The Hartley Transform (Oxford Engineering Science Series)
The author describes the fast algorithm he discovered for spectral analysis and indeed any purpose to which Fourier Transforms and the Fast Fourier Transform are normally applied.
Why Read This Book
You should read this if you want a focused, mathematically rigorous treatment of the Hartley transform and the fast algorithm Bracewell discovered, with direct relevance to real‑valued spectral analysis and practical DSP tasks. You will learn how the Hartley transform offers efficient, real‑only alternatives to complex FFTs and where that efficiency pays off in audio, radar, and communications work.
Who Will Benefit
Engineers and researchers with a solid mathematical background who work in DSP, audio/speech, radar or communications and want an efficient, real‑valued transform alternative to the FFT.
Level: Advanced — Prerequisites: Undergraduate calculus and linear algebra, familiarity with complex numbers and the Fourier transform, and basic signals-and-systems or DSP concepts (sampling, convolution, spectral analysis).
Key Takeaways
- Understand the definition and core properties of the Hartley transform (continuous and discrete).
- Implement the Fast Hartley Transform (FHT) and analyze its computational complexity relative to FFTs.
- Apply the Hartley transform to real‑valued spectral analysis tasks in audio, radar, and communications.
- Derive and use convolution, modulation, and sampling theorems in the Hartley domain.
- Extend the Hartley framework to multidimensional transforms and practical signal‑processing workflows.
Topics Covered
- Introduction and historical background
- Definition and elementary properties of the Hartley transform
- Relationship between Hartley and Fourier transforms
- The continuous Hartley transform and inversion
- The discrete Hartley transform (DHT)
- The Fast Hartley Transform (FHT) algorithm and derivation
- Convolution, modulation, and sampling in the Hartley domain
- Multidimensional Hartley transforms and separability
- Numerical and implementation issues (real‑valued efficiency, stability)
- Applications: spectral analysis, audio and speech processing, radar and communications
- Comparisons with FFT‑based approaches and practical considerations
- Appendices and mathematical proofs
How It Compares
Similar in spirit to Bracewell's own The Fourier Transform and Its Applications and complementary to Oppenheim & Schafer's Discrete‑Time Signal Processing, but this book zeroes in on the Hartley transform and the Fast Hartley algorithm with a bias toward real‑valued implementations.
