This book bridges the foundational theory of Fourier analysis with cutting-edge applications in computer vision and artificial intelligence, focusing on frequency-domain methods to enhance and accelerate modern learning systems.

In an era where convolutional neural networks (CNNs) dominate computer vision but face significant computational challenges—especially with large-scale image data—this work presents a timely and innovative alternative. By shifting computations to the Fourier domain, the authors address critical limitations in efficiency and scalability, offering readers a pathway to more intelligent, high-performance vision systems. Starting from harmonic waves and Fourier series, the book systematically progresses toward the Fourier transform, discrete transforms, and the Fast Fourier Transform (FFT). It further covers signal digitization, quantization, and fast convolution algorithms, culminating in the design of Fourier Convolutional Neural Networks (FCNNs). Key topics include spectral representations of images, frequency-based convolution, and practical FFT-based architectures that reduce computational load while preserving accuracy.

Readers will gain both deep theoretical insight and practical methodology for implementing Fourier-based vision systems. The book is suited for graduate students, researchers, and engineers in signal processing, computer vision, and machine learning who seek to leverage frequency-domain techniques to build faster, more scalable AI models. A basic understanding of linear algebra, calculus, and signal processing is recommended.

Arcangelo Distante was a research director at the National Research Council (CNR), where he conducted research in the fields of computer vision, pattern recognition, machine learning, neural computation, robot navigation, and computational models for the real-time analysis of space-time-varying image sequences. He directed the Institute for Studies on Intelligent Systems for Automation (ISSIA) and coordinated the ISSIA Computer Vision and Robotics Group. He taught courses in Image Processing Theory and Techniques at the Faculty of Engineering of the University of Salento. He is the co-author of over 350 scientific publications, including journal articles, chapters in internationally reviewed and published volumes, national and international conference proceedings, and patents. He co-authored the Handbook of Image Processing and Computer Vision: Volume 1: From Energy to Image; 2: From Image to Pattern; 3: From Pattern to Object (Springer Nature, 2020). He published The True History of VAR (Amazon, 2025) and History of a Researcher from Southern VAR (Amazon, 2025)

Cosimo Distante is a Research Director at the National Research Council (CNR), where he serves as the delegated head of the Lecce branch of the Institute of Applied Sciences and Intelligent Systems. His research focuses on Artificial Intelligence, with a particular focus on Computer Vision, Pattern Recognition, image processing, machine learning, and robotics. His academic background combines Computer Science (a Master's degree from the University of Bari in 1997) and Engineering (a PhD in Materials Engineering from the University of Salento in 2001). He has enhanced his international profile as a visiting scholar and lecturer at the Department of Computer Science at the University of Massachusetts (Amherst, USA), where he has dedicated himself to advanced research projects. Since 2003, he has been an adjunct professor at the University of Salento, where he teaches Computer Vision, Pattern Recognition, and Image Processing. He has received prestigious awards, including the "Premio dei Premi" for Innovation, awarded in 2012 by the President of the Senate. He is a Senior Member of the IEEE Signal Processing and Computer Societies. He also plays an active role as an innovation expert for the Ministry of University and Research (MUR), the Ministry of Business and Made in Italy (MIMIT), and regional agencies. He is also a member of the CMCC Foundation (Euro-Mediterranean Center on Climate Change).