Advanced analysis, design, and realization of digital filters. Efficient Discrete Fourier Transform algorithm implementations, finite wordlength arithmetic, fixed point implementation, limit cycles, noise shaping, decimation and interpolation, multi-rate digital filter design, Hilbert transformers, analytic signal generation, basic adaptive filtering.
Why take this course?
Digital filters and other signal processing algorithms have become integral aspects of many applications, for example in wireless communications, medical instrumentation, and various digital video and audio consumer products. Many of our graduates will be directly working in these areas, and need a solid background in the details necessary for efficient and practical implementations.
4624, STAT 4714
A solid background in deterministic digital filter concepts (as in 4624) and an introduction to probabilistic concepts used in the context of system analysis (as in STAT 4714) form the foundation upon which one builds the advanced analysis and design of digital filters and signal processing algorithms.
Major Measurable Learning Objectives
evaluate the effects of finite wordlength arithmetic in DFT algorithms;
evaluate the effects of finite wordlength arithmetic in digital filters;
analyze the existence of limit cycles in digital filters;
design digital filters for analytic signal generation;
design digital filters using interpolation and decimation stages;
design digital filters meeting given specifications;
improve digital filter implementations by the use of noise shaping;
apply basic adaptive filters effectively.
Percentage of Course
1. Efficient DFT implementations
2. Goertzel and Chirp-z transform
3. Hilbert transforms, analytic signal generation
4. Bandpass sampling
5. Sampling, interpolation, and decimation
6. Sigma-Delta conversion and noise shaping
7. Designing digital filters by multi-stage interpolation and decimation
8. Implementation issues:
a. filter structures
b. coefficient quantization and sensitivity
c. finite wordlength arithmetic or signal quantization