## EEC150B – Introduction To Signals And Systems II

4 units – Fall Quarter

Lecture: 3 hours

Discussion: 1 hour

Prerequisite: EEC 150A

Catalog Description:

Characterization and analysis of discrete time systems. Difference equation models. Z-transform analysis methods. Discrete and fast Fourier transforms. Introduction to digital filter design.

Expanded Course Description:

1. Discrete Signals and Systems
1. Discrete signals, system classification
2. Difference equations
3. Impulse response and convolution
4. Frequency response, discrete-time Fourier transform
2. The Z-Transform
1. Definition, region of convergence
2. Properties and examples of the Z-transform
3. The inverse Z-transform
4. The transfer function and stability
5. Solving of difference equations in the Z-domain
3. Sampling of Continuous-time Signals
1. Frequenct domain representation of sampling, aliasing
2. Reconstruction of bandlimited signals by samples interpolation
3. Discrete-time implementation of continuous-time filters
4. Upsampling and downsampling, rate conversion
4. Transform Analysis of Linear Time Invariant Systems
1. Frequency response: magnitude and phase response, group delay
2. Allpass, minimum-phase systems
3. Linear phase filters
5. Digital Filtering Structures
1. Block diagrams and signal flow graphs
2. Direct forms, cascade, parallel forms
3. Transposed form
6. Filter Design
1. IIR filter desgin by impulse invariance and by bilinear transformation
2. Fequency transformation of lowpass IIR filters
3. FIR filter design by windowing
4. Optimal (equiripple) FIR filters
5. Frequency sampling FIR filters (optional)
7. The Discrete and Fast Fourier Transforms
1. The DFT and its properties
2. Circular convolution, relation with linear convolution
3. Overlap and add, overlap and save implementations of long convolutions
4. Decimation in time FFT
5. Decimation in frequency FFT

1. A. Oppenhiem and R. Schafer, Discrete-Time Signal Processing,Prentice-Hall.

Computer Usage:

MATLAB is used to simulate discrete-time systems, to simulate sampling and rate conversion systems, and to design FIR and IIR filters.

Engineering Design Statement:

About 30% of the course focuses on the design of sampling and rate conversion systems, and on the design of IIR and FIR filters. Open-ended computer projects are assigned which require students to design digital filtering systems meeting various engineering specifications.

Relationship to Outcomes:

Students who have successfully completed this course should have achieved:

 Course Outcomes ABET Outcomes An ability to apply knowledge of mathematics, science, and engineering A An ability to design and conduct experiments, as well as to analyze and interpret data B An ability to use the techniques, skills, and modern engineering tools necessary for engineering practice. K

Professional Component: