Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Utah State Univ. ECE 3640 HW 7: Orthonormal Basis Functions & Signal Processing, Assignments of Signals and Systems

Utah State University (USU)Signals and Systems

The seventh homework assignment for the electrical and computer engineering (ece) 3640 course at utah state university. The assignment covers topics on orthonormal basis functions, fourier series, and signal processing. Students are required to plot and verify the orthonormality of given basis functions, express given functions as a linear combination of basis functions, determine fourier series representations for signals, and calculate the rms power in the ripple of a filtered signal.

Typology: Assignments

Pre 2010

Uploaded on 07/30/2009

koofers-user-9mk-1
koofers-user-9mk-1 ๐Ÿ‡บ๐Ÿ‡ธ

9 documents

1 / 2

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Utah State University
ECE 3640
Homework # 7
Due Friday, Mar 10, 2006
โ€ขReading
1. Chapter 3, Chapter 4.
โ€ขHomework:
1. (10 pts) Consider the following basis functions:
x1(t) = u(t)โˆ’u(tโˆ’1)
x2(t) = u(tโˆ’1) โˆ’u(tโˆ’2)
x3(t) = u(tโˆ’2) โˆ’u(tโˆ’3)
x4(t) = u(tโˆ’3) โˆ’u(tโˆ’4)
(a) Plot the basis functions and satisfy yourself that they are orthonormal.
(b) For the functions
f1(t) = 2u(t)โˆ’3u(tโˆ’1) + u(tโˆ’4)
f2(t) = โˆ’2u(t) + 3u(tโˆ’1) โˆ’u(tโˆ’3)
f3(t) = u(t)โˆ’2u(tโˆ’1) + 2u(tโˆ’2) โˆ’2u(tโˆ’3) + u(tโˆ’4)
f4(t) = u(t)โˆ’3u(tโˆ’1) + 4u(uโˆ’3) โˆ’2u(tโˆ’4)
defined over the interval 0 โ‰คtโ‰ค4:
i. Plot the functions.
ii. Express each function fi(t) as a linear combination of the basis functions
xi(t).
2. (10 pts) Problem 3.4-7(a)
3. (5 pts) Problem 3.4-9(a,c,e)
4. Problem 3.4-11. (There is a mistake in the book. There is nothing to do in this
problem, just read it carefully. You should understand that there are such things
as Walsh functions.)
1
pf2

Partial preview of the text

Download Utah State Univ. ECE 3640 HW 7: Orthonormal Basis Functions & Signal Processing and more Assignments Signals and Systems in PDF only on Docsity!

Utah State University

ECE 3640

Homework # 7

Due Friday, Mar 10, 2006

  • Reading
    1. Chapter 3, Chapter 4.
  • Homework:
    1. (10 pts) Consider the following basis functions: x 1 (t) = u(t) โˆ’ u(t โˆ’ 1) x 2 (t) = u(t โˆ’ 1) โˆ’ u(t โˆ’ 2) x 3 (t) = u(t โˆ’ 2) โˆ’ u(t โˆ’ 3) x 4 (t) = u(t โˆ’ 3) โˆ’ u(t โˆ’ 4) (a) Plot the basis functions and satisfy yourself that they are orthonormal. (b) For the functions f 1 (t) = 2u(t) โˆ’ 3 u(t โˆ’ 1) + u(t โˆ’ 4) f 2 (t) = โˆ’ 2 u(t) + 3u(t โˆ’ 1) โˆ’ u(t โˆ’ 3) f 3 (t) = u(t) โˆ’ 2 u(t โˆ’ 1) + 2u(t โˆ’ 2) โˆ’ 2 u(t โˆ’ 3) + u(t โˆ’ 4) f 4 (t) = u(t) โˆ’ 3 u(t โˆ’ 1) + 4u(u โˆ’ 3) โˆ’ 2 u(t โˆ’ 4) defined over the interval 0 โ‰ค t โ‰ค 4: i. Plot the functions. ii. Express each function fi(t) as a linear combination of the basis functions xi(t).
    2. (10 pts) Problem 3.4-7(a)
    3. (5 pts) Problem 3.4-9(a,c,e)
    4. Problem 3.4-11. (There is a mistake in the book. There is nothing to do in this problem, just read it carefully. You should understand that there are such things as Walsh functions.)

1

  1. (5 pts) Problem 3.4-12(a)
  2. (10 pts) Problem 3.5-
  3. (5 pts) Problem 3.5-
  4. (10 pts) A signal f 0 (t) = sin t passes through a full-wave rectifier, producing the signal f (t) = | sin(t)|. This, in turn, passes through a RC lowpass filter with C = 1F and R = 1ฮฉ. (a) Determine a Fourier series representation for f (t). (b) Determine the Fourier series for the output of the filter, y(t). (c) Determine an expression for the rms power in the ripple. How does this compare to the total power in y(t)?
  5. Problem 4.1-1.