Lecture 01 - Introduction

Lecture 01 - Introduction - 1 Lecture 01: Introduction...

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1 Lecture 01: Introduction Instructor: Dr. Gleb V. Tcheslavski Contact: gleb@ee.lamar.edu Office Hours: Room 2030 Class web site: http://ee.lamar.edu/gleb/dsp/ind ex htm ELEN 4304/5346 Digital Signal Processing Fall 2008 Based on ECE 4624 by Dr. A.A. (Louis) Beex, Virginia Tech ex.htm 2 Syllabus overview Pre-req.: ELEN 3313 Signals and Systems or their equivalent Required book: Sanjit K. Mitra, Digital-Signal Processing: A Computer-Based Approach, McGraw-Hill Co., Third edition, 2004, ISBN: 0-07-286546-6. Required software: The Mathworks, The Student Edition of MATLAB, Release 2006a or later. Structure: Two 75-minute lectures per week. One homework, three projects, midterm exam, and the final examination. Tests: The Midterm and Final exams will be closed book/notes. Your ELEN 4304/5346 Digital Signal Processing Fall 2008 performance on the Projects will account for the bulk of your grade. Honor System: Discussions on lecture subject material, to clarify your understanding, are highly encouraged. However, it is your personal understanding only that should be reflected in all work that you turn in. Any copyright violations (including copying articles and/or web pages to your reports) will be prosecuted!
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3 Styles, notations, legends… 1. Colors: Normal text and formulas Something more important (imho) Important formulas and results Very Important Formulas Miscellaneous 2. Equations notations: (2.17.3) Lecture # Slide # Formula # ELEN 4304/5346 Digital Signal Processing Fall 2008 4 Linear algebra overview It is convenient in many applications to represent signals and system coefficients by vectors and matrices. Therefore, a brief overview of linear algebra is considered. 1. Vectors A vector (denoted by a lowercase bold letter) is an array of real-valued or complex- valued numbers or functions. We will assume column vectors. The N -dimensional vector is: 1 2 x x = ⎢⎥ x # (1.4.1) ELEN 4304/5346 Digital Signal Processing Fall 2008 N x The transpose of a vector is a row vector: [ ] 12 T N x xx = x " (1.4.2)
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5 Linear algebra overview The Hermitian transpose is the complex conjugate of the transpose of x : * ** * HT xx x ⎡⎤ == " (1 5 1 ( ) 12 N ⎣⎦ It might be convenient in some cases to consider a set of values x n containing the signal values in the certain range: 1 n n x x = x (1.5.1) (1.5.2) ELEN 4304/5346 Digital Signal Processing Fall 2008 1 n nN x −+ ⎢⎥ # 6 Linear algebra overview The measure of the “magnitude” of the vector is the norm . 2 N The Euclidean or L 2 norm: 2 1 i i x = = x The L 1 norm: 1 1 N i i x = = x The L norm: max i i x = x We will be using the second norm (1.6.1) (1.6.2) (1.6.3) ELEN 4304/5346 Digital Signal Processing Fall 2008 We will be using the second norm. If the vector has a non-zero norm, it can be normalized as follows: x = x v x (1.6.4) The vector v x is a unit norm vector that lies in the same direction as x .
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7 Linear algebra overview The squared norm represents the energy in the signal: 1 22 N x = x (1 7 1 Lastly, the norm can be used to measure the distance between two vectors: () 2 1 , N ii i dx y = =−= xy x y (1.7.2)
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Lecture 01 - Introduction - 1 Lecture 01: Introduction...

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