Signals In White Gaussian Noise Research Articles

Approximations to the Cramer–Rao lower bound for a single damped exponential signal

It is demonstrated that the Cramer–Rao lower bounds on unbiased estimates of frequency, damping factor, amplitude and phase for a data record containing a single damped exponential signal in additive complex Gaussian white noise can be approximated by simple expressions. The approximations provide considerable insight into the nature of the bounds and are accurate to within about 15% over a wide range of data lengths, damping factors, etc. Further, it is indicated that this same approximation is also useful for the related case of multiple damped complex exponentials in complex noise and multiple real damped exponentials in real noise.

Extended version of Van Trees's receiver operating characteristic approximation

Approximate expressions are developed for the receiver operating characteristics (ROCs) of two binary detectors, one based on random-vector observations, the other seeking continuous-time Gaussian signals in white Gaussian noise. The approach used is to extend Van Trees's good-performance-regime results (P/sub F//spl les/0.5, P/sub D//spl ges/0.5) to a much larger ROC range. The accuracy of these approximations is illustrated via an example from the stationary-processes-long-observation-time (SPLOT) regime.

Statistical methods for detecting activated regions in functional MRI of the brain

Two statistical tests for detecting activated pixels in functional MRI (fMRI) data are presented. The first test ( t-test) is the optimal solution to the problem of detecting a known activation signal in Gaussian white noise. The results of this test are shown to be equivalent to the cross-correlation method that is widely used for activation detection in fMRI. The second test ( F test) is the optimal solution when the measured data are modeled to consist of an unknown activation signal that lies in a known lower dimensional subspace of the measurement space with added Gaussian white noise. A model for the signal subspace based on a truncated trigonometric Fourier series is proposed for periodic activation–baseline imaging paradigms. The advantage of the second method is that it does not assume any information about the shape or delay of the activation signal, except that it is periodic with the same period as the activation–baseline pattern. The two models are applied to experimental echo-planar fMRI data sets and the results are compared.

Mobilities of the cercal wind-receptor hairs of the cricket, Gryllus bimaculatus

The deflection sensitivities of cercal filiform hairs of the cricket, Gryllus bimaculatus, were determined by direct measurement. The tangential velocity of deflecting hair shafts in response to stimulus air motion was measured in situ by a laser-Doppler velocimeter with surface scattering of the shaft. The velocity of the stimulus air motion in a small wind tunnel was calibrated by the same velocimeter with smoke from a joss-stick. The mobility of the hair was obtained from former measurements with reference to the latter calibration of the single apparatus. A Gaussian white noise signal was employed as a stimulus waveform, and the stimulus-response transfer function was calculated through a cross-correlation method, which provides greater precision and wider frequency for a longer period of measurement. The mobility of hair was expressed in deflection amplitudes and phase shifts in reference to the velocity sinusoid of a stimulus at various frequencies. The measurements established the following conclusions. The wind receptor hairs comprise an array of mechanical band-pass filters whose best frequencies are inversely proportional to the length. The motion dynamics of the wind-receptor hairs have strong damping.

MMSE estimation of nonlinear parameters of multiple linear/quadratic chirps

An iterative algorithm similar to our MMSE estimation procedure proposed in another paper by the authors is applied to parameter estimation of multiple superimposed chirp signals in white Gaussian noise. The necessary parameter initializations of the procedure are accomplished by peak detections in the Choi-Williams (1981) time-frequency distribution of the data followed by application of the least-squares principle. A comparison between our scheme and the alternating projection (AP) method is demonstrated by computer simulation.

ISOFLURANE ATTENUATES THE SIGNAL TRANSMISSION BETWEEN VAGUS NERVE AND LEFE VENTRICLE IN DOGS

S448 We investigated the effect of isoflurane(ISF) on heart rate control by the external vagal impulse using transfer function analysis. METHODS: 11 dogs weighing 10-18kg, with an approval of the institutional animal care committee were studied. Each dog was anesthetized with alpha -chloralose (75mg/kg/h,iv) and vecuronium bromide (0.2mg/kg, iv) and artificial ventilation was performed throughout the experiment. After exteriorizing the bilateral vagus nerves through a midline neck incision, endogenous parasympathetic activity was blocked in the left vagus by sectioning the nerve and in the right vagus by infiltrating the nerve with 2% lidocaine and a pair of electrodes for vagal stimulation was placed on the right vagus 4cm caudal to the level of lidocaine blockade. In order to stimulate the vagus nerve with a broad-band signal, the waveform applied to the stimulatory electrode was a train of 2ms wide, supramaximal current pulses whose frequency varied about 6Hz in proportion to a Gaussian white-noise signal. Before and during inhalation of either 0.7% or 1.4% of ISF, the electrocardiogram and the stimulation impulse train were simultaneously recorded. Instantaneous heart rate(IHR) and instantaneous stimulation signal rate(SSR) were computed. Spectral analysis for IHR and SSR were estimated by a fast Fourier transform and cross spectrum between IHR and SSR was also obtained, then transfer magnitude and coherence for the relationship between SSR and IHR was calculated. Repeated measures ANOVA followed by Student-Newman-Keuls test was used for statistical analysis. RESULTS: Averaged magnitudes for low frequency component (0.04-0.15Hz,LF), high frequency component(0.15-0.5Hz,HF) and frequency(0.04-0.5Hz, TF), coherences and phases are shown below. (Table 1)Table 1CONCLUSIONS: Isoflurane significantly reduced transfer magnitude between SSR and IHR. Our results may suggest that isoflurane attenuates the signal transmission between vagus nerve and left ventricle.

A lower bound on the error probability for signals in white Gaussian noise

In this correspondence we apply a recent inequality by de Caen (1997) to derive a lower bound on the probability of error for M-ary signals derived from a binary linear code and used on the additive white Gaussian noise channel with a maximum-likelihood decoder. This bound depends only on the weight enumerator of the code and the signal-to-noise ratio E/sub b//N/sub 0/. We show that this bound converges to the union upper bound as E/sub b//N/sub 0/ goes to infinity. Finally, by means of examples, we compare our lower bound with those of Shannon and Swaszek and with Poltyrev's upper bound.

A lower bound on the error probability for signals in white Gaussian noise

The performance of specific signal constellations in digital communications problems is often described through use of the union bound, an upper bound which is asymptotically tight with respect to the signal-to-noise ratio. It is not unnatural to ask how tight this result is for small to medium values of signal-to-noise ratio; one way to answer this question is to develop an asymptotically tight lower bound. Such is the goal of the present paper. >

Dynamics of neurons controlling movements of a locust hind leg: Wiener kernel analysis of the responses of proprioceptive afferents

1. The response properties of proprioceptive sensory neurons providing input to the local circuits controlling leg movements of the locust have been analysed by the Wiener kernel method. The proprioceptor, the femoral chordotonal organ, encodes the position and movements of the tibia about the femorotibial joint. 2. Intracellular recordings were made from sensory neurons while the apodeme of the organ was moved with a band-limited Gaussian white noise signal with a cutoff frequency of 27, 58, or 117 Hz. To define the input-output characteristics of the neurons, the first- and second-order Wiener kernels were computed by a cross-correlation between the spike response of the afferents and the white noise stimulus. 3. White noise stimulation elicited sustained spiking in 50 out of 54 afferents throughout the 20 s periods of stimulation and recording. The first-order kernels, the linear response properties, of these afferents were of six basic types that were dependent on the cutoff frequency of the white noise stimulus. These included 1) flexion-sensitive afferents that were primarily position sensitive irrespective of stimulus frequency, 2) flexion-sensitive afferents that were position sensitive at low frequencies but also coded velocity at higher frequencies, 3) flexion-sensitive afferents that coded velocity at all stimulus frequencies, 4) flexion-sensitive afferents that coded velocity at low stimulus frequencies but also acceleration at high frequencies, 5) extension-sensitive afferents that coded velocity at all stimulus frequencies, and 6) extension-sensitive afferents that coded velocity at low stimulus frequencies and acceleration at high frequencies. A seventh type contained the four remaining afferents that adapted rapidly to the stimulus within 3-5 s. These were all extension-acceleration sensitive irrespective of stimulus frequency. 4. The gain curves (produced by Fourier transform of the 1st-order kernels) and the power spectra of the linear models (produced by convolving the 1st-order kernels with the white noise) demonstrated that responses in the position-sensitive afferents are representative of a constant gain low-pass filter with a cutoff frequency of approximately 80 Hz, whereas those in the velocity- and acceleration-sensitive afferents are band passed, having peaks at 80 Hz. 5. The main nonlinearity was a signal compression in which the diagonal peak(s) of the second-order nonlinear kernels offset one or more peaks of the first-order kernels and represents a rectification or directional sensitivity of the afferents.(ABSTRACT TRUNCATED AT 400 WORDS)

Asymptotic maximum likelihood estimator performance for chaotic signals in noise

The performance of the maximum likelihood estimator for a 1-D chaotic signal in white Gaussian noise is derived. It is found that the estimator is inconsistent and therefore the usual asymptotic distribution (large data record length) is invalid. However, for high signal-to-noise ratios (SNRs), the maximum likelihood estimator is asymptotically unbiased and attains the Cramer-Rao lower bound. >

Methods for chaotic signal estimation

A dynamic programming algorithm and a suboptimal but computationally efficient method for estimation of a chaotic signal in white Gaussian noise are proposed. The nonlinear map is assumed known so that only the initial condition need be estimated. Computer simulations confirm that both approaches produce efficient estimates at high signal-to-noise ratios. >

A filtered EM algorithm for joint hidden Markov model and sinusoidal parameter estimation

Derives finite-dimensional discrete-time filters for estimating the parameters of discrete-time finite-state Markov chains imbedded in a mixture of Gaussian white noise and deterministic signals of known functional form with unknown parameters. The filters that are derived estimate quantities used in the expectation-maximization (EM) algorithm for maximum likelihood (ML) estimation of the Markov chain parameters (transition probabilities and state levels) as well as the parameters of the deterministic interference. Two types of deterministic signals are considered: periodic or almost periodic signals with unknown frequency components, amplitudes, and phases, and polynomial drift in the states of the Markov process with the coefficients of the polynomial unknown. The filter-based EM algorithm has negligible memory requirements. In comparison, implementing the EM algorithm using smoothed variables (forward-backward variables) requires memory proportional to the number of observations. In addition, the filters are suitable for multiprocessor implementation unlike the forward-backward algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Tracking model of an adaptive lattice filter for a linear chirp FM signal in noise

The paper studies the behavior of the partial correlation (PARCOR) coefficients and the output misadjustment of the stochastic gradient adaptive lattice filter in response to a complex linear chirp FM signal in white Gaussian noise. Analytic expressions for the optimal PARCOR coefficients of the filter are derived. Analytic as well as iterative models for a three-stage filter are also derived. The analytic expressions show that the tracking and convergence properties of the filter are separate phenomena. Simulation results also show that the spectral contents of the PARCOR coefficients for the stochastic gradient update algorithm consist of a stationary and a linearly swept component. A single-stage model is developed to explain this behavior. Finally, output misadjustment plots for the filter show that an optimum value for the forgetting factor can be obtained to minimize the misadjustment, but the value required to achieve local minimum misadjustment varies with each stage of the filter. It is shown that in applications where the input has a high signal-to-noise ratio (SNR), the misadjustment decreases rapidly at each successive stage, thus implying that relatively short filter lengths are sufficient to provide effective tracking. >

Response dynamics and directional properties of nonspiking local interneurons in the cockroach cercal system

The response properties and directional receptive fields of nonspiking local interneurons in the cercal system of the cockroach are described. Wind-evoked responses were recorded intracellularly, and then analyzed by means of the Wiener kernel method in which a Gaussian white noise signal was used as a stimulus. Cross-correlation between the response and the white noise signal produced first- (linear) and second-order (nonlinear) kernels that were used to define input-output characteristics of the interneurons. Three sets of interneurons were distinguished on the basis of kernel analysis. First, responses in interneurons 101, 107, 111, and 203 were characterized predominantly by a differentiating first-order kernel, which suggests a linear relationship to the stimulus. The amplitude and waveform of the kernel changed with the change in stimulus angle, indicating that these four cells are directionally sensitive. Second, responses in interneurons 102 and 103 were also directionally sensitive but highly nonlinear. The first-order kernel was biphasic, whereas the second-order kernel had an elongated depolarizing peak on the diagonal. The response dynamics were accounted for by a cascade of two filters, a linear band-pass filter and a static nonlinear filter, in which the nonlinearity is a signal compression (or a rectification). Third, responses in interneurons 104 and 201 consist largely of the second-order nonlinear component. The second-order kernel, which had an elongated depolarizing peak or a hyperpolarizing valley on the diagonal, did not show any directional preference. The second-order nonlinearity was dynamic, and could be modeled by a band-pass linear filter-static nonlinearity-low-pass linear filter cascade, where the static nonlinearity is a full-wave rectification. The band-pass filter would simply reflect the mechanical property of cercal hair sensilla, whereas the low-pass filter represents the transfer at synapses between the cercal afferents and the interneurons. The nonlinear response thus explains the difference in the directional sensitivity while the differentiating first-order kernel explains the velocity sensitivity of the interneurons. We show that 101 and 107 respond most preferentially to wind from the left versus right, whereas 102, 103, 111, and 203 respond to wind from the front versus rear. Thus, it is suggested that there are two subsystems responding maximally to wind displacement along two coordinate directions, one for the longitudinal direction and the other for the transverse direction. On the other hand, the full-wave-rectifier nonlinear interneurons are omnidirectional, and thus suggested to code simply the power of the wind displacement.

Direction Sensitive Broadband Detection of Doppler Shifted Signals in White Gaussian Noise

In this paper a new receiver structure called the Direction Sensitive Detector has been derived for the detection of doppler shifted sonar signals. The receiver is shown to be a modified version of square law or energy detector in which the squaring operations are replaced by cross-correlation between two quadrature components and their Hilbert transformed versions. As a result, the new receiver structure possesses the important properties of indicating the sense of direction of motion of a target with respect to the platform and forming a notch around reverberation frequencies thereby improving the performance in reverberation limited situations. The receiver has been analysed for its performance and receiver operating characteristics have been plotted to compare its performance with that of conventional square law detector.

A fast recursive algorithm for the maximum likelihood estimation of the parameters of a periodic signal

Describes a new recursive algorithm for the estimation of the parameters of a periodic signal in additive Gaussian white noise. These parameters are the period, and the complex amplitudes of the harmonics present. The proposed algorithm is based on recursive maximum likelihood (ML) algorithms for incomplete data as described by Titterington (1985) and others. These algorithms are of complexity O(NM), where N is the number of harmonics, and M is the signal length. The performance of the method is compared to that of the extended Kalman filter with the aid of simulations.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Hidden Markov model signal processing in presence of unknown deterministic interferences

Expectation maximization algorithms are used to extract discrete-time finite-state Markov signals imbedded in a mixture of Gaussian white-noise and deterministic signals of known functional form with unknown parameters. Maximum-likelihood estimates of the Markov state levels, state estimates, transition possibilities, and the parameters of the deterministic signals are obtained. Two types of deterministic signals are considered: periodic, or almost periodic signals with unknown frequency components, amplitudes, and phases; and polynomial drift in the states of the Markov process with the coefficients of the polynomial unknown. The techniques and supporting theory appear more elegant and powerful than ad hoc heuristic alternatives. An illustrative application to extracting ionic channel currents in cell membranes in the presence of white Gaussian noise and AC hum is included. >

Discussion of the Paper by Donoho, Johnstone, Hoch and Stern

Discussion of the Paper by Donoho, Johnstone, Hoch and Stern

A compact Cramer-Rao bound expression for parametric estimation of superimposed signals

The problem of parameter estimation of superimposed signals in white Gaussian noise is considered. Closed-form expressions of the Cramer-Rao bound for real or complex signals with vector parameters are derived, extending recent results by P. Stoica and A. Nehorai (1989).< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Empirical Functionals and Efficient Smoothing Parameter Selection

SUMMARY A striking feature of curve estimation is that the smoothing parameter ĥ 0, which minimizes the squared error of a kernel or smoothing spline estimator, is very difficult to estimate. This is manifest both in slow rates of convergence and in high variability of standard methods such as cross-validation. We quantify this difficulty by describing nonparametric information bounds and exhibit asymptotically efficient estimators of ĥ 0 that attain the bounds. The efficient estimators are substantially less variable than cross-validation (and other current procedures) and simulations suggest that they may offer improvements at moderate sample sizes, at least in terms of minimizing the squared error. The key is a stochastic decomposition of the empirical functional ĥ 0 in terms of a smooth quadratic functional of the unknown curve. Examples include the estimation of densities, regression functions and continuous signals in Gaussian white noise.