Lectures on the Fourier Transform & Its Applications by Brad Osgood
Fourier Transform & Its Applications - Table of Contents
1. Fourier Series
2. Fourier Transform
3. Convolution
4. Distributions and Their Fourier Transforms
5. Sampling and Interpolation
6. Discrete Fourier Transform
7. Linear Time-Invariant Systems
8. n-Dimensional Fourier Transform
A. Mathematical Background
What You Will Learn in Fourier Transform & Its Applications
"Lectures on the Fourier Transform and Its Applications" by Brad Osgood is a comprehensive guide to understanding the "Fourier transform" and its practical applications in "signal processing". Based on lecture notes from Stanford’s EE261 course, the book blends rigorous "mathematical theory" with real-world examples, helping students and professionals grasp both the mechanics and the purpose of Fourier methods. It starts with Fourier series, progresses to continuous and discrete transforms, and introduces concepts such as "convolution" and sampling theory, providing a clear foundation for analyzing signals in engineering, physics, and applied mathematics.
The text includes numerous illustrations, examples, and over 200 exercises that encourage hands-on learning and the application of theory to practice. Advanced topics such as multi-dimensional Fourier transforms, generalized functions, and finite and continuous transform relationships are also covered, making it accessible to both advanced undergraduates and beginning graduate students. Practical problems and computational exercises help bridge the gap between theory and real-world signal analysis.
Designed to combine depth with clarity, "Lectures on the Fourier Transform & Its Applications" connects "Fourier theory" to engineering and scientific applications such as imaging, filtering, and system analysis. By integrating theory, computation, and applied examples, it equips readers with the skills to understand, analyze, and manipulate signals efficiently in modern technology and research contexts.
Book Details & Specifications
Title:
Lectures on the Fourier Transform & Its Applications by Brad Osgood
Publisher:
American Mathematical Society
Year:
2007
Pages:
428
Type:
PDF
Language:
English
ISBN-10 #:
1470441918
ISBN-13 #:
978-1470441913
License:
External Educational Resource
Amazon:
Amazon
About the Author: Brad Osgood
The author
Brad Osgood
is an American academic and "professor of electrical engineering" at "Stanford University", where he also teaches applied mathematics and interdisciplinary courses. He earned his Ph.D. in mathematics and works on "signal processing", "complex analysis", and the "mathematics of engineering education". Osgood has authored several textbooks and is known for popular lecture courses that make advanced topics accessible to students from science and engineering backgrounds. His work "Lectures on the Fourier Transform & Its Applications" is based on Stanford’s EE261 course and presents the "mathematical foundations" and practical uses of the "Fourier transform" in signals, systems, and imaging.
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