Intuitive Guide to Fourier Transform and the Spectrum

This book helps a practitioner develop an intuitive understanding of the Fourier transform and its application to data analysis. The authors start with the Fourier series and progress step-by-step from CTFT, DTFT, discrete Fourier transform (DFT) to the Fast Fourier Transform (FFT). Each equation is accompanied by a detailed explanation and graphs. The book also covers the application of the Fourier transform to random signals and how to assess their spectral distribution. Spectrum analysis using both the Parseval's and the Wiener-Khintchine-Einstein theorems of power estimation are discussed. Periodogram and Autopower, the two most common methods of doing non-parametric spectral analysis, are discussed and guidelines are given for creating low-variance, low-bias spectrum using windows and ACF truncation. The book includes numerous examples, detailed explanations and plots, making difficult concepts clear and easy to grasp.