Amplitude bias in the Fourier transforms of noisy signals

Fourier transforms are often useful in characterizing measured transient signals. It is shown that the amplitudes of such transforms are overestimated in the presence of normal zero-mean random noise. This bias is shown to be significant (greater than 5 percent) for signals with signal-to-noise ratios less than approximately 2.5:1. The result is independent of signal waveform.