Two-Dimensional Digital Filters (Electrical and Computer Engineering)
Presents basic theories, techniques, and procedures used to analyze, design, and implement two-dimensional filters; and surveys a number of applications in image and seismic data processing that demonstrate their use in real-world signal processing. For graduate students in electrical and computer e
Why Read This Book
You should read this book if you need a concentrated, theory-to-practice treatment of two-dimensional digital filtering: it walks through 2-D signal representations, Z-transform and frequency-domain analysis, and concrete design/implementation techniques. You will get worked examples and application notes (image and seismic) that show how 2-D filter concepts are applied in real signal-processing problems.
Who Will Benefit
Graduate students, DSP engineers, and researchers working on image, seismic or other 2-D signal problems who need solid theory and practical design methods for 2-D FIR/IIR filters.
Level: Advanced — Prerequisites: Undergraduate signals & systems (continuous/discrete-time), 1-D DSP concepts (z-transform, DFT/FFT, filter design), linear algebra, and comfort with complex-variable frequency analysis; MATLAB familiarity recommended for implementations.
Key Takeaways
- Formulate two-dimensional signals and systems using the 2-D z-transform and 2-D frequency response concepts.
- Analyze 2-D filter stability and frequency behavior, including regions of convergence for multidimensional rational systems.
- Design separable and nonseparable 2-D FIR filters using windowing, spectral factorization and transformation techniques.
- Design and evaluate 2-D recursive (IIR) filter structures and understand the specific stability issues they introduce.
- Implement 2-D filters using practical structures (row-column, cascade, lattice) and leverage 2-D FFTs for efficient processing.
- Apply 2-D filtering methods to real problems such as image enhancement and seismic data processing, with worked examples.
Topics Covered
- Introduction and motivation: applications of 2-D filters
- Two-dimensional signals and sampling
- The 2-D z-transform and regions of convergence
- 2-D frequency-domain analysis and the 2-D DFT/FFT
- Design of separable 2-D FIR filters (windowing, separable methods)
- Design of nonseparable 2-D FIR filters (spectral factorization, optimization)
- Two-dimensional IIR filters and stability considerations
- Implementation structures: row-column, cascade, lattice and transposed forms
- Fast algorithms and implementation using 2-D FFTs
- Design examples and case studies (image & seismic)
- Practical issues: quantization, numerical stability, and computational cost
- Appendices: mathematical background and references
Languages, Platforms & Tools
How It Compares
More narrowly focused on 2-D filter theory than Gonzalez & Woods' Digital Image Processing (which is broader and more application-oriented); it overlaps with Dudgeon & Mersereau's Multidimensional Digital Signal Processing but Lu emphasizes practical design/implementation examples for image and seismic problems.
