A method for generating random time intervals

433

Electroencephalography and Clinical Neurophysiology Elsevier Publishing C o m p a n y , A m s t e r d a m - Printed in The Netherlands

TECHNICAL

CONTRIBUTION

A M E T H O D F O R G E N E R A T I N G R A N D O M TIME I N T E R V A L S H. FEIN Department o/ Physioloqy Yale University, School Off Medicine, New Haven, Conn. 06510 (U.S.A.) (Accepted for publication : March 15, 1972)

Experimental designs in neurophysiology and psychology have often required the presentation of a stimulus at a time which is randomly delayed with respect to an initiating event. Methods to achieve this end range from digital computer programs for stimulus randomization to special purpose devices (Barlow 1964). The present method is another solution to the problem of stimulus randomization which is a novel and simple way in which the subject or experimenter can initiate an interval of unpredictable duration before lhe stimulus is presented. If the frequency of occurrence on one delay time is to be equally as likely as any other delay time within a given range of times, the probability density should be rectangular. A mathematical function of time which possesses such a uniform probability density is the sawtooth

~

- FAST SAWTOOTH

to TIME

(a)

function. When such a function is sampled at will, the resulting sampled voltage amplitudes will be random. These amplitudes can then be used to generate proportionate time delays that are also random. The basic principles of the method are illustrated in Fig. 1. A sawtooth oscillator, the so-called fast sawtooth. runs freely at a rate of t0/sec or faster. This rate is too fast for animals or humans to be able to interact with in any anticipatory or synchronous manner. When one initiates an event (a switch closure, for example), the event samples the fast sawtooth at some unpredictable voltage within its range. The voltage level at which the fast sawtooth is sampled is then translated to a different time base where the fast sawtooth is replaced by a slower sawtooth which completes the remainder of the excursion of the sawtooth range. As shown in Fig. 1, a, the action is as if part of a selected fast sawtooth wave were instantaneously stretched in time and the remainder of the cycle tx is proportional to the amplitude of the fast sawtooth at the instant of sampling. The statistical density of time intervals so generated by repeated trials would be ideally rectangular if sufficient trials were performed. The initiating event which samples the fast sawtooth causes the flip-flop shown in Fig. 1, b. to switch states, causing the sawtooth generator to change instantaneously from a 100

RESET

FAST

RI

SLOW

OUTPUT RIGGER

o 1.5

(b) Fig. 1

SECONDS

Fig. 2

Electroenceph. clin. Neurophysiol., 1972, 33:433 434

434 10/sec rate to a slower rate (1 every 3 sec, for example). Since the initiating event must occur at a level somewhere between the m i n i m u m and m a x i m u m voltage levels of the sawtooth, switching the flip-flop has the effect of instaneously changing the slope of the sawtooth ramp from rapid to slow. At the end of the slow rise in Fig. 1, a, the sawtooth generator triggers the reset of the flip-flop thus returning the sawtooth generator to the fast rate. The return of the flip-flop to the fast mode generates an output signal randomly delayed with respect to the initial event. One may vary the slope of the slow ramp, if desirable, and change the range of the delay. The actual circuit details are simple and conventional. In Fig. 2, a histogram of the device's performance for several hundred events is shown. It is approximately uniform as expected. In performing these tests, the tester waited for the completion of each trial, once initiated, before trying again since the instrument will not respond to an external activating signal until the slow ramp has completed its cycle and flip-flop then resets. The problem was suggested by Dr. T. Thach and the prototype device was built and tested by H. Abildgaard.

n . VEIN SUMMARY A method has been presented for randomization of time intervals in which the subject or the experimenter initiates each time interval. The probability density of the resulting time intervals is approximately rectangular. RESUME M E T H O D E S DE P R O D U C T I O N D ' I N T E R V A L L E S DI:, TEMPS ALEATOIRES L'auteur prdsente une m6thode de production d'intervalles de temps aldatoires dans laquelle le sujet ou l'experimentateur fait d6buter chaque intervalle de temps. La probabilit6 de densit6 des intervalles de temps qui ell resultent est approximativement rectangulaire. REFERENCE BARI.OW, J. S. Evoked responses ill relation to visual perception and oculomotor reaction times in man. Ann. N.Y. Acad. Sci., 1964, 112: 4 3 2 4 6 7 .

ReJbrence: FEIN, H. A method for generating r a n d o m time intervals. Electroenceph. clin. Neurophysiol., 1972, 33: 433~434.