Spectra of signals of short time duration may be obtained from either long or short samples.Long samples result in more accurate power-density spectra, but most of the spectrum power will be contributed by noise. Spectra from short samples are significantly altered by truncation effects. A process is described which makes use of the advantages of both methods. Truncation effects are reduced by "hanning" in the frequency domain. The average spectrum of noise immediately preceding the signal is subtracted from all spectra. A moving-window process allows investigation of signal spectra as a function of time. Examples of the same earthquake signal recorded on several types of instruments illustrate the broad, total spectral content of P waves.