Chapter 5Time vs. Frequency Domain

Every signal has two equally valid descriptions: a wiggle over time, or a list of "how much of each frequency is in here." The Fourier transform is the translator between them. This chapter lets you design a sound directly in the frequency domain and watch its time-domain shape appear.

Time domain — amplitude vs. time

Frequency domain — amplitude vs. frequency (the spectrum)

Click and drag any bar up or down to set that frequency's amplitude directly.

Presets

Reading the two views

The time domain (top) is the view your speaker actually plays — it's the sum of every active bin's sine wave, exactly as in Chapter 2, just with more ingredients. The frequency domain (bottom) is a bar chart: one bar per frequency, its height equal to that frequency's amplitude. Every bar you raise adds one more sine wave into the sum above.

What's actually being summed right now:

The spectrum is nothing but a picture of the coefficients $A_k$ in that sum — one number per frequency, instead of one number per instant in time. Both views contain exactly the same information about the signal; they're just organized differently.

Try this: click "Single tone," then slowly raise the 3rd bin. You're literally recreating the first two terms of the square wave's Fourier series from Chapter 3 — and you can watch the time-domain wave grow its first hint of a flatter top, live.