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 should read this book if you want a compact, practical introduction to designing and using digital filters without getting lost in heavy math. It gives straightforward formulas, implementation advice and worked examples so you can move quickly from filter specs to real-time implementations.
Who Will Benefit
Embedded and FPGA engineers, signal-processing practitioners, and students who need practical, implementable digital-filter designs for real-time systems.
Level: Intermediate — Prerequisites: Basic signals-and-systems concepts (sampling, frequency response), comfort with algebra and complex numbers; familiarity with a programming language (C or MATLAB/Octave) is helpful but not required.
Key Takeaways
- Design common IIR filters (Butterworth, Chebyshev, Bessel, Linkwitz-Riley) from specifications with simple formulas.
- Design practical FIR filters and understand trade-offs between order, transition width, and ripple.
- Implement stable filter structures (direct forms, biquads, cascaded sections) suitable for fixed-point hardware.
- Analyze and mitigate quantization, coefficient rounding, and finite-word-length effects in real-time implementations.
- Apply standard transform techniques (bilinear transform, impulse invariance) to convert analog prototypes to digital filters.
- Adapt filter designs for real-world tasks such as anti-aliasing, audio conditioning, decimation/interpolation, and noise reduction.
Topics Covered
- Introduction and motivation — where filters are used
- Basic discrete-time signals and frequency concepts
- FIR filters: fundamentals and windowed designs
- IIR filter types: Butterworth, Chebyshev, Bessel, Linkwitz–Riley
- Analog prototypes and transforms to digital (bilinear, impulse invariance)
- Filter structures: direct forms, transposed, cascaded biquads
- Fixed-point considerations and finite-word-length effects
- Design recipes and worked numerical examples
- Cascading, shelving, and practical filter topologies
- Multi-rate basics: decimation and interpolation
- Implementation tips for real-time and embedded systems
- Appendices: tables, reference formulas, and design shortcuts
Languages, Platforms & Tools
How It Compares
More hands-on and accessible than Oppenheim & Schafer's Discrete-Time Signal Processing and closer in practical spirit to Smith's The Scientist and Engineer's Guide to DSP, but with a stronger focus on ready-to-use filter formulas and implementation issues.
