DFT Math Outline

GUIDE: Mathematics of the Discrete Fourier Transform (DFT). DFT Math Outline

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DFT Math Outline

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

  1. Complex numbers
  2. Complex exponents
  3. Why $e$?
  4. Euler’s formula
  5. Projecting signals onto signals via the inner product
  6. The DFT as the coefficient of projection of a signal $x$ onto $N$ sinusoids
  7. The IDFT as a weighted sum of the $N$ projections
  8. Various Fourier theorems
  9. Elementary time-frequency pairs
  10. Practical spectrum analysis in Matlab

We will additionally discuss practical aspects of working with sinusoids, such as decibels (dB) and display techniques.

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