Nonlinear modeling of loudspeaker using adaptive second order Volterra filters

2007 ◽  
Author(s):  
D. Sankar ◽  
T. Thomas
Keyword(s):  
Nonlinear Modeling ◽  
Second Order ◽  
Volterra Filters

Nonlinear Modeling of Auditory-Nerve Rate Responses to Wideband Stimuli

2005 ◽  
Vol 94 (6) ◽  
pp. 4441-4454 ◽  
Author(s):  
Eric D. Young ◽  
Barbara M. Calhoun
Keyword(s):  
Auditory Nerve ◽  
Transfer Functions ◽  
Discharge Rate ◽  
Nonlinear Modeling ◽  
Nerve Fibers ◽  
Second Order ◽  
Spectral Processing ◽  
Spectrum Shape ◽  
Level Function ◽  
Auditory Nerve Fibers

The spectral selectivity of auditory nerve fibers was characterized by a method based on responses to random-spectrum-shape stimuli. The method models the average discharge rate of fibers for steady stimuli and is based on responses to ≈100 noise-like stimuli with pseudorandom spectral levels in 1/8- or 1/16-octave frequency bins. The model assumes that rate is determined by a linear weighting of the spectrum plus a second-order weighting of all pairs of spectrum values within a certain frequency range of best frequency. The method allows prediction of rate responses to stimuli with arbitrary wideband spectral shapes, thus providing a direct test of the degree of linearity of spectral processing Auditory-nerve fibers are shown to rely mainly on linear weighting of the stimulus spectrum; however, significant second-order terms are present and are important in predicting responses to random-spectrum shape stimuli, although not for predicting responses to noise filtered with cat head-related transfer functions. The second-order terms weight the products of levels at identical frequencies positively and the products of different frequencies negatively. As such, they model both curvature in the rate versus level function and suppressive interactions between different frequency components. The first- and second-order characterizations derived in this method provide a measure of higher-order nonlinearities in neurons, albeit without providing information about temporal characteristics.

scholarly journals A Family of Quaternion-valued Pipelined Second-order Volterra Adaptive Filters for Nonlinear System Identification

2021 ◽  
Author(s):  
Qianqian Liu ◽  
Yigang He
Keyword(s):  
System Identification ◽  
Nonlinear System ◽  
Adaptive Filters ◽  
Nonlinear System Identification ◽  
Linear Mapping ◽  
Second Order ◽  
Volterra Filters ◽  
Intermediate Space ◽  
Simulation Results ◽  
Output Space

Abstract This paper primarily proposes a family of quaternion Volterra filters based on the feedforward pipelined structure (QPSOVAFs) for nonlinear quaternion system identification to reduce the computational complexity. Then, the strictly nonlinear QPSOVAF (SNL-QPSOVAF), semi-widely nonlinear QPSOVAF(SWNL-QPSOVAF), and widely nonlinear QPSOVAF (WNL-QPSOVAF), are proposed. This architecture consists of several quaternion-valued second-order Volterra (SOV) modules. The structure's nonlinear subsection executes a nonlinear mapping from the input space to an intermediate space using the feedforward SOV; the linear combiner subsection performs a linear mapping from the intermediate space to the output space. Moreover, the theoretical analysis expresses the effectiveness of the proposed QPSOVAFs in a specific condition. Finally, simulation results further prove that the proposed QPSOVAFs have good performance in identifying the quaternion-valued nonlinear system.

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