📊 Nyquist Sampling (2D)

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📊 Nyquist Sampling (2D) — When Digital Captures Analogue

About this simulation

A continuous signal (the analogue source) is sampled at a rate you control. When the sample rate clears the Nyquist rate (fs ≥ 2f), sinc interpolation reconstructs the original from just its samples. Drop below it and a phantom low-frequency wave appears — aliasing — indistinguishable in the samples from a genuine slow signal.

How it works

• The top panel draws the true continuous signal at frequency f.
• Dots mark each sample taken at the chosen rate fs; stems drop to the axis.
• The bottom panel is the band-limited sinc reconstruction built purely from those samples.
• When fs < 2f the reconstruction collapses onto the aliased frequency f_alias.

Key equations

Nyquist rate: fs ≥ 2·f_max
Nyquist frequency: f_N = fs / 2
Aliased frequency: f_alias = |f − round(f/fs)·fs|
Sinc reconstruction: x(t) = Σ x[n]·sinc((t − n·T)/T), T = 1/fs

Controls

• Signal frequency f — frequency of the analogue source.
• Sample rate fs — how many samples per second are taken.
• Waveform — plain sine, or a two-tone mix (f and 2f) to see how the highest component drives the Nyquist requirement.
• Pause / Play — freeze or resume the animation.
• Reset — restore default frequency, sample rate and waveform.