Nonlinear Transducer Research Articles

Adaptation to sine-wave gratings selectively reduces the contrast gain of the adapted stimuli

Adapting to sinusoidal gratings selectively reduces contrast sensitivity to subsequent test stimuli. To investigate the perceptual processes underlying selective adaptation, we developed an external noise plus adaptation paradigm and a theoretical framework based on a noisy observer model (the contrast-gain-control Perceptual Template Model [cgcPTM]). After adapting to a 45 deg, 2-Hz counter-flickering sine grating of 0.8 contrast, observers performed two-interval forced-choice detection of Gabors of matched spatial frequency, tilted at either 45 or 135 deg and embedded in one of six levels of white external noise (Experiment 1) or embedded in orientation band-pass-filtered external noise (Experiment 2). On the basis of the cgcPTM, we found that adaptation selectively reduced the contrast gain of the perceptual template at the adapted spatial frequency and orientation without altering either pre- or post-gain-control (additive and multiplicative) noises or changing transducer nonlinearity. Modeled as notches on the perceptual templates, the estimated full orientation bandwidth of adaptation at half height was about 8.3 deg.

Focus on sensors

Focus on sensors

Spectral fine-structures of low-frequency modulated distortion product otoacoustic emissions

Biasing of the cochlear partition with a low-frequency tone can produce an amplitude modulation of distortion product otoacoustic emissions (DPOAEs) in gerbils. In the time domain, odd- versus even-order DPOAEs demonstrated different modulation patterns depending on the bias tone phase. In the frequency domain, multiple sidebands are presented on either side of each DPOAE component. These sidebands were located at harmonic multiples of the biasing frequency from the DPOAE component. For odd-order DPOAEs, sidebands at the even-multiples of the biasing frequency were enhanced, while for even-order DPOAEs, the sidebands at the odd-multiples were elevated. When a modulation in DPOAE magnitude was presented, the magnitudes of the sidebands were enhanced and even greater than the DPOAEs. The amplitudes of these sidebands varied with the levels of the bias tone and two primary tones. The results indicate that the maximal amplitude modulations of DPOAEs occur at a confined bias and primary level space. This can provide a guide for optimal selections of signal conditions for better recordings of low-frequency modulated DPOAEs in future research and applications. Spectral fine-structure and its unique relation to the DPOAE modulation pattern may be useful for direct acquisition of cochlear transducer nonlinearity from a simple spectral analysis.

Psychometric curves of lateral facilitation

Visibility of an oriented stimulus may be enhanced by nearby stimuli that are co-aligned with the target. However, the underlying mechanism governing this facilitation is controversial. Here we measured the dependence of percent correct detection on the target's contrast (psychometric curve) with and without flankers, where flankers were either collinear with or orthogonal to the target. We find that the effect of collinear flankers can be described as a translation of the psychometric function along the linear contrast axis. This behavior is consistent, within experimental error, with two types of models: (1) non-linear transduction of target contrast with collinear flankers having additive effects on contrast, and (2) uncertainty reduction (Pelli, 1985) by collinear flankers. We discuss properties of collinear facilitation that can help deciding between these two models.

Virtual curve tracer for estimation of static response characteristics of transducers

The paper proposed a new practical approach for optimal fitting of transducer characteristics to measured data using artificial neural network (ANN) based virtual curve tracer (VCT). The performance of the implemented system is examined experimentally for an industrial grade pressure transducer, connected across a data acquisition system (DAS) of a computer based measurement system. The core of applications used ANN architectures, based on multilayer perceptrons, trained with back-propagation learning algorithm, as solutions to transducer characteristic interpolation. However, a number of different variants of the standard basic gradient descent back-propagation learning algorithm, for training the multilayer perceptrons, are reported in the literature. But there are no specific rules to select the best learning algorithm for a given set of input–output pairs, where transducer non-linearity is the main factor to be considered. In this context, we present a comparative evaluation of the relative performance of different multilayer perceptron based models for optimal fitting of transducer static response characteristics, with particular attention paid to the speed of computation, accuracy achieved, architectural complexity and computational load for a given set of training data. This type of performance comparison has not been attempted so far.

Binocular, Monocular and Dichoptic Pattern Masking

It has been reported that a quadratic summation rule can account for threshold versus masker contrast (TvC) functions for binocular, monocular and dichoptic masking. However, the present study suggests that inputs from two eyes are summed in different ways. Foley’s model was revised to describe TvC functions for binocular, monocular and dichoptic masking. The revised model has the following two characteristics. First, the revised model receives two monocular inputs. Secondly, excitations and inhibitory signals are subjected to nonlinear transducer functions before and after summation of the monocular signals. A two-alternative forced-choice procedure was used to measure contrast thresholds for Gaussian windowed sine-wave gratings (target) in the presence of sine-wave gratings (masker). Thresholds were measured for 11 masker contrasts and the three masking conditions. It was shown that this revised model fitted the data resonably well. The revised model indicates how monocular inputs are summed in contrast processing.

Non-linear transduction strategies for chemo/biosensing on small length scales

As the function of optically-based chemo/biosensors (CBsensors) evolves towards micro- and nanoscale dimensions, the sensitivity of the device is compromised because there are simply too few reporting active sites. We see this issue as the fundamental challenge confronting the design of small length scale CBsensors, providing an imperative for the development of new optical transduction strategies. To address this challenge, we are currently fabricating: (i) new materials that will amplify the primary optical signal from the CBsensing active site in micro- and nano-environments and (ii) new sensing elements and devices to achieve high gain from a non-linear optical response. We present here the synthesis and characterization of two platforms poised for sensing by non-linear transduction.

Cochlear compression: Effects of low-frequency biasing on quadratic distortion product otoacoustic emission

Distortion product otoacoustic emissions (DPOAEs) are generated from the nonlinear transduction n cochlear outer hair cells. The transducer function demonstrating a compressive nonlinearity can be estimated from low-frequency modulation of DPOAEs. Experimental results from the gerbils showed that the magnitude of quadratic difference tone (QDT, f2-f1) was either enhanced or suppressed depending on the phase of the low-frequency bias tone. Within one period of the bias tone, QDT magnitudes exhibited two similar modulation patterns, each resembling the absolute value of the second derivative of the transducer function. In the time domain, the center notches of the modulation patterns occurred around the zero crossings of the bias pressure, whereas peaks corresponded to the increase or decrease in bias pressure. Evaluated with respect to the bias pressure, modulated QDT magnitude displayed a double-modulation pattern marked by a separation of the center notches. Loading/unloading of the cochlear transducer or rise/fall in bias pressure shifted the center notch to positive or negative sound pressures, indicating a mechanical hysteresis. These results suggest that QDT arises from the compression that coexists with the active hysteresis in cochlear transduction. Modulation of QDT magnitude reflects the dynamic regulation of cochlear transducer gain and compression.

Cochlear hysteresis: observation with low-frequency modulated distortion product otoacoustic emissions.

Low-frequency modulation of distortion product otoacoustic emissions (DPOAEs) can be used to estimate a nonlinear transducer function (fTr) of the cochlea. From gerbils, DPOAEs were measured while presenting a high-level bias tone. Within one period of the bias tone, the magnitudes of the cubic difference tone (CDT, 2f1 - f2) demonstrated two similar modulation patterns (MPs) each resembled the absolute value of the third derivative of the fTr. The center peaks of the MPs occurred at positive sound pressures for rising in bias pressure or loading of the cochlear transducer, and more negative pressures while decreasing bias amplitude or unloading. The corresponding fTr revealed a sigmoid-shaped hysteresis loop with counterclockwise traversal. Physiologic indices that characterized the double MP varied with primary level. A Boltzmann-function-based model with negative damping as a feedback component was proposed. The model was able to replicate the experimental results. Model parameters that fit to the CDT data indicated higher transducer gain and more prominent feedback role at lower primary levels. Both physiologic indices and model parameters suggest that the cochlear transducer dynamically changes its gain with input signal level and the nonlinear mechanism is a time-dependent feedback process.

Fitting transducer characteristics to measured data using a virtual curve tracer

Abstract This paper presents an artificial neural network based approach of transducer modeling in a computer-based measurement system. Transducer’s static response characteristic is generally highly non-linear. However, if linear approximations were acceptable, for a given accuracy level, noise and measurement errors are always present. Therefore, curve-fitting procedures are required frequently to average these effects. With the facility of computation now available through digital computers and microprocessors, the problem of estimation of transducer’s input–output static response characteristics is being increasingly tackled using software techniques. However, for an inherent nonlinear transducer, a software solution depends upon the proper approach through mathematical modeling of the response curve. An artificial neural network based virtual curve tracer is proposed for modeling, testing and calibration of transducers. The implemented functions are described. Experimental results of the comparative study in modeling the static response characteristic of a strain-gauge pressure transducer using adaptive single-layer linear network and multilayer feed-forward back-propagation network are presented.

Method of quadratic approximation: A new approach to identification of analysers and channels in human vision

Models comprising, in sequence, linear analysers, Ψ 1, …, Ψ n , non-linear transducer functions, and the Minkowski decision rule, are widely used to fit detection and discrimination data, especially when necessary to take into account the effect of probability summation. However, the analysers’ characteristics cannot be derived from detection/discrimination data because of an unavoidable trade-off between these characteristics and the decision rule. Here we show how to overcome this problem, i.e. how to identify the analysers Ψ i= ∑ m aijφ j=1 despite the probability summation between them. The observer's performance is assumed to be quantitatively defined in terms of an equi-detection (discrimination) surface. Each analyser Ψ i is expressed as a weighted sum of linear (coordinate) functionals φ j :Ψ 1,…,Ψ n , so that an identification of the analysers ϕ i is then reduced to evaluating the weight matrix A={ a ij }. It is proved that A can be uniquely recovered from a quadratic approximation of the equi-detection (discrimination) surface at the neighbourhood of at least two points. More specifically, the following equation holds true: A T D( A T ) #= H 1 H 2 #, where A # is the generalised inverse of the matrix A, D is an unknown diagonal matrix, H 1 and H 2 are the matrices of the quadratic forms determining the quadratic surfaces approximating the equi-detection (discrimination) surface at two different points. Thus, the matrix H 1 H 2 # known from experiment is a similarity transform of the diagonal matrix, the rows of A being the eigenvectors of H 1 H 2 #. Hence, any eigensystem routine can be used to derive A from H 1 H 2 #.

Triple resonant states and chaos control in an electrostatic transducer with two outputs

The dynamics of a non-linear electrostatic transducer with two outputs is studied. The amplitudes and stability conditions of oscillations for the Triple Resonant States are obtained and discussed. It is found that chaos can appear in the system. A retroactive control strategy is therefore applied to tune these chaotic oscillations to regular target orbits. The stability analysis of the feedback controller is also investigated, and an estimation of the feedback strength under which no efficient control is possible is derived. The analytic study is confirmed by numerical simulations.

Audio signal processing by neural networks

In this paper a review of architectures suitable for nonlinear real-time audio signal processing is presented. The computational and structural complexity of neural networks (NNs) represent in fact, the main drawbacks that can hinder many practical NNs multimedia applications. In particular efficient neural architectures and their learning algorithm for real-time on-line audio processing are discussed. Moreover, applications in the fields of (1) audio signal recovery, (2) speech quality enhancement, (3) nonlinear transducer linearization, (4) learning based pseudo-physical sound synthesis, are briefly presented and discussed.

ANN based Virtual Instrumentation System for Estimation of Non-linear Static Characteristics of Sensors

Non-linearity associated with the sensors and transducers gives rise to several difficulties for direct digital readout, on-chip interface, testing and calibration. With the facility of computation now available through digital computers, the problem of transducer non-linearity is being increasingly tackled by them through software packages. However, for an arbitrary non-linear transducer response characteristic, a software solution depends upon the proper approach through mathematical modeling of the response curve. There are no rules to select the best curve-fitting method for a given set of data. The problem is of great importance in measurement applications. In this paper, a universal approach using artificial neural network (ANN) based direct modeling of pressure transducers is proposed. An ANN based versatile algorithm integrated in the form of a soft-instrumentation system developed around a PC-based data acquisition system for real time applications is presented. The response of a sensor is expressed in terms of its input by a polynomial series and the associated non-linearity is estimated in terms of the unknown coefficients. Attempts are made to devise an important submodule of an auto-calibration system for different types of sensor, transducers and signal conditioning circuits. Fourth generation object oriented graphical programming language is used to develop the user interactive software based virtual instrumentation system. Experimental results of the estimation of non-linearity in a strain gauge based pneumatic pressure sensor are presented.

Motion sharpening and contrast: Gain control precedes compressive non-linearity?

Blurred edges appear sharper in motion than when they are stationary. We ( Vision Research 38 (1998) 2108) have previously shown how such distortions in perceived edge blur may be accounted for by a model which assumes that luminance contrast is encoded by a local contrast transducer whose response becomes progressively more compressive as speed increases. If the form of the transducer is fixed (independent of contrast) for a given speed, then a strong prediction of the model is that motion sharpening should increase with increasing contrast. We measured the sharpening of periodic patterns over a large range of contrasts, blur widths and speeds. The results indicate that whilst sharpening increases with speed it is practically invariant with contrast. The contrast invariance of motion sharpening is not explained by an early, static compressive non-linearity alone. However, several alternative explanations are also inconsistent with these results. We show that if a dynamic contrast gain control precedes the static non-linear transducer then motion sharpening, its speed dependence, and its invariance with contrast, can be predicted with reasonable accuracy.

Acoustic input impedance measurements on brass instruments

Measurement of the acoustic input impedance of a brass instrument can reveal something about the instrument’s intonation, its reasonable playing range, its tone color, and perhaps whether the mouthpiece used for the impedance measurement is appropriate for the instrument. Such measurements are made at sound-presssure levels much lower than those encountered under playing conditions. Thus, impedance measurements may offer the only feasible way to infer something about the playing characteristics of instruments, typically museum specimens, that are too rare or too fragile to be played. In this paper the effects of some of the available choices of sound source and stimulus signal on measurement accuracy will be explored. Driver–transducer nonlinearity, source impedance, signal-to-noise ratio, and any necessary signal processing will be discussed.

Deriving a cochlear transducer function from low-frequency modulation of distortion product otoacoustic emissions.

In this paper, a new method is introduced to derive a cochlear transducer function from measuring distortion product otoacoustic emissions (DPOAEs). It is shown that the cubic difference tone (CDT, 2f1-f2) is produced from the odd-order terms of a power series that approximates a nonlinear function characterizing cochlear transduction. Exploring the underlying mathematical formulation, it is found that the CDT is proportional to the third derivative of the transduction function when the primary levels are sufficiently small. DPOAEs were measured from nine gerbils in response to two-tone signals biased by a low-frequency tone with different amplitudes. The CDT magnitude was obtained at the peak regions of the bias tone. The results of the experiment demonstrated that the shape of the CDT magnitudes as a function of bias levels was similar to the absolute value of the third derivative of a sigmoidal function. A second-order Boltzmann function was derived from curve fitting the CDT data with an equation that represents the third derivative of the Boltzmann function. Both the CDT-bias function and the derived nonlinear transducer function showed effects of primary levels. The results of the study indicate that the low-frequency modulated DPOAEs can be used to estimate the cochlear transducer function.

The receptor potential in type I and type II vestibular system hair cells: a model analysis

Several studies have shown that type I hair cells present a large outward rectifying potassium current ( g K,L) that is substantially activated at the resting potential, greatly reducing cell input resistance and voltage gain. In fact, mechanoelectrical transducer currents seem not to be large enough to depolarize type I hair cells to produce neurotransmitter release. Also, the strongly nonlinear transducer currents and the limited voltage oscillations found in some hair cells did not account for the bidirectionality of response in hair cell systems. We developed a model based in the analysis of nonlinear Goldman–Hodgkin–Katz equations to calculate the hair cell receptor potential and ionic movements produced by transducer current activation. Type I hair cells displaying the large g K,L current were found to produce small receptor potentials (3–13.8 mV) in response to mechanoelectrical transducer current input. In contrast, type II cells that lack g K,L produced receptor potentials of about 30 mV. Properties of basolateral ionic conductances in type II hair cells will linearize hair bundle displacement to receptor potential relationship. The voltage to obtain the half maximal activation of g K,L significantly affects the resting membrane potential, the amplitude, and the linearity of the receptor potential. Electrodiffusion equations were also used to analyze ionic changes in the intercellular space between type I hair cell and calyx endings. Significant K + accumulation could take place at the intercellular space depending on calyx structure.

Disentangling signal from noise in visual contrast discrimination.

Human ability to detect stimulus changes (Delta C) decreases with increasing reference level (C). Because detection performance reflects the signal-to-noise ratio within the relevant sensory brain module, this behavior can be accounted for in two extreme ways: first, the internal response change Delta R evoked by a constant Delta C decreases with C (that is, the transducer R = f(C) displays a compressive nonlinearity), whereas the internal noise is independent of R; second, Delta R is constant with C but the noise level increases with R. A newly discovered constraint on human decision-making helps solve this century-old problem: in a detection task where multiple changes occur with equal probabilities, observers use a unique response criterion to decide whether a change has occurred. For contrast discrimination, our results supported the first account above: human performance was limited by the contrast transducer nonlinearity and an almost constant noise.

Nonlinear Coupling between Evoked rCBF and BOLD Signals: A Simulation Study of Hemodynamic Responses

The aim of this work was to investigate the dependence of BOLD responses on different patterns of stimulus input/neuronal changes. In an earlier report, we described an input-state-output model that combined (i) the Balloon/Windkessel model of nonlinear coupling between rCBF and BOLD signals, and (ii) a linear model of how regional flow changes with synaptic activity. In the present investigation, the input-state-output model was used to explore the dependence of simulated PET (rCBF) and fMRI (BOLD) signals on various parameters pertaining to experimental design. Biophysical simulations were used to estimate rCBF and BOLD responses as functions of (a) a prior stimulus, (b) epoch length (for a fixed SOA), (c) SOA (for a fixed number of events), and (d) stimulus amplitude. We also addressed the notion that a single neuronal response may differ, in terms of the relative contributions of early and late neural components, and investigated the effect of (e) the relative size of the late or “endogenous” neural component. We were interested in the estimated average rCBF and BOLD responses per stimulus or event, not in the statistical efficiency with which these responses are detected. The BOLD response was underestimated relative to rCBF with a preceding stimulus, increasing epoch length, and increasing SOA. Furthermore, the BOLD response showed some highly nonlinear behaviour when varying stimulus amplitude, suggesting some form of hemodynamic “rectification.” Finally, the BOLD response was underestimated in the context of large late neuronal components. The difference between rCBF and BOLD is attributed to the nonlinear transduction of rCBF to BOLD signal. Our simulations support the idea that varying parameters that specify the experimental design may have differential effects in PET and fMRI. Moreover, they show that fMRI can be asymmetric in its ability to detect deactivations relative to activations when an absolute baseline is stipulated. Finally, our simulations suggest that relative insensitivity to BOLD signal in specific regions, such as the temporal lobe, may be partly explained by higher cognitive functions eliciting a relatively large late endogenous neuronal component.