Zwicker Tone Illusion and Noise Reduction in the Auditory System

The Zwicker tone is an auditory aftereffect. For instance, after switching off a broadband noise with a spectral gap, one perceives it as a lingering pure tone with the pitch in the gap. It is a unique illusion in that it cannot be explained by known properties of the auditory periphery alone. Here we introduce a neuronal model explaining the Zwicker tone. We show that a neuronal noise-reduction mechanism in conjunction with dominantly unilateral inhibition explains the effect. A pure tone’s “hole burning” in noisy surroundings is given as an illustration.

Figure 1

A Zwicker tone is generated by various noise configurations. The horizontal axis denotes increasing frequency, the vertical one indicates the corresponding sound amplitude (arbitrary units). Shaded areas denote noise and vertical lines ending in a filled circle indicate pure tones. Zwicker-tone generating sounds (left column) are low-pass noise (a), noise with a gap (b),(c), or noise plus a pure tone (d),(e). The pitch of the Zwicker tone is indicated by a downward arrow. Dashed lines denote auditory excitation [3, 4] and dotted lines indicate the threshold in silence. No Zwicker tone has been observed in (f)–(j). Cases (e) and (j) represent new experimental results [5], motivated by the hole burning concept of the noise-reduction model presented here. As the gap decreases, the Zwicker tone is first perceived less clearly (c) until it is no longer audible (g).

Figure 2

Habituation (left column) and noise reduction (right column). (a) Neuronal implementation of asymmetric lateral inhibition. Grey circles denote output neurons, small filled circles indicate excitatory, and small open circles inhibitory synapses. (b),(c) Response (upper panels) of the habituation model (a) to the sounds (lower panels) of Figs. 1a, 1e. Firing rates of the output neurons before (horizontal dotted line, spontaneous rate), during (dashed line) and immediately after (solid line) the sound presentation are shown. As in (e) and (f), they are the result of a numerical simulation of a single run of 1000 neurons with best frequencies between 0.2 and 16 kHz; for simulation details, see 10, 11. Downward arrows indicate Zwicker tones predicted by the model. In case (c), habituation predicts a Zwicker tone (crossed arrow) to the right of the pure tone whereas in experiment there is one to the left. (d) Neuronal implementation of the full model with asymmetric inhibition and noise detection. The responses in (e) and (f) correspond to (b) and (c), respectively. Dash-dotted lines stand for firing rates of noise-detection neurons. Their distribution of firing rates is shifted to the left as we go from (e) to (f), which is due to the pure tone’s “hole burning” in (f); see Fig. 3 and the text below.

Figure 3

Implementation of the noise-reduction model through noise-detection (type IV) neurons. Same notation as in Fig. 2d, with best frequency (arrow) as horizontal axis. The horizontal bar indicates half an octave, which has been emulated here by 80 neurons. The feature detectors (type II) are active, if there is a steeply rising edge, i.e., a rising spectral intensity as frequency increases. Feature detectors asymmetrically inhibit noise-detection neurons, which, in turn, inhibit corresponding output neurons; see 10 for the details of the synaptic connectivity (dashed lines).

Figure 4

Numerical simulation of a Zwicker tone. Firing rates (color coded) of 1000 output neurons are a function of time and the neurons’ best frequency. Frequencies are equidistant on a logarithmic scale. The stimulating sound is low-pass noise plus a pure tone at the edge, 1700 Hz; cf. Figs. 1e, 2f. Sound is on between 3 and 6 s. Feature detectors respond to the pure tone, causing a “hole burning” in the noise-detector layer since noise-detector neurons are inhibited by feature detectors; cf. Figs. 2, 3. The Zwicker tone, brought about by the mechanism described in the main text, is perceived below the pure tone and is indicated by an arrow head, pointing at the yellow strip. Data are binned. A bin consists of the rates of a neuron and its two left and right neighbors. Each data point is an average over its bin and 250 ms.