The Intuitive Guide to Fourier Analysis & Spectral Estimation - Hardcover

Charan Langton; Victor Levin

Hardcover

ISBN 10: 0913063266 ISBN 13: 9780913063262

Publisher: Mountcastle Company, 2017

Synopsis

To be released May 2017 - Written in an easy conversational style, this book will deepen your understanding of Fourier analysis making it easier to advance to more complex topics in digital signal processing and data analysis in mathematics, physics, astronomy, bio-sciences, and financial engineering. With numerous examples, detailed explanations, and plots, the difficult concepts become clear and easy to grasp.

Fourier transform developed slowly, from the Fourier series 200 years ago to Fourier transform as implemented by the FFT today. We tell you this story, in words and, of course, equations and help you understand how each step came about.

We start with the development of Fourier series using harmonic sinusoids to represent periodic signals in continuous and discrete-time domains.

From here, we examine the complex exponential to represent the Fourier series basis functions.

Next, we describe the development of the continuous-time and discrete-time Fourier transforms (CTFT, DTFT) for non-periodic signals.

We show how the DTFT is modified to develop the Discrete Fourier Transform (DFT), the most practical type of the Fourier transform.

We look at the properties and limitations of the DFT and its algorithmic cousin, the FFT. We examine the use of Windows to reduce leakage effects due to truncation.

We examine the application of the DFT/FFT to random signals and the role of auto-correlation function in the development of the power spectrum.

Lastly, we discuss methods of spectral power estimation. We focus on non-parametric power estimation of stationary random signals using the Periodogram and the Autopower.

Edition details

• Publisher: Mountcastle Company
• Publication date: 2017
• Language: English
• ISBN 10: 0913063266
• ISBN 13: 9780913063262
• Binding: Hardcover
• Number of pages: 320