### 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

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