Correlation · Fourier analysis

Spectrum by sweep

Correlating a mixture of whole-cycle sinusoids against a sine template at frequency k returns A/2 when k matches a component of amplitude A and exactly zero otherwise, so sweeping k recovers every amplitude.

Taught in Sines & Spectra.

A fixed mixture of 0.80, 0.50 and 0.30 at 4, 11 and 17 cycles per window is correlated against one template frequency at a time. Sweep k by hand or run all 24; each bar is twice the correlation, and the bars reach the true amplitudes only at 4, 11 and 17.

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