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.

Presents a comprehensive course on data analysis using Fourier transform, and how to use it with ease

Aides in comprehending the Fourier analysis and its myriad forms, such as DFT, DTFT, CTFT etc

Includes numerous examples, detailed explanations and plots, making difficult concepts clear and easy to grasp

Autorentext

Charan Langton has had a 40-year career in satellite engineering. She was the first women graduate in Aeronautical Engineering California Polytechnic University, San Luis Obispo, CA. She received an MS in Electrical Engineering, from the University of Southern California, Los Angeles. She was designated "Distinguished Engineer" at Maxar prior to retiring, served on Industrial Advisory Board for Aerospace Engineering Department at California Polytechnic University at San Luis Obispo, CA, and was recognized specialist in communication system performance simulation. She has given numerous talks during her career, taught in-house classes in communications engineering at Loral Space Systems, and is the author of numerous papers, tutorials and articles.

Victor Levin is a Senior RF Engineer at Apple Inc. Previously, he worked with a startup, developing low-cost satellite phones. He also developed and won a competition for an early-warning system for campus students. He received his MSEE from the Georgia Institute of Technology and a BSEE from the University of California, Santa Barbara.

Inhalt
Introduction.- Trigonometric Representation of CT Periodic Signals.- Complex Representation of CT Periodic Signals.- Discrete-Time Signals and Fourier Series Representation.- Fourier Transform of aperiodic and periodic signals.- DT Fourier Transform of Aperiodic and Periodic Signals.- Discrete Fourier Transform.- Leakage Mitigation with Windows.- Fourier Analysis of Random Signals.- Power Spectrum of Random Signals.- Conclusion.<p