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The Fourier Transform: A Tutorial Introduction
The Fourier transform is a fundamental tool in the physical sciences, with applications in communications theory, electronics, engineering, biophysics and quantum mechanics. In this brief book, the essential mathematics required to understand and apply Fourier analysis is explained. The tutorial style of writing, combined with over 60 diagrams, offers a visually intuitive and rigorous account of Fourier methods. Hands-on experience is provided in the form of simple examples, written in Python and Matlab computer code. Supported by a comprehensive Glossary and an annotated list of Further Readings, this represents an ideal introduction to the Fourier transform.
104 pages, Hardcover
Published May 1, 2021
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About the author
James V. Stone
21 books34 followersHonorary Associate Professor, University of Sheffield, England.
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July 22, 2023
I think the book is living proof that maths can be one's hobby. I meant that this was the first time I read a math book non-stop as if it were a novel. I digest, I follow the mathematical derivation, and all the pieces come together. It clicked, and I felt very happy as if I were the one who discovered it. It's all thanks to the author's excellent writing and intuitive explanation. Perhaps, the analysis is secondary-school-level in essence, hence the French Academy of Science reluctantly awarded Fourier his price. Nonetheless, its role in scientific development is undeniable and it's pleasant to grasp the intuition behind it.
The book is divided into eight chapters. Chapters 1 to 4 build up the groundwork and arrive at the equation to compute Fourier coefficients. I understand this bottom-up approach makes sense, but it took me three times to review and connect things with the Python code at the end to arrive at the algorithm myself. I think a chapter 4B with the algorithm laid bare could be a good add-on. Chapter 5-6 expands to the realm of complex numbers with the same proof. Chapter 7 is a nice cherry on top, discussing the implied properties of the Fourier transform. I particularly like the discussion of the Nyquist-Shannon sampling theorem (why when you open an audio file, the highest frequency is always 20kHz?), localization of signal in time and its corresponding amplitude spectrum, and how many components that the Fourier transform produces in practice. Chapter 8 is supposed to be the most exciting, yet I admit I could not follow all the arguments and technical domains it mentions, especially the transformation of 2D images.
That said, this is the best book I've read from James V Stone and I'm looking forward to his next one.
The book is divided into eight chapters. Chapters 1 to 4 build up the groundwork and arrive at the equation to compute Fourier coefficients. I understand this bottom-up approach makes sense, but it took me three times to review and connect things with the Python code at the end to arrive at the algorithm myself. I think a chapter 4B with the algorithm laid bare could be a good add-on. Chapter 5-6 expands to the realm of complex numbers with the same proof. Chapter 7 is a nice cherry on top, discussing the implied properties of the Fourier transform. I particularly like the discussion of the Nyquist-Shannon sampling theorem (why when you open an audio file, the highest frequency is always 20kHz?), localization of signal in time and its corresponding amplitude spectrum, and how many components that the Fourier transform produces in practice. Chapter 8 is supposed to be the most exciting, yet I admit I could not follow all the arguments and technical domains it mentions, especially the transformation of 2D images.
That said, this is the best book I've read from James V Stone and I'm looking forward to his next one.
Displaying 1 of 1 review