Some Effects of Bandwith‐Duration Constraints on Frequency Discrimination

It has been suggested that at very short durations, frequency spread of the signal is what determines the frequency resolving power of the auditory system. The validity of this notion is examined by applying a version of the “uncertainty principle,” which says that the product of “effective bandwidth” and “effective duration” is a constant that depends on the signal envelope. This bandwidth‐duration constraint permits several different envelopes to be used for the carrier signal in a frequency‐discrimination experiment, while at the same time restricting all the signals to the same nominal bandwidth. Rectangular, exponential, Gaussian, and gamma functions were used as envelope functions for a 1000‐Hz carrier. Parameter values were selected to equate the signal bandwidths to the bandwidth of a rectangular envelope signal, which had a duration ranging from 2 to 32 msec. The frequency‐discrimination data indicate that equating signal bandwidth in this way does not serve to make the signals equally discriminable. A more accurate way to estimate the discriminability for the different envelope sinusoids is to measure how long each signal envelope provides an acceptable signal‐to‐noise ratio.