Spectrographic analysis of animal vocalizations: implications of the "uncertainty principle"

Many animal vocalizations are non-periodic, frequency-modulated signals. Because this type of signal varies simultaneously in two dimensions, time and frequency, spectrographic measurement is constrained by the "uncertainty principle": to increase accuracy of measurement in one dimension we must sacrifice accuracy of measurement in the other dimension. Although this trade-off is unavoidable, inherent in the measurement of frequency, for any particular frequency-modulated, non-periodic signal, there is an intermediate, optimal setting of spectrographic bandwidth, equal to the square root of the average rate of change of the measured signal. This optimal bandwidth minimizes the time-frequency smear, and thus permits the most accurate measurement of the instantaneous frequency. Investigators analyzing the microstructure of animal vocal signals therefore should choose their analyzer bandwidths to match the signals under study.