An introduction to Discrete Fast Fourier Transform aimed at those who would like to understand the concept and the mechanics behind the transform and the algorithm.
To compile the LaTeX source code you can use either texlive (Linux) or MiKTeX (Windows).
- Complex Numbers
- Imaginary Roots
- Complex Numbers
- Complex plane and complex conjugate
- Vector, Banach, Hilbert spaces
- Vector addition
- Vector subtraction
- Scalar multiplication
- Linear vector space
- Banach space
- Hilbert space
- Vector space basis
- Orthogonality and projection
- Changing coordinates
- Euler’s identity
- Exponentials
- Euler’s number
- Taylor series
- Derivative
- Sinusoids
- Complex sinusoids
- Sampled complex sinusoids
- Roots of unity & sinusoids
- The Discrete Fourier Transform
- The Fast Fourier Transform
- Notes
- References