SPFirst-L22

# SPFirst-L22 - 3/27/2004 © 2003, JH McClellan & RW...

This preview shows pages 1–3. Sign up to view the full content.

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: 3/27/2004 © 2003, JH McClellan & RW Schafer 1 Signal Processing First Lecture 22 Introduction to the Fourier Transform 3/27/2004 © 2003, JH McClellan & RW Schafer 3 READING ASSIGNMENTS ¡ This Lecture: ¡ Chapter 11, Sects. 11-1 to 11-4 ¡ Other Reading: ¡ Recitation: Ch. 10 ¡ And Chapter 11, Sects. 11-1 to 11-4 ¡ Next Lecture: Chapter 11, Sects. 11-5, 11-6 3/27/2004 © 2003, JH McClellan & RW Schafer 4 LECTURE OBJECTIVES ¡ Review ¡ Frequency Response ¡ Fourier Series ¡ Definition of Fourier transform Relation to Fourier Series ¡ Examples of Fourier transform pairs ∫ ∞ ∞ − − = dt e t x j X t j ω ω ) ( ) ( 3/27/2004 © 2003, JH McClellan & RW Schafer 5 Everything = Sum of Sinusoids ¡ One Square Pulse = Sum of Sinusoids ¡ ??????????? ¡ Finite Length ¡ Not Periodic ¡ Limit of Square Wave as Period Æ infinity ¡ Intuitive Argument 3/27/2004 © 2003, JH McClellan & RW Schafer 6 Fourier Series: Periodic x(t) x ( t ) = x ( t + T ) T − 2 T − T 2 T t x ( t ) = a k e j ω k t k =−∞ ∞ ∑ a k = 1 T x ( t ) e − j ω kt dt − T / 2 T / 2 ∫ Fundamental Freq. ω = 2 π / T = 2 π f Fourier Synthesis Fourier Analysis 3/27/2004 © 2003, JH McClellan & RW Schafer 7 Square Wave Signal a k = e − j ω kt − j ω kT − T /4 T / 4 = e − j π k...
View Full Document

## This note was uploaded on 03/03/2010 for the course EE 48976 taught by Professor Nayak during the Spring '10 term at USC.

### Page1 / 6

SPFirst-L22 - 3/27/2004 © 2003, JH McClellan & RW...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online