The Intuitive Guide to Fourier Analysis & Spectral Estimation

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 random signal. There is a 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.

This book presents the topic of spectrum analysis from a practical perspective. With its readable language, and loads of examples, it tells the full story of Fourier transform that your university professors didn't have time to tell.

If you want to know the meaning behind all the Fourier transform equations, this is the book for you. -- Richard Lyons, Author of the best-selling book, Understand Digital Signal Processing.

The book is in second printing. some typos/errors etc. from the first printing have been corrected, both in the Kindle and hard cover. If you would like to exchange your 2017 first printing copy for the newer version of the book, please contact the author at her website at complextoreal.

The author has been writing communications engineering tutorials for over 20 years. Her web site is one of the premier sites for this topic and is used by universities around the word for supplemental education.