{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

MIT6_003S10_assn10

MIT6_003S10_assn10 - System B x 1 t x 3 t System C x 2 t x...

This preview shows pages 1–5. Sign up to view the full content.

6.003 Homework 10 Problems 1. DT Fourier Series Due at the beginning of recitation on Wednesday, April 21, 2010 . Find the Fourier transforms of the following signals, which are 0 for | n | > 7 . Determine the Fourier Series coefficients for each of the following DT signals, which are periodic in N = 8 . n 1 x 1 [ n ] 1 / 2 n 1 x 2 [ n ] n 1 x 3 [ n ] n 1 x 4 [ n ] 1 / 2 2. Inverse DT Fourier Series Determine the DT signals with the following Fourier series coefficients. Assume that the signals are periodic in N = 8 . k 1 a k 1 / 2 k 1 b k 3. DT Fourier transforms n x 1 [ n ] 1 n x 2 [ n ] 1 n x 3 [ n ] 1 1 n x 4 [ n ] 1

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

View Full Document
6.003 Homework 10 / Spring 2010 2 4. Which are True? For each of the DT signals x 1 [ n ] through x 4 [ n ] (below), determine whether the conditions listed in the following table are satisfied, and answer T for true or F for false. X ( e j 0 ) = 0 π π X ( e j ) d Ω = 0 X ( e j ) is purely imaginary e jk X ( e j ) is purely real for some integer k x 1 [ n ] x 2 [ n ] x 3 [ n ] x 4 [ n ] 1 n x 1 [ n ] 1 n x 2 [ n ] 1 n x 3 [ n ] 1 n x 4 [ n ]= x 4 [ n + 5]
3 6.003 Homework 10 / Spring 2010 5. Input/Output Pairs The following signals are all periodic with period T = 1 . 1 x 1 ( t )= x 1 ( t + 1) t 0 1 4 1 1 x 2 ( t )= x 2 ( t + 1) t 0 1 4 1 1 x 3 ( t )= x 3 ( t + 1) t 0 π 10 1 Indicate which of the systems could or could not be linear and time-invariant. System A x 1 ( t ) x 2 ( t ) System B

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.

Unformatted text preview: System B x 1 ( t ) x 3 ( t ) System C x 2 ( t ) x 1 ( t ) System D x 2 ( t ) x 3 ( t ) System E x 3 ( t ) x 1 ( t ) System F x 3 ( t ) x 2 ( t ) 4 6.003 Homework 10 / Spring 2010 Engineering Design Problem 6. Image reconstruction The rows and/or columns of the following images have been blurred. Figure out a way to sharpen each image, and identify the building. Here are thumbnails of the images: a1 a2 b1 b2 c1 c2 The images are available in machine-readable form (buildings.zip) on our website. MIT OpenCourseWare http://ocw.mit.edu 6.003 Signals and Systems Spring 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
View Full Document

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern