Digital Filters for Everyone: Third Edition
Performing such functions as noise mitigation and signal conditioning, digital filters are everywhere: in your car, in your TV, in your music player, in your phone, everywhere. But an engineering degree or expensive software is not required to design and analyze them. In fact, whoever you are and whatever your background, this book will help you understand, design, analyze and use digital filters. This book was written to make digital filters more accessible to everyone. Practicing engineers will appreciate its straightforward approach and the simple formulas that readily lend themselves to real-time applications. Others will find that digital filter design and analysis is really not as difficult as they may have thought. For each IIR filter type (Butterworth, Linkwitz-Reilly, Bessel, Chebychev I & II, Variable Q, Allpass, Equalization, Notch and Shelf), the reader will find one equation for each coefficient. Plug in what you know – cutoff frequency, sample rate – and the equations will give you the coefficient values; no expensive software, transforms or complicated manipulations are needed. This approach does have its limitations. Although the book does explain how to create higher orders by combining lower orders, there are no equations for IIR filters larger than fourth order. Several FIR methods (Fourier Series and Frequency Sampling Methods) are included and they do apply to any order. Since elliptical (Cauer) IIR filters and the Remez and Parks-McClellan algorithms for equiripple FIR design require specialized software and do not lend themselves to simple formulas, they are not included. The third edition includes a new chapter on two-dimensional (2D) filters and a new section on software filter implementation. In addition, there are language and formatting changes aimed at making the book clearer and easier to use. As with the first and second editions, the book gives the simplest possible equations for the design of IIR and FIR filters and examples for their use. Nothing from the earlier editions has been omitted.
Why Read This Book
You will get a practical, low-friction path into designing and using digital filters without needing a heavy math background or expensive tools. The book gives ready-to-use formulas, clear design recipes, and real-world examples (audio, speech, radar, and communications) so you can move from concept to implementation quickly.
Who Will Benefit
Practicing engineers, technologists, and technically-minded hobbyists who need to design, analyze, or implement digital filters for audio, communications, radar, or general signal-conditioning tasks.
Level: Intermediate — Prerequisites: Basic algebra, trigonometry, and complex numbers; a familiarity with signals/systems concepts (sampling, frequency) is helpful but not required; basic programming experience (MATLAB/Octave/Python/C) is recommended for implementations.
Key Takeaways
- Design practical FIR and IIR filters using simple, implementable formulas and recipes.
- Select and apply the right IIR prototype (Butterworth, Chebyshev, Bessel, Linkwitz‑Reilly) for your frequency-response and phase requirements.
- Analyze signals with FFT-based spectral tools and apply windowing and filtering to real audio, speech, radar, and communications examples.
- Implement filters in real-time systems, including considerations for fixed-point arithmetic and efficient C implementations.
- Use adaptive filtering concepts for noise cancellation and tracking, and understand when adaptive methods are appropriate.
- Translate analog specifications to digital designs using bilinear transform and impulse-invariance methods.
Topics Covered
- 1. Why Digital Filters? Practical motivations and overview
- 2. Signals, Sampling, and Frequency: intuition and key concepts
- 3. The z‑Transform and Frequency Response: tools you need
- 4. FIR Filters: window methods, frequency sampling, and design recipes
- 5. IIR Filters: Butterworth, Chebyshev, Bessel, and Linkwitz‑Reilly prototypes
- 6. Analog‑to‑Digital Mapping: bilinear transform, impulse invariance, prewarping
- 7. Filter Tradeoffs: stability, phase, group delay, and implementation cost
- 8. Spectral Analysis and the FFT: practical use and pitfalls
- 9. Adaptive Filtering and Noise Cancellation: LMS and variants
- 10. Implementing Filters: fixed‑point issues, efficient algorithms, and C code examples
- 11. Applications: audio & speech processing, radar signal conditioning, and communications
- 12. Design Tables, Quick Reference Formulas, and Worked Examples
- Appendix: Further reading, MATLAB/Octave/Python snippets, and tables
Languages, Platforms & Tools
How It Compares
More applied and design‑recipe focused than Oppenheim & Schafer's Discrete‑Time Signal Processing, and more filter‑centric and formula-driven than Richard Lyons' Understanding Digital Signal Processing.
