Digital Filters (Dover Civil and Mechanical Engineering)
Digital signals occur in an increasing number of applications: in telephone communications; in radio, television, and stereo sound systems; and in spacecraft transmissions, to name just a few. This introductory text examines digital filtering, the processes of smoothing, predicting, differentiating, integrating, and separating signals, as well as the removal of noise from a signal. The processes bear particular relevance to computer applications, one of the focuses of this book.
Readers will find Hamming's analysis accessible and engaging, in recognition of the fact that many people with the strongest need for an understanding of digital filtering do not have a strong background in mathematics or electrical engineering. Thus, this book assumes only a knowledge of calculus and a smattering of statistics (reviewed in the text). Adopting the simplest, most direct mathematical tools, the author concentrates on linear signal processing; the main exceptions are the examination of round-off effects and a brief mention of Kalman filters.
This updated edition includes more material on the z-transform as well as additional examples and exercises for further reinforcement of each chapter's content. The result is an accessible, highly useful resource for the broad range of people working in the field of digital signal processing.
Why Read This Book
You should read this book if you want a clear, intuitive grounding in digital filtering without wading through heavy formalism — Hamming emphasizes practical ideas such as smoothing, prediction, differentiation, and noise removal and shows how to implement them on computers. The writing is compact and conversational, so you will gain useful engineering insight and design intuition that complements more formal DSP texts.
Who Will Benefit
Practicing engineers and students with basic calculus who need a practical, conceptual introduction to digital filtering for applications in communications, audio, or instrumentation.
Level: Intermediate — Prerequisites: Single-variable calculus and basic algebra; a familiarity with complex numbers and basic signals/systems concepts is helpful but not strictly required.
Key Takeaways
- Design and implement simple FIR and recursive (IIR) digital filters as difference equations for smoothing and prediction tasks
- Analyze filter behavior using frequency response and basic z-domain concepts to assess stability and transient response
- Apply digital filtering techniques to noise reduction and signal separation in practical computer-based applications
- Construct and reason about filters for differentiation and integration of discrete-time signals
- Recognize practical implementation issues (finite precision, quantization, and computational considerations) that affect real-world filters
Topics Covered
- Introduction: What digital filters are and why they matter
- Mathematical preliminaries: sequences, transforms, and notation
- The z-transform and difference equations
- Linear time-invariant discrete systems and impulse/step responses
- FIR filters and moving-average smoothing
- Recursive filters (IIR) and predictive filters
- Frequency response and basic spectral considerations
- Design approaches for smoothing, differentiation, and prediction
- Noise removal and signal separation strategies
- Implementation on digital computers and practical considerations
- Quantization, finite-precision effects, and numerical issues
- Examples and applications in communications and audio
- Appendices: supplementary mathematics and reference material
How It Compares
Less formal and more conversational than Oppenheim & Schafer's Discrete-Time Signal Processing, Hamming's book offers more intuition and fewer proofs; for modern, example-rich tutorials with MATLAB, compare Lyons' Understanding Digital Signal Processing.
