This sandbox was generated by Claude (Anthropic) for the DSP 101 course materials. Every number and every curve on it is computed in your browser: the reduced rate factor L/M = f_s'/f_s (reduced by gcd), the new sample count N' = round(N·L/M), the anti-alias cutoff f_c = min(f_s, f_s')/2, the resampled series y[m] for each kernel, and the RMS reconstruction error each makes against the true band-limited signal. The resampled dots you see are the reconstruction kernel evaluated at the new sample instants; nothing is sketched.

Resampling by L/M is: upsample by L, lowpass, downsample by M. That lowpass is the interpolation kernel — a rectangle (zero-order hold), a triangle (linear), or the ideal windowed sinc. Move the input and target rates and watch L/M reduce, the sample count change, and the cutoff track the LOWER of the two Nyquist limits. Turn the anti-alias filter off while downsampling and a high tone folds to a lower frequency — the aliasing the filter exists to prevent.

Every relation on this page is a definition the course itself states — the L/M multirate pipeline, N' = round(N·L/M), the cutoff at the lower Nyquist, and ideal reconstruction x(t) = ∑ x[n]·sinc((t−nT)/T). Nothing here rests on a figure transcribed from a standards document, so this page raises no “verify against the source” flag.

Chosen rather than computed, and marked where it matters: the preset signal shapes, the default rates (48000 → 44100, the CD/DAT classic), the default tone frequency, the input length, and the windowed-sinc half-width. The signals are band-limited so that sinc reconstruction is near-exact and the comparison between kernels is fair.