Introduction to Fourier Transform and Spectral Analysis
What you'll learn
- introduction to fourier analysis of signals, spectral analysis
- college level mathematics and physics
There are hundreds of textbooks that cover the complicated mathematics of the Fourier transform but no materials that explain its most basic principles. After many years working in signal and image processing, I have discovered that simple explanations are often overlooked. This course is targeted towards individuals who may have little experience in the area but have a desire to understand how things work.
This course will provide an introduction to the Fourier transform. The first section is a review of the mathematics core to understanding Fourier integrals. We will review trigonometric functions, derivatives, integrals, and power series – both exponential and complex exponential. The course will not focus on complicated details and will instead concentrate on the basic skills required.
The second section will begin to introduce Integral Fourier transform. We will dive into the properties of Fourier transform as well as their application to engineering and communication challenges. Here, we will cover convolution, cross-correlation, modulation, demodulation, and more.
The goal of the class is to provide fundamental knowledge that can be applied to the analysis of linear systems, filtering, sampling, and some of the more advanced topics in signal processing. The course includes slides, two problem sets, and their solutions in an Adobe Acrobat file.
Discrete Fourier Transform and signal processing examples in Matlab are covered in a separate course "Discrete Fourier Transform and Spectral Analysis (MATLAB)"
Who this course is for:
- Engineering and physics students/professionals with an interest in electrical engineering, mechanical engineering, or the biomedical sciences.
I received a PhD in physics and have spent nearly four decades in the field in both an academic and professional capacity. Some of the areas I’ve worked in include biomedical engineering, image processing, magnetic recording, ultra-high-speed digitizers, as well as communication and signal processing algorithms.
As an educator, I have the opportunity to teach at leading universities including Stanford University, Santa Clara University, the Israel Institute of Technology (Technion), and the Moscow Physical-Technical Institute. My courses aim to instill the most core and essential skills necessary to build a deep and thorough understanding of the topic at hand. I omit unnecessary and complicated details that leave students overwhelmed to clarify what information is actually important.
I currently hold more than 20 US patents, contribute extensively to technical journals, and have published 6 books as well as over 60 scientific papers. I was fortunate to start my career working with Vladimir Kotelnikov, who is considered one of the inventors of sampling theorem and modern signal and communication theory alongside Claude Shannon and Harry Nyquist. For many years I worked within the IBM Research Center. Today, I am a fellow at Western Digital Corporation in California and enjoy teaching in my spare time.