The Rich Man’s Square Wave Generator

What you will learn

• Software: python, matplotlib
• Domain: a different way of looking at Fourier series

Do this in python, mainly for the visualization capabilities

Rich man’s square wave generator

• Create a sine wave of a given frequency and amplitude. Plot it for one period
• Create a second sine wave of twice the frequency and half the amplitude as the first. Add the two cycles to the one from the previous step.
• Continue with a third, fourth, … nth sine wave of successively higher frequencies and smaller amplitudes.
• What waveform do we get as we add higher frequency components?

Analysis

• Plot the error between your square wave and a true square wave at each step. Can you bring this down to zero? what is the limit? Can you prove this limit?

Other combinations

• Take odd multiples of frequency and divide the amplitudes by the multiple squared
• Take odd multiples of frequency and divide the amplitudes by the multiple squared