## DFT Math Outline

In summary, understanding the DFT takes us through the following topics:

- Complex numbers
- Complex exponents
- Why ?
- Euler's identity
- Projecting signals onto signals via the inner product
- The DFT as the coefficient of projection of a signal onto a sinusoid
- The IDFT as a sum of projections onto sinusoids
- Various Fourier theorems
- Elementary time-frequency pairs
- Practical spectrum analysis in matlab

We will additionally discuss various practical aspects of working with signals and spectra.

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Factoring a Polynomial

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Mathematics of the DFT