This playground was generated by Claude (Anthropic) for the DSP 101 course materials. Every curve, stem and number on it is computed in your browser: a real radix-2 FFT; a real Butterworth anti-alias filter designed by pre-warped bilinear transform from its analog prototype poles; the exact fold algebra; the exact sinc reconstruction; and the real zero-order-hold staircase with its measured sin(x)/x droop. Nothing here is a plausible-looking curve, and the sound is generated from the same reconstruction the plots draw — so what you hear cannot disagree with what you see.
“Continuous time” is simulated, and that has one honest consequence. The analog side runs on a grid 64 times finer than fs, which is what lets a browser filter and then sample. That grid has its own limit, so a square wave’s harmonics above it are dropped and counted rather than quietly folded — the note under the spectrum says how many. Without that, raising the fundamental would manufacture aliases that have nothing to do with fs, which is the very thing this page exists to explain.
Standard rates quoted for scale only: 8 kHz (telephony), 44.1 kHz (CD audio), 48 kHz (video and studio). The sampling theorem is Nyquist–Shannon; the filter is the Butterworth magnitude-squared form; the wagon-wheel illusion is the same fold formula with a camera as the sampler. All of these are stated in this course’s own lessons — nothing on this page rests on a figure transcribed from a standards document, so unlike the wireless demos it raises no “verify against the source” flag.
Chosen rather than computed, and marked where it matters: the default frequencies and amplitudes, how many terms of the square-wave series to generate, the strobe rate, and the -60 dB floor used to decide when a filtered component has stopped mattering. The square wave itself is a genuine truncated Fourier series, so its harmonics and their aliases are computed — only the number of terms is a choice.
Course demo — linked from the Module 2 lesson decks in both languages; the page itself is English‑only for now. Built for DSP-101 Lessons 2.1, 2.2 and 2.4 and for the lab those lessons declare, “Hear and See Aliasing”. The lesson deck already has the time-domain picture, so the centre of gravity here is the one the course lacks entirely: the replica spectrum. Sampling copies the whole spectrum to every multiple of fs, and aliasing is simply those copies touching. Four things this topic is routinely got wrong, each with its own panel: Nyquist rate is not Nyquist frequency, frequencies fold rather than wrap, an anti-alias filter has a skirt and not a cliff, and a real DAC is not the ideal interpolator the theorem assumes.