ECE 4413/6413

Digital Signal Processing

CATALOG DATA: ECE 4413/6413 Digital Signal Processing. (3)

(Prerequisite: Grade of C or better in ECE 3163).

Three hours lecture. Discrete-time signals, Z-Transform, Discrete Fourier Transform, digital filter design including IIR, FIR, and FFT synthesis.

PREREQUISITES BY TOPIC:

1. System Modeling and Block Diagrams
2. Introductory Fourier Transforms
3. Introductory Z Transforms
4. Sampling

TEXTBOOK(S) AND OTHER REQUIRED MATERIAL:

1. Sophocles J. Orfanidis, Introduction to Signal Processing, Prentice-Hall, 1996.

GENERAL COURSE OBJECTIVES AND RELATIONSHIP TO PROGRAM OBJECTIVES:

1. To further develop students’ understanding of Fourier transforms and their ability to use Fourier transforms in digital signal processing applications [1,2].
2. To develop students’ understanding of analog-to-digital and digital-to-analog conversions: sampling, quantization, and reconstruction [1].
3. To develop students’ ability to design and implement FIR and IIR digital filters [1,2].
4. To develop students’ ability to deal with infinitely long signals and real-time processing [1,2].

TOPICS COVERED:

1. Syllabus, Tests, Reviewing Test Solutions, etc (5 classes)
2. Review of Fourier Transforms (3 classes)
3. Review of Digital System Properties (1 classes)
4. Sampling (Nyquist Theory, Folding, Aliasing, Reconstruction) (4 classes)
5. Quantization (2 classes)
6. Convolution (Graphical, Table, Overlap-Add, FIR filtering) (3 classes)
7. Correlation (Cross, Auto) (2 classes)
8. Review of Z-transforms (2 classes)
9. Transfer Functions and Digital Filter Realizations (Direct, Parallel, Canonical, Transpose) (3 classes)
10. FIR & IIR Filter Design - Pole Zero Placement (3 classes)
11. Windowing and Physical Frequency Resolution (Rectangular, Hamming, Hanning) (3 classes)
12. DTFT, DFT, IDFT (direct formula, matrix) (3 classes)
13. DFT and Computational Frequency Resolution (2 classes)
14. Alternative Transforms (DCT, Hadamard, Haar, Wavelet) (1 classes)
15. FFT Algorithms and Fast Convolution (3 classes)
16. FIR Filter Design – Windowing (Ideal, Rectangular, Hamming, Kaiser) (5 classes)

CONTRIBUTIONS TO PROFESSIONAL COMPONENT:

1. Engineering Topics : 2 hours
2. Engineering Design : 1 hours
3. Math and Basic Science : 0 hours

ASSESSMENT:

1. Homework (handwritten problems)
2. Homework (Matlab assignments)
3. Tests
4. Comprehensive Exam

SPECIFIC COURSE OBJECTIVES AND RELATIONSHIP TO MEASURABLE OUTCOMES:

Objective 1:

• Demonstrate ability to use common Fourier transform pairs and properties to determine Fourier transforms of relatively complicated signals and to prove basic DSP theories, such as Nyquist theory, physical frequency resolution theory, etc. (1,5)
• Demonstrate ability to sketch Fourier transforms of practical signals, both before and after sampling. (1,2)
• Demonstrate ability to compute discrete-time Fourier transforms (DTFT) and discrete Fourier transforms (DFT). (1)
• Demonstrate ability to determine which DFT coefficients correspond with specific frequency components of a signal. (1,2,4)
• Demonstrate ability to utilize DFT’s to conduct “fast convolution”. (1,2,4,5)
• Demonstrate ability to compute computational complexities of direct convolution, fast convolution, DFT’s, and radix-2 FFT’s. (1,5)

Objective 2:

• Demonstrate ability to determine appropriate sampling rates for practical signals. (1)
• Demonstrate ability to sketch Fourier transforms of practical signals, both before and after sampling. (1)
• Demonstrate ability to determine appropriate quantization rates for practical signals. (1)
• Demonstrate ability to utilize simple probability density functions to model quantization error. (1,2,4,5)
• Demonstrate ability to model ideal and practical reconstructors. (1,2)

Objective 3:

• Demonstrate ability to analyze pole-zero plots to determine FIR and IIR filter frequency responses, impulse responses, and time delays. (1,2,5)
• Demonstrate ability to design simple lowpass, highpass, bandpass, bandstop, and notch filters (FIR and IIR) using pole-zero placement. (1,5)
• Demonstrate ability to design simple lowpass and highpass FIR filters using windowing methods (rectangular, Hamming, and Kaiser). (1,2)
• Demonstrate ability to implement FIR and IIR filters via block diagram realizations (direct, parallel, canonical, and transpose forms), with ability to relate the block diagrams to both customized hardware and customized software. (1,5)
• Demonstrate ability to utilize DFT’s to conduct “fast convolution”. (1,2)

Objective 4:

• Demonstrate ability to distinguish between physical and computational frequency resolution. (1,2,4)
• Demonstrate ability to design signal windowing systems, accounting for both window type (Rectangular, Hamming, etc) and window length. (1,2,5)
• Demonstrate ability to determine appropriate DFT orders for signal spectral analysis. (1,2,5)
• Demonstrate ability to implement overlap-add convolution. (1)

PREPARED BY:

Dr. Lori Mann Bruce, Associate Professor, Department of Electrical and Computer Engineering, 2004.