Spectral estimation for transient waveforms

For steady-state waveform analysis, the classical (possibly smoothed) periodogram of the sampled waveform gives one an adequate spectral representation. For transient waveforms of unknown duration in noise, however, the periodogram generally fails in that it is tied to a fixed time interval. As an alternative, a digital computer program which will do time-varying spectral estimation has been developed. Briefly, the program may be described as a digital equivalent of a constant Q-comb filter bank wherein one can vary the frequency range covered and the frequency resolution (i.e., the Q). For a given specified frequency range, as one increases the frequency resolution, the program automatically selects more filters and spaces them so as to cover the specified frequency range; the various contiguous filters are overlapped at the -3 dB points. The instantaneous energy contained in each filter is used to modulate the z axis of a CRT display and hence provide a time-frequency-intensity plot of the time-varying spectrum. Results obtained from the computer program upon real data are given.