The Superposition Principle, The Fourier Series and Fourier Transform
This tutorial covers the Suerposition Principle, the Fourier Series and the Fourier Transform. The Fourier Transform must be last by necessary order of learning, because it is based on the Fourier Series, which is, in turn, based on the Superposition Principle.
Motivation
In engineering and science the Fourier Transform is used to break down a complex wave form by its frequency components. These components are the building blocks of waves. You can study a wave's components and better understand what gave rise to it, and you can take out and add components in order to alter its nature. One of the uses for it can be to look at sound waves propagating speech to better understand how speech works. You could also remove certain frequencies that are causing noise in order to better see the signal you want to look at, or you could add components to change the nature of a sound. But, Fourier applies to all waves across all medium, so you can apply them to light waves, sound waves, etc.
Road Map
Here are key concepts this tutorial will cover:
-
Superposition Principle
- Fourier Series
- Periodicity
- Fundamental Frequency
- Fundamental Period
- Orthogonality Principle
- Fourier Coefficients
- DC Coefficient
- Sinusoidal Coefficient
- Frequency Domain (aka Frequency Spectrum)
- Non-Periodicity
- Fourier Transform
