of the following continuous functions, is the function periodic, and if so what is the period? If it is not periodic, explain why. a. x 1 ( t ) = sin(2 πt ) + sin( 2 πt ) b. x 2 ( t ) = sin(2 2 πt ) + sin( 2 πt ) 3. A continuous-time signal x is given by x ( t ) = 2 cos(68 πt ) + 5 sin(170 πt ) - 7 cos(306 πt - π/ 6) where t is in seconds. a. Determine the fundamental frequency of x ( t ) and specify the units. b. What is the period of x ( t )? c. Convert the expression for x ( t ) from sin and cos functions to complex exponentials and determine the amplitudes ( a 0 , a 1 , a 2 , . . . ) for the Fourier series expansion of x ( t ). Your a k values should be in
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}