As Easy As (Circles of) Pi: A Love Story in Frequencies - IMRAN®
My fascination with Fourier—and Laplace—transforms began back in the early '80s during my Electrical Engineering days at UET Lahore. These mathematical tools break down any complex signal into a sum of sine and cosine waves, each with its own frequency. It’s a beautiful trick that makes even the most daunting waveforms easier to work with.
The idea goes all the way back to the early 1800s, when Joseph Fourier suggested that even the most intricate patterns—like shifting tides or rustling winds—could be formed from simple, repeating waves. It was revolutionary.
Think of those Spirograph toys we used as kids: plastic gears spinning around to create intricate patterns. Now imagine those circles representing different frequencies, combining and rotating in sync to draw something as elegant as the Pi symbol. Complexity, unspooled into rhythm and rotation—with a touch of childhood wonder.
This image is a collage of four screenshots to illustrate the idea. The short reels/videos I linked in comments below bring it to life in a magical way that feels both modern and nostalgic.
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