Q-Markov Cover identification using pseudo-random binary signals

An Algorithm for Iterative Identification and Control Design using an Improved Q-Markov Cover

Maximum likelihood estimation of a nonparametric signal in white noise by optimal control

An application of the wavelet transform to electrocardiography is described in the paper. To detect the weak signals buried in noises is a fundamental and important problem. The proposed technique is based on the decomposition of the ECG signal into a set of basic functions covering the time- frequency domain. It has been found that digital filters are not suitable for processing weak signals in noises, while discrete wavelet transform (DWT) is used to analyze weak digital signal and extract small-features. In this paper, a new procedure is proposed, called sub-band filter. The performance for our method is investigated by detecting the ECG signal in white noise. The results show that the DTW is a quite effective method for the extraction features of weak signal and improving the ratio of signal to noise.

This paper presents a general approach to solving the problem of defining the time of arrival of a signal in the noise, or the similar one of defining the position of a peak in a histogram. In particular, it solves the problem of a signal in white noise, giving the well know result that the optimum filter before a zero crossing discriminator should have an impulse response function equal to the derivative of the waveform to be observed. It then solves the problem of estimating the position of a peak in a histogram in which the number of counts in each bin has a variance equal to the number of counts in that same bin. The resulting optimum filter is the derivative divided by the function itself. Examples of applying the results are given and the un iqueness of the solution to the set of non-linear simultaneous equations resulting from the problem is demonstrated.

The detectability of a pulsed sinusoidal signal in white noise was studied as a function of frequency for three signal durations (1000, 100, and 10 msec). For the two longer signal durations the data are consistent with results obtained in previous experiments; the results obtained with the shortest duration are not. At the higher frequencies the 10 msec signal is easier to hear than either the 100 or 1000 msec signal. At low frequencies the 10 msec signal is easier to hear than the 1000 msec signal but not the 100 msec signal. This interaction of signal frequency and signal duration somewhat complicates the problem of developing a simple model to account for the influence of signal duration on signal detectability. (This research was conducted at the Electronic Defense Group, University of Michigan, under a U. S. Air Force contract monitored by the Operational Applications Laboratory.)

Recent results on joint detection-estimation for discrete data are extended to the continuous data case for Gaussian signals in White Gaussian noise. Stochastic differential equations are obtained describing the temporal evolution of the sufficient statistic for minimum Bayes-risk detection and the optimal mean-square error estimate of the signal state vector. An approximate solution for the estimation equation is suggested.

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 (SNR's), the maximum likelihood estimator is asymptotically unbiased and attains the Cramér-Rao lower bound (CRLB). © 1995 IEEE

Pulsars are the most stable natural frequency standards. They can be applied to a number of principal problems of modern astronomy and time-keeping metrology. The full exploration of pulsar properties requires obtaining unbiased estimates of the spin and orbital parameters. These estimates depend essentially on the random noise component being revealed in the residuals of time of arrivals (TOA). In the present paper, the influence of low-frequency ("red") timing noise with spectral indices from 1 to 6 on TOA residuals, variances, and covariances of estimates of measured parameters of single and binary pulsars are studied. In order to determine their functional dependence on time, an analytic technique of processing of observational data in time domain is developed which takes into account both stationary and non-stationary components of noise. Our analysis includes a simplified timing model of a binary pulsar in a circular orbit and procedure of estimation of pulsar parameters and residuals under the influence of red noise. We reconfirm that uncorrelated white noise of errors of measurements of TOA brings on gradually decreasing residuals, variances and covariances of all parameters. On the other hand, we show that any red noise causes the residuals, variances, and covariances of certain parameters to increase with time. Hence, the low frequency noise corrupts our observations and reduces experimental possibilities for better tests of General Relativity Theory. We also treat in detail the influence of a polynomial drift of noise on the residuals and fitting parameters. Results of the analitic analysis are used for discussion of a statistic describing stabilities of kinematic and dynamic pulsar time scales.

Optimal detection of a known FSK-modulated binary signal in additive white Gaussian noise using a matched filter receiver requires knowledge of second-order noise statistics. The dependence on noise statistics causes the probability of detection to be sensitive to errors in the noise variance value. This makes the optimal scheme of limited use in situations where the noise statistics are unknown and cannot be estimated reliably. We propose an alternative approach, which has a more easily calculated test statistic than the optimal method and yields a constant false detection rate, regardless of noise statistics. While this approach has sub-optimal detection probability, it is significantly advantageous in applications where a primary interest is to limit false detections strictly. In addition, it allows one to determine easily the required detection length (in symbols) to achieve a desired performance level.

A designing system for adaptively characterizing an audio transmitting system has a white noise generating unit for generating a white noise signal. A speaker radiates the white noise generated by the white noise generating unit into an acoustic space. A microphone is placed at a predetermined position in the acoustic space and collects sound radiated from the speaker. A FIR adaptive filter receives the above white noise signal. An LMS algorithm processing unit updates each tap coefficient of the adaptive filter by using the LMS algorithm. A computation unit calculates the difference between a detection signal output from the microphone and an output of the adaptive filter and outputs the difference as an error signal e. By using a white noise signal having an average power of one, the range of the step size parameter of the LMS algorithm required for stably operating the adaptive filter is fixed. According to the method for characterizing the audio transmitting system and the method for setting an audio filter, the stable operation of the adaptive filters is ensured without increasing the complexity of the overall system.

This paper outlines some of signal analysis methods based on deterministic data models. These models assume the data consists of a small number of deterministic components embedded in noise. As with all model based signal processing the performance of the methods described herein critically depends upon the accuracy of the underlying model. If the model chosen is appropriate for the data measured then excellent results can be obtained. However, use of an inappropriate model can, at best, be suboptimal and possibly produce misleading results. It is concluded that, for the problem of estimating the frequencies of sinusoidal signals in white noise, there is a wide variety of methods available (only a very limited subset have been dealt with herein). The Fourier transform gives near optimal results if only one sinusoid is present or if the signals are well separated. In other circumstances probably the most desirable method is that of maximum likelihood, however, the required non-linear optimisation is tedious. The iterative formulation of this method offers a more feasible approach and should be considered. The eigen based methods, such as MUSIC, offer a more palatable alternative, by sacrificing some performance to reduce the problem to one dimension.

We consider the discrete-time detection of a known time-varying deterministic signal in white noise, where the univariate noise density is known perfectly only on an interval about the origin. We present a method to enhance the asymptotic performance of the detector by exploiting this knowledge, and at the same time preserve robustness properties of the detector to the remaining inexact knowledge of the univariate noise density. We then provide examples to show that improved performance is indeed obtained.

The 1/f family of fractal processes provides useful models for the extraordinary variety of natural and man-made phenomena that exhibit long-term dependence. Using algorithms based on a multiscale-state-space representation, we address the problems of parameter estimation of discrete 1/f signals in white noise, estimation of deterministic signals in 1/f noise, and prediction of discrete 1/f processes. Among other results, distant past data are shown to have a dramatically greater effect on these estimators than when ARMA processes are involved.

A simple multiple cross-correlations phase delay method (MCC) for unbiased estimation of the phase-shift between two real sinusoidal signals in white noise is proposed. The estimator removes the bias of the correlation methods and enhances the signal-to-noise ratio (SNR) by utilizing multiple cross-correlations of the real signals. The results obtained by MCC in simulations and on real samples are given. A comparison between the phase delay results estimated by MCC, general cross correlation (GCC) method, quadrature delay estimator (QDE), unbiased QDE (UQDE), Sliding Goertzel algorithm (SGA), and discrete-time Fourier transform (DTFT) algorithm is presented. Computer simulations and field test results validate the effectiveness of the proposed method (MCC).

A method for model reduction of linear discrete systems is proposed. It is based on the impulse-response Gramian proposed by the authors (1989) for discrete systems. This Gramian is an extension of the one proposed for linear continuous systems and contains information on the input-output behavior of the system. The rth-order reduced-order models are made to retain the first r Markov parameters and the first r*r elements of the impulse-response Gramian of the original system. The relation between this method and the q-Markov cover method is also discussed. The method is illustrated by a numerical example. >