BerinatoFall 11

# BerinatoFall 11 - 1 Introduction to Math Methods in...

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

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

View Full Document

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

View Full Document

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

View Full Document

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: 1 Introduction to Math Methods in Electrical Engineering An EE100 Lecture Dr. Bob Berinato [email protected] www.dynetics.com Fall 2011 2 • Good Engineers are Good Problem Solvers … and the best problem solvers have a large toolbox of math methods and techniques • Several tools we will consider today ¾ Complex Number Notation and Applications ¾ Properties of Curves ¾ Derivatives ¾ Integrals 3 EE (and Math) at Work: Synthetic Aperture Radar (SAR) • Radar can measure range (round-trip time delay) and Doppler shift • A moving radar can use the data it collects to create an “image” • Math methods are central to understanding and engineering SAR systems ¾ Complex Math and Fourier Transforms are essential tools www.sandia.gov/radar/imageryku.html 4 What are the 5 most important “numbers” in mathematics? 2 integers: 0, 1 2 irrationals: π , e 1 complex: Could these possibly be related in one equation? 1 − = j 5 Leonhard Euler – An Amazing Individual! 1 = + π j e 1 , sin cos − = + = j j e j θ θ θ a jb 1 θ cos θ sin θ Euler’s Formula: expresses sines and cosines in complex number notation ∑ ∞ = = 1 2 2 6 1 k k π 6 Application: Signal Notation • Real Signal Notation: • Complex Signal Notation: ( ) ( ) ( ) [ ] t t f t a t s o φ π + = 2 cos ( ) ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) { } [ ] ( ) ( ) ( ) [ ] t t f t ja t s t t f j t a t f j t j t a t f j t m t z o o o o φ π φ π π φ π + + = + = = = 2 sin 2 exp 2 exp exp 2 exp Magnitude Phase Center Frequency Complex Envelope, or Amplitude Magnitude Phase Re[ z ( t )] = s ( t ), the “real” signal 7 Application: The Phasor • Consider the following complex signal, called a phasor • This is the complex notation for a sinusoid with phase φ and amplitude A • Note that at time...
View Full Document

## This note was uploaded on 12/14/2011 for the course EE 1001 taught by Professor Hite during the Fall '11 term at University of Alabama - Huntsville.

### Page1 / 20

BerinatoFall 11 - 1 Introduction to Math Methods in...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online