Zero-padded DFT: amplitude uses real N, frequency uses padded N

When reading a tone off a zero-padded DFT plot, students reach for one N in both formulas. Amplitude is A = 2|X[k]|/N_real because only real samples add to the sum, while frequency is W = 2 pi k fs/N_padded because k counts along the padded grid. A quick identification check for shuffled plots: every other bin of the padded DFT exactly equals the unpadded DFT, double height means more real data, and lower peaks with vanishing side lobes mean a Hamming window. A window only multiplies samples by values of 1 or less, so it can't raise a peak.