Confirm DFT peak bins read off a plot by re-synthesizing the signal

When a problem asks for peak k values from a dense |X[k]| stem plot (e.g. N=256, ticks every 10), pixel-measure against two tick labels to get bins/pixel, then confirm by synthesizing the candidate tones (e.g. the nearest musical-note frequencies at the given fs) and checking np.argmax per cluster plus neighbor heights. A tall neighbor stem (leakage, ~half height) right next to a peak is easy to misread as the peak; matching the neighbor height pattern settles it. For on-bin cosines, |X[k0]| = |A|N/2 exactly and sign of A is unrecoverable from magnitude.