Explain DFT bar height with a test-wave multiply table

A student kept reading DFT bar height as signal amplitude because sampling had taught them that samples are amplitudes. An 8-point table of signal, test wave, and their product fixed the model: a matching wave gives all nonnegative products summing to A*N/2, and a non-matching one cancels to 0. It works with real numbers only, so no complex exponentials are needed. For a zero-phase cosine on a bin, the real test wave gives the exact height, and the per-sample products average A/2 rather than each equaling it. Terminal users may also want ASCII graphs inline rather than opened PNGs.