White Noise Input Signal Research Articles

Modeling and Identification of Piezoelectric-Actuated Stages Cascading Hysteresis Nonlinearity With Linear Dynamics

In this paper, we propose a new modeling and identification approach for piezoelectric-actuated stages cascading hysteresis nonlinearity with linear dynamics, which is described as a Hammerstein-like structure. In the proposed approach, the hysteresis and linear dynamics together with the delay time and higher order dynamic behaviors are obtained with three data-driven identification steps under designed input signals. In the first step, the step input signal is applied to estimate the delay time of the piezoelectric-actuated stages. In the second step, the autoregression with exogenous signal identification algorithm is adopted to identify the linear dynamics using a small-amplitude band-limited white noise input signal. In the third step, with the identified linear dynamics model, the parameters of the rate-independent Prandtl–Ishlinskii hysteresis model are identified by the particle swarm optimization algorithm using a simple low-frequency triangle input signal with different amplitudes. Finally, the experimental results on a piezoelectric-actuated stage show that both the hysteresis and dynamic behaviors of the piezoelectric-actuated stage are well predicted by the proposed modeling method. In addition, we provide the analysis of quantitative prediction errors of the identified model with comparison to experimental data, which clearly demonstrate the effectiveness of the proposed approach.

On the Asymptotic Properties of Closed-Loop CCA-Type Subspace Algorithms: Equivalence Results and Role of the Future Horizon

In this paper, we shall consider a class of subspace algorithms for identification of linear time invariant systems operating in closed loop. In particular we study algorithms based on the so-called state-sequence approach; we first show that the ADAPTx algorithm by Larimore is asymptotically equivalent to a number of recently developed algorithms, which we call CCA-type algorithms. Based on this equivalence result, we then study the effect of the horizon, which is one of the principal user choices in subspace identification. It is well known that for the CCA algorithm the asymptotic variance of any system invariant is a non increasing function of the future horizon when input signals are white (or absent). In particular we extend this result, valid for white noise input signals to a slightly more general class of input signals, which include proportional (output or state) feedback controllers and LQG controllers, provided the reference input is white. The condition on the input will be expressed in terms of its state space, which we regard as a rather natural condition in this framework. For the situations not covered by the above result, we shall also describe a computational procedure, based on some recently derived asymptotic variance formulas, which allows to optimize the choice of the future horizon. Some simulation results are included.

Digital-domain self-calibration technique for video-rate pipeline A/D converters using Gaussian white noise

A digital-domain self-calibration technique for video-rate pipeline A/D converters based on a Gaussian white noise input signal is presented. The proposed algorithm is simple and efficient. A design example is shown to illustrate that the overall linearity of a pipeline ADC can be highly improved using this technique.

Time-frequency analysis of heart murmurs. Part I: Parametric modelling and numerical simulations.

The object of this study is to compare the performance of two new bilinear time-frequency representation techniques with the spectrogram to characterise the behaviour of heart murmurs produced by bioprosthetic heart valves implanted in the mitral or aortic position. The murmurs are those of mitral stenosis, mitral regurgitation, aortic stenosis, aortic regurgitation, a diastolic musical murmur and a systolic musical murmur. In the first part of the study, the general characteristics of the amplitude and the spectral content of these murmurs are determined by visual observation of the spectrogram of phonocardiograms obtained from several patients with known valvular pathology complemented with a literature review. A parametric model is then generated for each murmur signal. Stenotic and regurgitant murmurs are modelled as the sequential output of a bank of low-pass filters excited by a white noise input signal. The basic parameters of each filter are selected to simulate, as a function of time, the basic characteristics of random heart murmurs. Musical murmurs are modelled as a frequency-modulated deterministic sinusoid of constant amplitude. Numerical simulations of these random and musical heart murmurs are then generated and will be used in Part II to determine the best of three time-frequency representation techniques for analysing heart murmur signals.

Roundoff noise analysis of state-space digital filters implemented on floating-point digital signal processors

An expression is obtained for the output floating-point roundoff noise variance of a general Nth-order state-space digital filter with zero-mean white noise input signal. This expression is then simplified for the case there the filter is implemented on a floating-point digital signal processor. Such processors carry extended precision bits in the accumulation register, so that the primary source of roundoff error in the output arises from the final quantization of the mantissa. Under this condition of extended precision during multiply-accumulate, it is found that the floating-point roundoff noise gain is identical to the fixed-point roundoff noise gain used extensively in the past for designing optimal and near-optimal fixed-point digital filters. Therefore, previous work to optimize fixed-point realizations is directly applicable to the floating-point realizations. This conclusion is verified by actual roundoff noise measurements using a digital signal processor simulator. Since floating-point digital filters do not require scaling, optimal floating-point realizations require N fewer multiplies than fixed-point filters. Simple design equations are presented for the floating-point minimum-noise second-order state-space structure with two trivial unity multiplies.

A nonlinear cascade model for action potential encoding in an insect sensory neuron

Action potential encoding in the cockroach tactile spine neuron can be represented as a single-input single-output nonlinear dynamic process. We have used a new functional expansion method to characterize the nonlinear behavior of the neural encoder. This method, which yields similar kernels to the Wiener method, is more accurate than the latter and is efficient enough to obtain reasonable kernels in less than 15 min using a personal computer. The input stimulus was band-limited white Gaussian noise and the output consisted of the resulting train of action potentials, which were unitized to give binary values. The kernels and the system input-output signals were used to identify a model for encoding comprising a cascade of dynamic linear, static nonlinear, and dynamic linear components. The two dynamic linear components had repeatable and distinctive forms with the first being low-pass and the second being high-pass. The static nonlinearity was fitted with a fifth-order polynomial function over several input amplitude ranges and had the form of a half-wave rectifier. The complete model gave a good approximation to the output of the neuron when both were subjected to the same novel white noise input signal.

Hardware for Detection and Partial Correction of PCM Transmission Errors

In pulse code modulation (PCM) of speech, transmission errors cause changes in the statistical properties of the received samples. Recently published work describes computer simulations of a difference detection and correction (DDC) system which detect errors on the basis of these changes. The system examines the differences between adjacent received samples. If a particular difference exceeds a threshold, which is dependent on the rms value of a block of 64 differences, the quantized sample responsible for this large difference is deemed to be erroneous. A nonlinear filter of the median type is then introduced as a corrector. We now present a comprehensive description of the hardware realization of this system, and present measured results of signal-to-noise ratio (snr) as a function of bit error rate, input power and the error criterion for narrow-band white noise input signals. An improvement of 6 dB in snr is achieved for error rates between 0.2 and 2.0%. The snr results are consistent with subjective impressions of the quality of speech processed by the DDC system.

Application of the normal spectrum technique to the calculation of distortion noise in delta modulators

The paper establishes the theoretical behaviour of the linear delta modulator with the aid of the normal spectrum technique. The spectral density functions of the signal at the output of the decoder and of the distortion due to quantization effects are calculated for band-limited white noise input signals. The expressions of these spectral density functions derived with the normal spectrum technique enable the results of computer simulation to be easily explained. Graphical results are presented of the spectral density function of the distortion signal for the coder having different step-sizes and clock rates, and of the decoded signal to noise ratio against input signal power. The computer simulation verifies the authenticity of the theory.

Simulation of stationary stochastic processes

A ‘spectral-factorisation’ procedure involving the solution of a Riccati matrix differential equation is considered to determine systems which, with white-noise input signals, may be used in the simulation of stochastic processes having prescribed stationary covariances. More spe$itically, the specification of a system is made so that the covariance of the system output is a prescribed stationary covariance R(t – ~) for all t and -r greater than or equal to the ‘switch-on’ time of the system. The advantage of the ‘spectralfactorisation’ procedure described compared with those previously given is that, assuming an initial-state mean of zero, a suitable initial-state covariance is calculated as an intermediate result in the procedure. The calculation of an appropriate initial-state covariance is of interest since, if zero initial conditions are used in an attempted simulation, an undesirable time lapse may be necessary for the output covariance to be acceptable as a simulation of the prescribed stationary covariance. For the case when the system is given or is determined using alternative procedures to those described in the paper, the initial-state covariance is calculated from the solution of a linear matrix equation. The problem considered in the paper is the simulation of stationary stochastic processes with prescribed covariances using linear, finite-dimensional, time-invariant systems with white-noise input. Of particular interest is the selection of an initial-state covariance, so that the covariance of the outputs will be indistinguishable from that observed over the same time interval for the hypothetical limiting case as the initial time approaches – m. Systems which may be used in the simulation of stationary stochastic processes with prescribed covariances may be determined from any of a number of spectral-factorisation procedures, ] z,* With regard to the initial conditions, Cttrrent practice is to set these to zero and ignore the outputs for a period corresponding to a few time constants of the system. The inadequacy of this procedure has been recognised.3 In the paper two results are presented. The first is a method for selecting an initial-state covariance for a given system, so that the application of white noise at the input results in outputs that may be considered, after the switch-on, as sample functions of a stationary stochastic process; this is the best possible real-time simulation for a stationary stochastic process. All that is required in order to obtain the result is the solution of a linear matrix equation. The second result of the paper is a spectral factorisation of a specified covariance matrix using theorems from Anderson. t The procedure gives a system having a stable transferfunction matrix with a stable inverse (often required in certain optimisation problems), together with the initial-state covariance; the advantage of the particular approach presented is that all the information necessary for the simulation is given in one procedure. The key step in the procedure is the solution of a quadratic matrix equation which satisfies certain constraints. This solution, which is unique, may be found using algebraic means similar to those of Reference 4 or by determining the steadystate solution of a Riccati matrix differential equation. t The method avoids the need to carry out any of the procedures in References 1, 2 or *, which prove very complex in cases where the covariance is a matrix rather than scalar.