Reciprocal Spreading Effects on Frequency Discrimination

Abstract

The reciprocal spreading phenomenon tells us that short-duration signals are poorly defined in the frequency domain, while line spectra exist only for signals of infinite duration. Formally, ΔfΔt = CONST describes how “effective” bandwidth and “effective” duration are constrained by a reciprocal relation. The value of the constant is unique to the envelope of the signal and varies considerably for the types of signal envelopes that occur in actual waveforms. Only a few studies have examined frequency discrimination at short durations where reciprocal spreading effects might be important. Liang and Chistovich found that for durations less than about 40 msec, the difference limen for frequency is proportional to signal bandwidth. To investigate this bandwidth hypothesis in more detail, several different waveforms were selected as envelopes for short-duration sinusoids. These included a rectangular, a Gaussian, two exponentials, and a gamma function, which were equated for “effective” bandwidth. From the ΔtΔf = CONST relation, it can be seen that sinusoids with these different envelopes have different “effective” durations, and we might expect that this would have some effectjon the ability to detect frequency differences. The experimental results indicate that such is indeed the case: wide differences are observed for these signals that are nominally equivalent in bandwidth. [This research was supported by the National Institutes of Health, Public Health Service, U. S. Department of Health, Education, and Welfare, and an NIMH—Postdoctoral Fellowship.]