In Search of The Fourth Wave
Last year I participated in the first DSP Related online conference, where I presented a short talk called "In Search of The Fourth Wave". It's based on a small mystery I encountered when I was working on Think DSP. 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 the talk, I suggest four ways to solve this mystery, and in the Q&A, one of the attendees suggests a fifth.
You can watch the talk here:
And you can run the Jupyter notebook on Colab by clicking here.
Which was the suggested 5th method?
Convolving a square wave with itself.
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