Filter Design for Signal Processing Using MATLAB and Mathematica
A complete up-to-date reference for advanced analog and digital IIR filter design rooted in elliptic functions. Revolutionary in approach, this book opens up completely new vistas in basic analog and digital IIR filter design--regardless of the technology. By introducing exceptionally elegant and creative mathematical stratagems (e.g., accurate replacement of Jacobi elliptic functions by functions comprising polynomials, square roots, and logarithms), optimization routines carried out with symbolic analysis by Mathematica, and the advance filter design software of MATLAB, it shows readers how to design many types of filters that cannot be designed using conventional techniques. The filter design algorithms can be directly programed in any language or environment such as Visual BASIC, Visual C, Maple, DERIVE, or MathCAD. Signals; Systems; Transforms; Classical Analog Filter Design; Advanced Analog Filter Design Case Studies; Advanced Analog Filter Design Algorithms; Multi-criteria Optimization of Analog Filter Designs; Classical Digital Filter Design; Advanced Digital Filter Design Case Studies; Advanced Digital Filter Design Algorithms; Multi-criteria Optimization of Digital Filter Designs; Elliptic Functions; Elliptic Rational Function.
Why Read This Book
You will learn a rigorous, elliptic-function–based approach to designing analog and digital IIR filters that can handle specifications conventional techniques struggle with, and you'll see working examples implemented in MATLAB and symbolic routines in Mathematica. The book gives you practical algorithms and approximation tricks (e.g., for Jacobi elliptic functions) so you can implement and optimize advanced filters in real tools.
Who Will Benefit
Engineers or graduate students working on filter design who need advanced IIR/elliptic-filter techniques and practical MATLAB/Mathematica implementations.
Level: Advanced — Prerequisites: Solid undergraduate DSP and signals background (frequency-domain filter theory), calculus and complex variables, and familiarity with MATLAB; basic experience with symbolic math (Mathematica) helps but is not mandatory.
Key Takeaways
- Design elliptic and other advanced IIR filter prototypes using elliptic-function theory
- Transform analog prototypes into stable, high-performance digital filters (bilinear, impulse invariance, etc.)
- Implement and test filter-design algorithms in MATLAB and perform symbolic manipulations with Mathematica
- Approximate Jacobi elliptic functions with rational/polynomial forms useful for practical implementation
- Optimize filter responses to meet tight multi-band or atypical specifications that standard toolboxes can’t handle
Topics Covered
- Introduction and design goals; review of classical filter families
- Mathematical preliminaries: complex analysis and special functions
- Jacobi elliptic functions and elliptic integrals
- Elliptic (Cauer) filters: theory and properties
- Polynomial approximations and rational representations of elliptic functions
- Analog IIR filter synthesis using elliptic prototypes
- Digital IIR design: bilinear transform, impulse invariance, and frequency transformations
- Numerical techniques and stability considerations
- Symbolic analysis and optimization with Mathematica
- Algorithm implementation and examples in MATLAB
- Advanced designs: multiband, equiripple, and customized shapes
- Practical issues: realization, finite-precision effects, and validation
Languages, Platforms & Tools
How It Compares
Compared with Parks & Burrus' classic numerical treatments of digital filter design, Lutovac emphasizes elliptic-function theory and symbolic techniques and provides direct MATLAB/Mathematica implementations; compared to Zverev's practical analog/digital filter texts, this book is more mathematical and specialized.
