Welcome to the Sonic Labs Engineering Playground

Welcome to Sonic Labs — the future home of my personal technological, engineering and financial interests.
A place where curiosity is encouraged, ideas become experiments, and engineering understanding takes
precedence over merely obtaining results.

When you encounter a mathematical operation in an equation (think DSP or whatever field), don't merely ask how do I execute it? I'd first look at it ans ask: “What did the mathematician see that made this operation (e.g. multiplication by a rotating phasor) worth doing?”

In the inverse DFT equation, why are bin scores/summations multiplied by a counter-clockwise rotating phasor with bigger and bigger phase strides for each visited bin (what's the counter-rotation actually doing or undoing)?
In FFT, why do samples have to be initially separated into even and odd-indexed sequences - what;s the end game? Enter the exponential-driven extra twiddle common to all odd-indexed samples.

As a new student of EE, I once looked at a live oscilloscope signal trace. It was jumping all over the screen, and fast.
So the young me was like - No way! But what does a Fourier spectrum mean or look like if the signal is itself time varying like this - surely the spectrum must be time varying too.

I quietly backed off, disappointed, feeling I was missing a point somewhere.
Enter wavelets - discovered through a research project we had two years later. They looked like time-aware Fourier spectra.

So I was like - picture a detective saying: "I'm not only interested at knowing who was at the crime scene (frequency components), in addition I wanna know who came and left when (when did those frequencies show up and faded)."

Again - If we have a sinusoidal Morlet wavelet, then What did the mathematician see that made another wavelet basis function worth creating?

Areas of Interest