EE103 Signals and Systems

Catalog copy:
The course covers the following topics: characterization and analysis of
continuous-time signals and linear systems, time domain analysis using
convolution, frequency domain analysis using the Fourier series and the
Fourier transform, the Laplace transform, transfer functions and block
diagrams, continuous-time filters, sampling of continuous time signals,
examples of application to communications and control systems.
Prerequisite: EE70, Introduction to Electronic Circuits.

Explanation of prerequisite:
EE103 solves circuit design for systems that resolve to first or
second order differential equations. This circuit analysis is
introduced in EE70.  Knowledge of solving differential equations is
taught in other math courses that are prerequisites for EE70.

Required skills to pass the course:
1. Ability to define basic operations such as time scale, time
   shift, time reverse, and combining of these operations for signals. 
2. Ability to recognize whether a system is linear or
   nonlinear, causal or non-causal, with memory or without memory, stable or
   non-stable, time-invariant or time-variant. 
3. Ability to represent a circuit with mathematical model and
   solve the equations to create system equations in terms of differential or
   difference equations. 
4. Understanding of sinusoidal, exponential, impulse (delta), step
   functions. Also capability of using these functions in equations with
   other signals. 
5. Ability to determine whether or not a signal is an energy or power signal.
6. Ability to derive the Generalized Fourier series expansion of a
   signal with a given set of orthogonal basis function. Also, the ability to
   evaluate if a set of basis signals are orthogonal. 
7. Ability to solve first and second order systems, find
   system impulse responses, compute the response of the system to initial
   conditions and any input signal. 
8. Ability to define spectra and bandwidth of a CT signals. 
9. Ability to represent a CT signal over an interval by Fourier
   Fourier series representations of periodic signals and aperiodic energy
   signals
10. Ability to compute Fourier transform and understand its
    properties. Also ability to compute Fourier transform of electric
    circuits. 
11. Ability to derive frequency response of a system, specially
    using differential equation and understand Group delay concept. 
12. Ability to compute Laplace transform (single sided and
    double sided) and understand its properties and related theorems. 
13. Solving electric circuits using Laplace transform. 
14. Ability to understand ideal sampling theorem and practical
    effects of sampling. 

Core topics (must be taught): 
1. Basic definitions of Signals and Systems 
2. Signal and System Characteristics and Models 
3. Time-Domain Representation of continuous-time (CT) Signals,
   including Sinusoidal, Exponential signals, Signal energy and power 
4. Time-Domain Analysis of CT Systems, including impulse
   response, zero state response, and CT convolution and their properties 
5. Frequency-Domain Representation of CT Signals, including
   Fourier series representations of periodic signals and aperiodic energy
   signals
6. Frequency-Domain Analysis of CT Systems, including frequency
   response determination and some examples 
7. Analysis of CT Systems using Laplace Transform, including LT
   definitions and theorems, system transfer function 
8. Sampled CT Signals, including ideal sampling and sampling theorem 

Optional Topic:
1. Basic concept on ideal filters, butterworth and Chebyshev
   filter design (if time allows).

Text:
Gordon E. Carlson, Signal and Linear System Analysis, second edition, John
Wiley.

Prepared by Hamid R. Sadjadpour, 10/24/2002.