Course Information:
Concepts for the analysis of sampled-data and continuous time linear systems including convolution, Pulse and impulse responses, continuous and discrete Fourier series and transforms, frequency responses and Bode diagrams, Laplace and Z-transforms and transfer functions, state equations. Notions of stability including the Nyquist Criterion and Lyapunov's test. Introduction to digital communication concepts including the Shannon-Nyquist Sampling Theorem, digtal filtering, the fast fourier transform and AM and FM modulation. Introduction to feedback including digital control concepts for robotic systems.

Organization:
The course meets on Mondays and Wednesdays from 9:00am to 10:15am. There are approximately eleven weekly homework assignments. There is a mid-term and a final in-class exam.

Course Text:
Signals and Systems, A. V. Oppenheim and A. S. Willsky, Prentice Hall, 2nd Edition, 1996

Instructor:
Prof. A. Stephen Morse
Electrical Engineering
Dunham Lab 509
(203)432-4295
email: as.morse@yale.edu

Teaching Assistant:
Sudhakar Chelikani
Applied Physics
Dunham Lab 108
(203)432-4324
email: sudhakar.chelikani@yale.edu


Contents:

Week 1:   continuous and discrete-time signals; transformations; exponential and sinusoidal signals; impulse and step signals.

Week 2:   continuous and discrete systems; system memory, causality, stability, time invariance, linearity. Convolution sum.

Week 3:   convolution integral; properties of linear systems; introduction to linear dynamical discrete and continuous systems; characterizations via impulse and step responses.

Week 4:   continuous-time Fourier series; series convergence; properties; discrete-time Fourier series; properties; examples

Week 5:   continuous-time Fourier transform; transforms of periodic signals; convolution and multiplication properties.

Week 6:   Fourier transform of an impulse response; the frequency response of a linear dynamical system; how your hi-fi amplifier works.

Week 7:   discrete Fourier transform; time and frequency characterizations of signals and systems; magnitude and phase relations; Bode diagrams; examples.

Week 8:   sampling of signals; zero-order holds; signal reconstruction: the Shannon-Nyquist Sampling Theorem; introduction to digital signal processing.

Week 9:   introduction to communication systems; amplitude modulation and demodulation; introduction to frequency modulation; time and frequency multi-plexing; how your radio works.

Week 10:   introduction to Laplace transforms; block diagrams; the transfer function of a continuous-time linear dynamical system; z-transforms; the transfer function of a discrete-time linear dynamical system.

Week 11:   introduction to feedback; root locus; the Nyquist stability test; gain and phase margin; how an autopilot works; how your cruise control works; why a public address system sometimes screeches; the age of robots is coming.