301test1

# 301test1 - 4 4 x 10 3.5 3 2.5 2 1.5 1 0.5 0 2 0 2 4 6 8 10...

This preview shows pages 1–8. Sign up to view the full content.

A-AE 301 Exam 1, Fall 2009. Please put your best answer clearly written on the exam in a box. Two page of notes and no calculators. NAME: 1

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

View Full Document
Problem 1. Find the real and imaginary part of 4 i (2 + i ) (1 ¡ i )(2 + 2 i ) = Problem 2. Compute the following ( i ¡ 1) 12 = 2
Problem 3. Find i (2+2 i ) = Problem 4. Find all the roots of the equation 3 + p 2 1+ i = 0. 3

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

View Full Document
Problem 5. Find Z 2 0 j 2 ¡ 4cos(40 t ) ¡ 2sin(75 t ) j 2 dt = Problem 6. Graph the following function and indicate the direction of the curve g ( ± ) = p 2 (1 + { ) e for 0 ± …: 4
Problem 7. Consider the function g ( t ) = 10 + 16 cos(2 t ) + 2cos(6 t ) ¡ 2sin(6 t ) : Assume that an approximation for g is given by p ( t ) = 10 + 8 e 2 {t + 8 e ¡ 2 {t : Then compute the error 1 2 Z 2 0 j g ( t ) ¡ p ( t ) j 2 dt = 5

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

View Full Document
Problem 8. Consider the function g 2 L 2 (0 ; 2 ) given by g ( t ) = 10 + 16 cos( t ) + 2cos(6 t ) ¡ 2sin(6 t ) Find a Fourier series expression for this function of the form g ( t ) = 1 X k = ¡1 a k e ¡ {kt : 6
Problem 9. Suppose that g ( t ) 2 L 2 (0 ; 2 ) admits a Fourier series expansion of the form g ( t ) = 2 + 2cos(2 t + …= 4) + 4 cos(4 t ) + 2 sin(4 t ) : Then plot the power spectrum for g for k 0.

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.

## This document was uploaded on 12/29/2011.

### Page1 / 12

301test1 - 4 4 x 10 3.5 3 2.5 2 1.5 1 0.5 0 2 0 2 4 6 8 10...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online