Sampling · Digital audio

Sinc interpolation

Each stored sample contributes one sinc pulse that is 1 at its own instant and 0 at every other sample instant, so the sum y(t) = Σ x[n]·sinc(fₛt − n) passes through every sample and, for a wave below fₛ/2, reproduces the original between them.

Builds on Samples per cycle, Nyquist fold. Taught in Waves & Buckets.

Pick a sample rate and a wave frequency, highlight one sample to see its pulse, and watch the faint pulses of all the samples add up to the green curve through the dots. Readouts show that the other pulses sum to zero at the highlighted instant and how far the sum strays from the original; push the wave past half the sample rate and the sum traces a different, slower wave instead.

The claim above is what this widget demonstrates. Disagree with it?

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