Fourier Transforms

Exercise 7.1: Fourier transforms of simple functions

Write Python programs to calculate the coefficients in the discrete Fourier transforms of the following periodic functions sampled at N = 1000 evenly spaced points, and make plots of their amplitudes:

a) A single cycle of a square-wave with amplitude 1
b) The sawtooth wave yn = n
c) The modulated sine wave yn = sin(πn/N) sin(20πn/N)