DFT Math Outline

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

• Complex numbers
• Complex exponents
• Why $e$?
• Euler's identity
• Projecting signals onto signals via the inner product
• The DFT as the coefficient of projection of a signal $x$ 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.