Fast Fourier Transform - Algorithms and Applications (Signals and Communication Technology)
This book presents an introduction to the principles of the fast Fourier transform. This book covers FFTs, frequency domain filtering, and applications to video and audio signal processing.
As fields like communications, speech and image processing, and related areas are rapidly developing, the FFT as one of essential parts in digital signal processing has been widely used. Thus there is a pressing need from instructors and students for a book dealing with the latest FFT topics.
This book provides thorough and detailed explanation of important or up-to-date FFTs. It also has adopted modern approaches like MATLAB examples and projects for better understanding of diverse FFTs.
Why Read This Book
You will gain a clear, application-focused grounding in FFT theory and practice, learning not just the math but how to apply a variety of FFT algorithms to real problems in audio, video, radar and communications. The book emphasizes practical MATLAB examples and projects so you can prototype, analyze performance trade-offs, and move quickly from concept to working code.
Who Will Benefit
Graduate students, advanced undergraduates, and practicing engineers in signal processing, communications, audio/video and radar who need a practical, hands-on reference for FFT algorithms and frequency-domain methods.
Level: Intermediate — Prerequisites: Basic signals and systems (DTFT/DFT), complex numbers and linear algebra, and familiarity with programming (MATLAB recommended).
Key Takeaways
- Implement classic and modern FFT algorithms (radix-2 DIT/DIF, mixed-radix, prime-factor, real/complex optimizations).
- Apply FFTs for efficient convolution, correlation, and frequency-domain filtering including block methods (overlap-add/overlap-save).
- Analyze spectra using windowing and spectral-estimation techniques and interpret results for audio, speech and radar signals.
- Design and prototype FFT-based systems (audio processing, OFDM communications blocks, image/video transforms) using MATLAB projects.
- Choose and optimize FFT algorithms for length, numerical precision and computational resource constraints.
- Extend FFT techniques to multidimensional transforms and specialized variants (chirp-z, DCT/MDCT links) used in compression and filtering.
Topics Covered
- 1. Introduction: DFT, motivation for fast algorithms, applications overview
- 2. Mathematical Foundations and Notation for FFTs
- 3. Radix-2 FFT Algorithms: Decimation-in-Time and Decimation-in-Frequency
- 4. Mixed-Radix, Split-Radix and Prime-Factor Algorithms
- 5. Real-Input, Real-Output and Trigonometric Transforms (DCT/DST/MDCT)
- 6. FFT Implementation Issues: Memory, Complexity, and Fixed-Point Considerations
- 7. Non-Power-of-Two Lengths, Chirp-Z and Other Specialized Transforms
- 8. Multidimensional FFTs and Separable Implementations (images and video)
- 9. Frequency-Domain Filtering and Fast Convolution (overlap-add/overlap-save)
- 10. Spectral Analysis, Windowing and Statistical Considerations
- 11. Applications: Audio and Speech Processing
- 12. Applications: Image and Video Processing
- 13. Applications: Radar and Communications (including OFDM examples)
- 14. MATLAB Examples and Project Exercises
- Appendices: Mathematical tables, algorithm summaries, and implementation hints
Languages, Platforms & Tools
How It Compares
Covers similar ground to Brigham's The Fast Fourier Transform and Its Applications but with more applied MATLAB projects and modern application examples; broader FFT application focus than the DSP-theory-heavy Discrete-Time Signal Processing by Oppenheim & Schafer.
