ATR Human Information Processing Res. Labs., 2-2 Hikaridai, Seikacho, Sorakugun, Kyoto 619-02, Japan
It was discovered that specific FM (frequency-modulated) tones induce a ringing of a perceived pitch. A mathematical model was derived to explain this phenomenon. An abrupt change of the slope in a unidirectional FM tone induces ringing of the perceived pitch. The typical ring-inducing FM tone had a piecewise linear frequency trajectory in the log frequency axis with three parts: (1) frequency onset at 1 kHz rising to 0.732 kHz in 200 ms; (2) constant frequency at 1.732 kHz for 200 ms; and (3) frequency rising to 3 kHz in 200 ms. Several listeners reported one to three ringings around the middle part of the piecewise linear sweep. Frequent repetition of the listening test decreased the sensitivity of ringing perception. The ringing phenomenon can be explained by a second-order system as a functional model of sweep tracking. In order to provide experimental evidence for the second-order tracking system, specific values for the natural frequency and the damping factor were estimated. An inverse filter of this system was then constructed and was called the antiringing filter. In a psychophysical experiment, subjects compared the original piecewise sweep tone to that tone processed by the antiringing filter. Results demonstrated that pitch ringing was significantly suppressed by the antiringing filter.