No definitions, no formulas dropped from the sky. You start in front of a single bar — the push of a sound at one instant — and watch a whole signal become a row of them. You feed a box one spike and learn its one law. You discover that any signal is just a row of spikes, so the output is nothing but a stacked copy of the box’s single answer — and only then, once you have built it with your own hands, does it get the name convolution. From there: flip-and-slide, echoes, filters, cascades, and finding a known shape buried in noise. Every chapter follows one rule — silence every word and the picture alone still teaches it. After Smith’s Guide to DSP (ch. 5–7), in the spirit of Petzold’s CODE. Built for someone who has never met a signal; honest enough for an engineer.
A sound pushes a membrane; the push right now is one height. A moment later, another. The whole row of heights is the sound — that is a signal.
Feed a box one bump. Out comes a shape. Twice the bump, twice the shape; move the bump, move the shape. That one shape is everything the box does.
Two voices share one wire out. Could it blend them into a third new voice neither made? Send two bumps through the box and watch what really comes back.
Take a lumpy signal and pull it apart: every reading lifts onto its own row as a single spike. Drop them back, and the signal returns exactly.
A box answers one spike with a shape. Scale the spike, the shape scales; move it, the shape moves; add spikes, the shapes add. Build the whole output from one answer.
Pick one output bar. Only the few inputs near it reached it; the fingerprint sits reversed underneath. Multiply each by the value above it, add the products — that bar. Slide one step; the next falls out the same.
Now you hold the fingerprint. Place one spike and the signal passes untouched. Make it taller, move it later, add a second smaller one — and watch the output answer.
A signal buried in jitter — a slow swell with a fast rattle on top. One shaped kernel averages the rattle away; its complement keeps only the wiggle. Build both from a hump of taps.
Two boxes wired one after the other. Whatever the pair does to a single spike is one fixed shape — so two boxes are one box. Then convolve a lumpy blob with itself, round after round, and watch it settle into a bell.
A radar return: a noisy mess of bars with a known little pulse hidden inside. Slide a copy of the pulse along the return, tally how well it matches at each spot — the tally leaps to a peak where the pulse was hiding.