Identification of the Nonlinear Vibration Characteristics Based on the Wiener Kernels

Wiener series are the important functional series describing nonlinear system. If an input signal is the Gaussian white noise, the wiener kernels are estimated through calculating the cross-correlation functions of the input and output of a nonlinear system. In this paper, a single-DOF quadratic nonlinear system is identified by the Wiener series. The results show that the intensity of the nonlinear response can be expressed by the second-order kernel.

Wiener Kernels of Chinchilla Auditory-Nerve Fibers: Verification Using Responses to Tones, Clicks, and Noise and Comparison With Basilar-Membrane Vibrations

Responses to tones, clicks, and noise were recorded from chinchilla auditory-nerve fibers (ANFs). The responses to noise were analyzed by computing the zeroth-, first-, and second-order Wiener kernels (h0, h1, and h2). The h1s correctly predicted the frequency tuning and phases of responses to tones of ANFs with low characteristic frequency (CF). The h2s correctly predicted the frequency tuning and phases of responses to tones of all ANFs, regardless of CF. Also regardless of CF, the kernels jointly predicted about 77% of the features of ANF responses to “frozen” samples of noise. Near-CF group delays of kernels and signal-front delays of responses to intense rarefaction clicks exceeded by 1 ms the corresponding basilar-membrane delays at both apical and basal sites of the chinchilla cochlea. This result, confirming that synaptic and neural processes amount to 1 ms regardless of CF, permitted drawing a map of basilar-membrane delay as a function of position for the entire length of the chinchilla cochlea, a first for amniotic species.

Nonspiking and Spiking Proprioceptors in the Crab: White Noise Analysis of Spiking CB-Chordotonal Organ Afferents

The proprioceptors that signal the position and movement of the first two joints of crustacean legs provide an excellent system for comparison of spiking and nonspiking (graded) information transfer and processing in a simple motor system. The position, velocity, and acceleration of the first two joints of the crab leg are monitored by both nonspiking and spiking proprioceptors. The nonspiking thoracic-coxal muscle receptor organ (TCMRO) spans the TC joint, while the coxo-basal (CB) joint is monitored by the spiking CB chordotonal organ (CBCTO) and by nonspiking afferents arising from levator and depressor elastic strands. The response characteristics and nonlinear models of the input-output relationship for CB chordotonal afferents were determined using white noise analysis (Wiener kernel) methods. The first- and second-order Wiener kernels for each of the four response classes of CB chordotonal afferents (position, position-velocity, velocity, and acceleration) were calculated and the gain function for each receptor determined by taking the Fourier transform of the first-order kernel. In all cases, there was a good correspondence between the response of an afferent to deterministic stimulation (trapezoidal movement) and the best-fitting linear transfer function calculated from the first-order kernel. All afferents also had a nonlinear response component and second-order Wiener kernels were calculated for afferents of each response type. Models of afferent responses based on the first- and second-order kernels were able to predict the response of the afferents with an average accuracy of 86%.