EECE 3464: Linear Systems

Develops the basic theory of continuous and discrete systems, with emphasis on linear time-invariant
systems. Discusses the representation of signals and systems in both the time and frequency domain.
Topics include linearity, time-invariance, causality, stability, convolution, system interconnection, and
sinusoidal response. The Fourier and Laplace transforms are developed for the discussion of frequencydomain
applications. Sampling and quantization of continuous waveforms (A/D and D/A conversion) are
analyzed, leading to the discussion of discrete-time FIR and IIR systems, recursive analysis, and
realization. The Z-transform and the discrete-time Fourier transform are developed, and applied to the
analysis of discrete-time signals and systems.

Prerequisites: EECE 2410, MATH 2341
Credit hours: 4 SH
Textbooks:
Signals and Systems using MATLAB, by L.F. Chapparo, Academic Press, New York, 2010
Signals and Systems 2nd Edition, by A. Oppenheim, and A. Willsky with S. Nawab. Prentice Hall, 1997
Schaum’s Outline of Signals and Systems 2nd Edition, by Hwei Hsu, McGraw-Hill, 2010

Topics Covered:
1. Basic signals and systems
   a. Continuous and discrete time signals
   b. Signal manipulation
   c. Basic system properties
2. Linear time invariant (LTI) systems
   a. Discrete time convolution
   b. Continuous time convolution
   c. Relationship of generic system properties to the impulse response for an LTI system
   d. Use of differential and difference equations as models for LTI systems
3. Continuous time Fourier transform (CTFT)
   a. Definition and derivation of the CTFT
   b. Fourier transform representation of periodic signals using the CTFT
   c. Properties of the CTFT
   d. Convolution-multiplication duality and the CTFT
4. Discrete time Fourier transform (DTFT)
   a. Definition and derivation of the DTFT
   b. Fourier transform representation of periodic signals using the DTFT
   c. Properties of the DTFT
   d. Convolution-multiplication duality and the DTFT
5. Sampling
   a. Derivation and application of the Sampling Theorem for bandlimited signals
   b. Derivation and application of bandlimited (sinc) interpolation
   c. Aliasing
6. The Laplace transform
   a. Definition and relationship of Laplace transform to CTFT
   b. Region of convergence
   c. Inverse Laplace transform via partial fraction expansion method
   d. Geometry evaluation of the CTFT via the pole zero plot.
   e. Properties of the Laplace transform
   f. Relationship of causality and stability to structure in the Laplace s plane
7. Z transform
   a. Derivation of Z transform from Laplace assuming ideal, delta function sampling
   b. Relationship of Z transform to DTFT
   c. Region of convergence
   d. Inverse Z transform via partial fraction expansion method
   e. Geometry evaluation of the DTFT via the pole zero plot.
   f. Properties of the Z transform
   g. Relationship of causality and stability to structure in the Z transform z plane

Course Outcomes:
Students should:
1. Demonstrate the ability to recognize, analyze, and manipulate basic continuous time (CT) and
discrete time (DT) signals and to classify continuous and discrete time systems as to their linearity,
time invariance, causality, and stability.
2. Analyze both continuous and discrete linear time invariant (LTI) systems in the time domain
including leveraging the use of the impulse response, setting up and carrying out convolution
integrals and sums, using mathematical properties of the convolution operator to manipulate,
combine, and decompose systems and sub-systems, determine stability and causality from the
impulse response, and use linear constant coefficient differential / difference equations (LCCDEs) as
models for LTI systems.
3. Analyze both CT and DT LTI signals and systems in the frequency domain by using the appropriate
Fourier representation, including calculation of forward and inverse Fourier representation,
determining outputs using the frequency response, characterizing systems based on their frequency
response characteristics, and applying relevant properties of these representations.
4. Apply the Shannon sampling theorem and the sinc interpolation formula and quantify the effects of
aliasing.
5. Analyze CT and DT systems using the bilateral Laplace and Z transforms, including calculating
regions of convergence (ROCs) and interpreting the implications of those regions for the forms of
time domain behavior, determining specific time signals from their transform and ROCs using partial
fraction expansion, relating LCCDEs to the corresponding transform and vice-versa, determining
causality and stability from ROCs, and interpreting the relationship between pole / zero locations and
system frequency response.
Contribution of course to meeting