Four experiments were conducted to develop and test a method of determining the frequency-response characteristic of the observer when he listens for single-frequency signals presented against a continuous background of wide-band noise. After observers were trained to detect primary signals of a single frequency, probe signals of various other frequencies were presented infrequently, in lieu of the primary signal. Primary signals and all probe signals were presented with very similar amplitudes that would be expected to render them all equally detectable if presented alone in single-frequency experiments. Estimates of the detectability of the signals of the various frequencies were obtained concurrently in a two-alternative forced-choice procedure. The results from 14 observers were quite similar and show differences in detection as a function of signal frequency when the primary signal was of 1000 or of 1100 Hz. In general, the primary signal was correctly detected 75%–90% of the time while signals with frequencies at approximately 150 to 200 Hz on either side of the primary-signal frequency were detected at the chance level, 50% correct. In as few as three experimental sessions, the observer's frequency-response characteristic was obtained using the probe-signal method.

The method of free response refers to the following listening situation. Against a background of noise, a weak signal is presented several times in a long (2-min) observation interval. The temporal intervals between the presentations of the tones are randomly distributed; consequently, the listener does not know when a tone will occur, and he does not know how many tones will be presented. From one series of observation intervals to the next, the listener is instructed to adopt various criteria and to press the single response-key each time he “hears a tone.” The problem consists in the determination of a procedure that allows the total number of yes responses to be partitioned meaningfully between “hits” and “false alarms.” A model is developed in which the measurable quantity, rate of response, is related to the “hit rate” and to the “false-alarm rate.” Although the criterion adopted by the listener cannot be directly evaluated, the use of a wide range of criteria makes it possible to estimate the detectability ds of the signal. Two experiments are described, and the results support the model.

With the theory of signal detectability as a framework, two psychophysical experiments were conducted in which each observation interval was well defined for the listener. Each interval contained noise, and it either did or did not (p=0.5) contain a signal (1000 cps, 0.5 sec in duration). In separate sessions of the first experiment, either the listener gave a yes-no decision or he responded with a rating (1–4) after each observation interval. Operating characteristics were obtained with E/N0 equal to 15.8. It is clear from the data that the trained listener can perform as well when he adopts the multiple criteria necessary for the rating method as when he adopts the single criterion required by the binary-decision procedure. In the second experiment, only the rating method was used to determine the relation between d′ and E/N0. The resulting function, for d′ ⩽ 3.0, approximates straight line which passes through the origin and which has nearly the same slope as that obtained in other laboratories.

Three experiments were conducted to measure the decrement in performance that results from uncertainty in the time of onset of a signal presented against a continuous background of noise. The fixed-interval observation experiment was employed. A light defined an observation interval for the listener during which the signal, a tone of 1000 cps, either was or was not presented [p(SN)=0.5]. The signal, when presented, started at an instant randomly selected within the observation interval. Thus, the listener was uncertain as to (1) whether or not the signal would occur in the observation interval, and (2) the onset time of the signal, if in fact the signal occurred. The interval of time uncertainty (ITU) during which the tone might start was systematically varied from one series of trials to the next, and the listener knew the duration of ITU in each series. After each observation interval, the listener indicated his confidence that a tone was presented by using a rating scale. Operating characteristics [p(y|SN) against p(y|N)] were plotted on normal-normal coordinates, and measures of detectability were computed. The functional relation between the detectability index d, and the interval of time uncertainty is presented for each experiment.

With the theory of signal detectability as a framework, two psychophysical experiments were conducted in which each observation interval was well defined for the listener. Each interval contained noise, and it either did or did not (p=0.5) contain a signal (1000 cps, 0.5 sec in duration). In separate sessions of the first experiment, either the listener gave a yes-no decision or he responded with a rating (1–4) after each observation interval. Operating characteristics were obtained with E/N0 equal to 15.8. It is clear from the data that the trained listener can perform as well when he adopts the multiple criteria necessary for the rating method as when he adopts the single criterion required by the binary-decision procedure. In the second experiment, only the rating method was used to determine the relation between d′ and E/N0. The resulting function, for d′ ⩽ 3.0, approximates a straight line which passes through the origin and which has nearly the same slope as that obtained in other laboratories. [This research was supported by the Operational Applications Laboratory, Air Force Cambridge Research Center, under Contract AF 19(604)-1962.]