Introduction to Fourier Transform and Spectral Analysis

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)"