Intuitive Guide to Fourier Analysis and Spectral Estimation with Matlab_Chapter1-4

Written in conversational style, this book will help you comprehend the Fourier analysis and its myriad forms, such as DFT, DTFT, CTFT etc. as never before. Our goal in this book is to help you develop an intuitive understanding of what is happening when you do a FFT of a discrete random signal. There is a whole long story behind this apparently easy-to-compute yet hard-to-understand concept. We start the story with the Fourier series in its original trigonometric form as imagined by Baron Fourier, and then progress through all its developments with contributions from other notables along the way to the end point, the spectral estimation of random signals using the discrete Fourier transform. In the last two chapters of this book, we cover application of the Fourier analysis to spectral analysis of random signals. The first five chapters set the stage for the DFT. We start with the easy to understand trigonometric form of the Fourier series in Chapter 1, and then its more complex form in Chapter 2. From there, we go to discrete time signals in Chapter 3 which introduce new complexity to the topic. The development of the Fourier transform from the Fourier series, specifically the continuous time Fourier transform (CTFT) is discussed next. We combine the last two chapters to get to the discrete-time Fourier transform (DTFT) in Chapter 5. From here, it is a manageable leap to the DFT, our main quarry in Chapter 6. From there we spend the last three chapters on how the Fourier transform is used in “real life”. Chapter 7 explains how windows can improve the spectrum by mitigating leakage. Chapters 8 and 9 explain spectral estimation of stationary signals, specifically the non-parametric spectral estimation of random signals. Altogether this book should help fill in the details and the big concepts in Fourier analysis and, importantly, how to use them with comfort and ease. This book is suitable for graduate engineering, physics, math and computer science students. If you are a professional in these areas, you may also find this book illuminating and helpful in deepening your understanding of signal processing.