Lab
Build the maths yourself
Short lessons that build one idea at a time, like a lecture on a whiteboard, except you can drag the sliders and test every step. Each lesson keeps the key equations on the board as you go.
Harmonics, from scratch
Sines and cosines
A point going round a shaft, traced over time: amplitude, frequency, phase, and why a sine plus a cosine is one shifted sine.
6 steps · interactive · calculator exercise Lesson 2Build a signal from harmonics
Why only whole multiples of running speed fit a repeating signal, and how sines and cosines add up to any shape.
7 steps · interactive · calculator exercise Lesson 3Why the even harmonics vanish
Shift a wave half a turn, flip it, and see why a symmetric wave has exactly zero 2X, 4X, 6X, and what breaks it.
9 steps · interactive · calculator exerciseComing next
Sampling and the FFT
What the FFT actually computes from sampled data, and the two traps: leakage and aliasing.
In progressWavelets for engineers
When a signal changes over time and one spectrum isn't enough.
PlannedEach lesson goes with a post in the harmonics series. The code for every board is plain JavaScript in this site's repository.