Spectrum Analysis Tutorial, Part 1: The Discrete Fourier Transform
David A. Jaffe · Computer Music Journal · 1987
This tutorial is an outgrowth of a course in signal processing given by Julius O. Smith at Stanford University in the fall of 1984 (see Smith 1981, as well). It provides an elementary mathematical introduction to spectrum analysis. This is the first of two parts. In part one, the discrete Fourier transform is introduced and analyzed in depth. In part two, some fundamental spectrum analysis theorems and applications are discussed. The only mathematical background assumed is high school trigonometry, algebra, and geometry. No calculus is required. Familiarity with summation formulae, complex numbers, and vectors is helpful, although not essential.