Fast Algorithms for Signal Processing
Efficient signal processing algorithms are important for embedded and power-limited applications since, by reducing the number of computations, power consumption can be reduced significantly. Similarly, efficient algorithms are also critical to very large scale applications such as video processing and four-dimensional medical imaging. This self-contained guide, the only one of its kind, enables engineers to find the optimum fast algorithm for a specific application. It presents a broad range of computationally-efficient algorithms, describes their structure and implementation, and compares their relative strengths for given problems. All the necessary background mathematics is included and theorems are rigorously proved, so all the information needed to learn and apply the techniques is provided in one convenient guide. With this practical reference, researchers and practitioners in electrical engineering, applied mathematics, and computer science can reduce power dissipation for low-end applications of signal processing, and extend the reach of high-end applications.
Why Read This Book
You will learn how to find and implement the most computationally efficient algorithms for real-world signal processing tasks, reducing computation, power, and latency. The book blends rigorous mathematical foundations with practical algorithm structure and comparisons so you can choose or derive the optimal fast method for audio, radar, communications, imaging, and embedded systems.
Who Will Benefit
Signal-processing engineers, researchers, and advanced graduate students who need to design or select highly efficient algorithms for audio/speech, radar, communications, or large-scale imaging applications.
Level: Advanced — Prerequisites: Solid undergraduate-level linear algebra and calculus, familiarity with basic DSP concepts (DFT, convolution, filtering), and comfort with complex arithmetic and basic probability/statistics.
Key Takeaways
- Derive and implement a range of fast transform algorithms (FFTs, DCTs, DFT variants) and choose the best variant for your constraints
- Design and optimize fast convolution and circular convolution techniques for convolutional filtering and correlation
- Apply algebraic and number-theoretic methods (e.g., NTT, polynomial factorization) to accelerate transforms and convolutions
- Develop efficient multirate, wavelet, and filter-bank implementations suited to embedded and power-limited platforms
- Optimize adaptive filtering and statistical signal-processing routines (LMS/RLS, fast estimation) for low-complexity real-time use
- Evaluate algorithmic trade-offs (operation count, memory, numerical stability, fixed-point effects) for practical implementation
Topics Covered
- 1. Introduction and Motivation: Efficiency in Signal Processing
- 2. Mathematical Foundations: Polynomials, Matrices, and Number Theory
- 3. Circulant Structures, Convolution, and Polynomial Methods
- 4. Fast Fourier Transform Algorithms and Variants
- 5. Discrete Cosine/Sine Transforms and Related Fast Transforms
- 6. Number-Theoretic Transforms and Integer-Based Fast Methods
- 7. Fast Algorithms for Digital Filter Design and Multirate Processing
- 8. Spectral Analysis and Efficient Eigenvalue Techniques
- 9. Wavelets and the Fast Wavelet Transform
- 10. Adaptive Filtering: Fast Implementations of LMS/RLS and Variants
- 11. Fast Statistical Signal Processing: Estimation and Detection
- 12. Applications: Audio/Speech, Radar, and Communications
- 13. Implementation Considerations: Complexity, Memory, and Fixed-Point
- 14. Case Studies and Comparative Performance
Languages, Platforms & Tools
How It Compares
Covers a broader, algebraic and algorithmic toolbox than Brigham's FFT-focused treatments and complements Vetterli & Kovacevic's wavelet/filter-bank emphasis by tying transforms to fast polynomial and number-theoretic methods.
