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...

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

View Full Document Right Arrow Icon
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
Background image of page 1

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

View Full DocumentRight Arrow Icon
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
Background image of page 2
Problem 3. Find i (2+2 i ) = Problem 4. Find all the roots of the equation 3 + p 2 1+ i = 0. 3
Background image of page 3

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

View Full DocumentRight Arrow Icon
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
Background image of page 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
Background image of page 5

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

View Full DocumentRight Arrow Icon
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
Background image of page 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.
Background image of page 7

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

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

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 Right Arrow Icon
Ask a homework question - tutors are online