In Search of the Fourth Wave
When I was working on Think DSP, I encountered a small mystery. As you might know:
- A sawtooth wave contains harmonics at integer multiples of the fundamental frequency, and their amplitudes drop off in proportion to 1/f.
- A square wave contains only odd multiples of the fundamental, but they also drop off like 1/f.
- A triangle wave also contains only odd multiples, but they drop off like 1/f².
This pattern suggests that there is a fourth simple waveform that contains all integer multiples (like a sawtooth) and drops off like 1/f² (like a triangle wave). Do you know what it is?
In this talk, I'll suggest three ways we can solve this mystery and show how to compute each of them using Python, NumPy, and SciPy. This talk is appropriate for beginners in both DSP and Python.