Chapter-1-Reviews-Student

Chapter-1-Reviews-Student - ELEC 215 Signals and Systems II...

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ELEC 215: Tim Woo Spring 2009/10 Chapter 1 - 1 ELEC 215: Signals and Systems II Chapter 1: Reviews: Signals and Systems Spring 2009/10 Lecture: Tim Woo
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ELEC 215: Tim Woo Spring 2009/10 Chapter 1 - 2 Laplace Transform Where we are Differential equations State-space model CTFT Hardware Implementation System Characteristics System Responses Closed-loop Systems Continuous-time z-Transform Difference equations State-space model DTFT Hardware Implementation System Characteristics System Responses Closed-loop Systems Discrete-time Mapping Done in 211 To be covered In progress Done Will be covered if available Open-loop Systems Open-loop Systems
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ELEC 215: Tim Woo Spring 2009/10 Chapter 1 - 3 Reviews • Before reaching the first outcome of this course, we would like to review some fundamental concepts of signals and systems those you learned in ELEC 211. • In the reviews, some expected outcome from you – Classify different categories of Signals and Systems – Understand LTI systems and its properties – Distinguish the time and frequency representations of signals and systems – Apply suitable analytical tools to solve the engineering problems.
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ELEC 215: Tim Woo Spring 2009/10 Chapter 1 - 4 Reviews – Signals • A vague definition: Something that carries information. Signal may describe a wide variety of physical phenomena. Speech signal Image signal
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ELEC 215: Tim Woo Spring 2009/10 Chapter 1 - 5 Reviews – Signals • Signals can be represented in the ways of waveform (graphical) and mathematical expression • Two classes of signals are considered in this course. Continuous Time (CT) and Discrete Time (DT) signals x ( t ) x [ n ] tn
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ELEC 215: Tim Woo Spring 2009/10 Chapter 1 - 6 Reviews – Signals interval infinite over power average DT ] [ lim ] , [ interval over power average DT ] [ power ous instantane DT ] [ interval infinite over power average CT ) ( lim ) , ( interval over power average CT ) ( power ous instantane CT ) ( 2 1 2 1 2 1 2 1 2 1 1 2 1 2 2 2 1 2 1 2 1 2 1 2 2 1 + = + N N N N n n n n n T T T T t t t t n x n n n x n x dt t x t t dt t x t x Instantaneous and Average power
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ELEC 215: Tim Woo Spring 2009/10 Chapter 1 - 7 Reviews – Signals • Transformations of the independent variables – Time shifting – Time reversal – Time scaling ] [ ] [ ) ( ) ( 0 0 n n x n x t t x t x ] [ ] [ ) ( ) ( n x n x t x t x ) / ( ) ( a t x t x = otherwise k a ka n a n x n x an x n x , 0 integers are , ; ], / [ ] [ ] [ ] [
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ELEC 215: Tim Woo Spring 2009/10 Chapter 1 - 8 Reviews – Signals
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ELEC 215: Tim Woo Spring 2009/10 Chapter 1 - 9 Reviews – Signals Basic signals – Real and complex signals • Real exponential signals – an impulse response of (non-ideal) lowpass filter • Real sinusoidal signals – Carriers of modulator in communication system – Fundamental components of real periodic signals in Fourier Series Representation • Complex exponential signals – Eigen-functions of Fourier Series Representation / Fourier Transform Modulator () = + + = 1 0 ) ) / 2 ( cos( 2 ) ( k k k a t T k a a t x π (3.3.1) on page 189 of textbook t T jk k k e a t x ) / 2 ( ) ( −∞ = = dt e t x
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Chapter-1-Reviews-Student - ELEC 215 Signals and Systems II...

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