Fourier Analysis for Engineers, Data Scientists, AI & Applied Mathematics: From Signals and Images to Machine Learning

Master one of the most powerful mathematical tools ever developed—and discover how it drives modern engineering, data science, artificial intelligence, scientific computing, image processing, wireless communication, and signal analysis.Fourier Analysis for Engineers, Data Scientists, AI & Applied Mathematics provides a practical, intuitive, and application-focused approach to Fourier analysis, helping students and professionals move beyond formulas to develop genuine understanding.Unlike traditional texts that emphasize theory alone, this book combines mathematical rigor with real-world applications, visual explanations, and step-by-step worked examples. Every concept is introduced with intuition first, followed by detailed solutions that build confidence and mastery.Inside this book, you'll learn:The foundations of frequency-domain thinkingFourier series and harmonic decompositionComplex numbers, Euler's formula, and orthogonalityContinuous Fourier transforms and inverse transformsDiscrete Fourier Transform (DFT) and Fast Fourier Transform (FFT)Signal processing and spectral analysisAudio, image, and communication system applicationsFiltering, noise reduction, and compression techniquesFourier methods for differential equations and scientific computingMachine learning applications, Fourier features, and spectral methodsAI, neural operators, and modern computational approachesThis book includes:Hundreds of worked examplesClear visual illustrationsStep-by-step derivationsPractice problems with solutionsEngineering and data science applicationsReal-world case studiesAI and machine learning connectionsWhether you are an engineering student, applied mathematics major, data scientist, machine learning practitioner, researcher, or self-learner, this book provides a comprehensive pathway from fundamental concepts to advanced applications.You will learn not only how Fourier analysis works, but also why it has become one of the most important mathematical tools in modern science and technology. From signal processing and image compression to wireless communications, scientific computing, and artificial intelligence, Fourier methods continue to shape the technologies that power the modern world.If you want to understand how frequencies shape signals, images, physical systems, and AI systems—and learn the mathematics behind some of the most important advances in engineering and data science—this book will give you the foundation and practical insight needed to apply Fourier analysis with confidence.