Fourier Transform and Its Applications, 2nd Edition (McGraw-Hill electrical and electronic engineering series)
This text is designed for use in a senior undergraduate or graduate level course in Fourier Transforms. This text differs from many other fourier transform books in its emphasis on applications. Bracewell applies mathematical concepts to the physical world throughout this text, equipping students to think about the world and physics in terms of transforms. The pedagogy in this classic text is excellent. The author has included such tools as the pictorial dictionary of transforms and bibliographic references. In addition, there are many excellent problems throughout this book, which are more than mathematical exercises, often requiring students to think in terms of specific situations or asking for educated opinions. To aid students further, discussions of many of the problems can be found at the end of the book.
Why Read This Book
You should read Bracewell if you want an intuitive, application-driven introduction to Fourier methods that connects the math to real engineering problems such as spectral analysis, imaging, and communications. The book gives you a strong practical toolbox (including a pictorial dictionary of transforms and many worked problems) so you can think in the transform domain with confidence.
Who Will Benefit
Senior undergraduates, graduate students, and practicing engineers working on spectral analysis, radar, communications, audio or imaging who need a clear, applied understanding of Fourier techniques.
Level: Intermediate — Prerequisites: Undergraduate calculus, basic complex numbers and linear systems (Fourier series and basic differential equations recommended).
Key Takeaways
- Explain the theory and key properties of Fourier series and the continuous and discrete Fourier transforms
- Apply convolution, modulation and transform-pair manipulation to solve practical signal and system problems
- Analyze sampling, aliasing, and reconstruction and apply the sampling theorem to real signals
- Compute and interpret spectra for signals encountered in communications, audio, imaging and optics
- Use discrete transforms (DFT) and understand computational considerations related to the FFT
- Apply transform methods to solve linear differential equations and physical/engineering problems
Topics Covered
- Introduction and motivation; review of complex numbers and signals
- Fourier series: basics, convergence and examples
- The continuous Fourier transform: definitions and interpretation
- Properties of the Fourier transform (linearity, scaling, modulation, duality)
- Convolution, correlation and energy spectral concepts
- Sampling, aliasing and the sampling theorem
- The discrete Fourier transform and computational aspects (FFT)
- Spectral analysis and filtering applications
- Transforms in solving differential equations and physical problems
- Optics and imaging: Fourier methods in physical systems
- Communications and modulation examples
- Pictorial dictionary of transforms, tables and problem discussions
How It Compares
More applied and intuition-focused than Oppenheim & Willsky's Signals and Systems, and less measure-theoretic than Stein & Shakarchi's Fourier Analysis — ideal when you want engineering applications rather than pure proofs.
