Polarity Coincidence Correlator Research Articles

Robust Speech Filter and Voice Encoder Parameter Estimation Using the Phase–Phase Correlator

In recent years, linear prediction voice encoders have become very efficient in terms of computing execution time and channel bandwidth usage while providing, in the absence of impulsive noise, natural sounding synthetic speech signals. This good performance has been achieved via the use of a maximum likelihood parameter estimation of an auto-regressive model of order ten that best fits the speech signal under the assumption that the signal and the noise are Gaussian stochastic processes. However, this method breaks down in the presence of impulse noise, which is common in practice, resulting in harsh or non-intelligible audio signals. In this paper, we propose a robust estimator of correlation, the Phase-Phase correlator that is able to cope with impulsive noise. Utilizing this correlator, we develop a Robust Mixed Excitation Linear Prediction encoder that provides improved audio quality for voiced, unvoiced, and transition speech segments. This is achieved by applying a statistical test to robust Mahalanobis distances for identifying the outliers in the corrupted speech signal, which are then replaced with filtered signals. Simulation results reveal that the proposed estimator of correlator outperforms in variance, bias, and breakdown point compared to three other robust approaches based on the arcsin law, the polarity coincidence correlator, and the median-of-ratio estimator without sacrificing the encoder bandwidth efficiency and the compression gain while remaining compatible with real-time applications. Furthermore, in the presence of impulsive noise, the proposed speech encoder speech subjective quality outperforms the state-of-the-art in terms of mean opinion score.

Polarity Coincidence Correlator

The construction of a clipped correlator using a polarity coincidence multiplier is deseribed. Subjective measurement taken indicate that the equipment is well suited for signal detection especially when the background noise level is very high.

On The Positive Definiteness of Polarity Coincidence Correlation Coefficient Matrix

Polarity coincidence correlator (PCC), when used to estimate the covariance matrix on an element-by-element basis, may not yield a positive semi-definite (PSD) estimate. Devlin et al. [1], claimed that element-wise PCC is not guaranteed to be PSD in dimensions p>3 for real signals. However, no justification or proof was available on this issue. In this letter, it is proved that for real signals with p<=3 and for complex signals with p<=2, a PSD estimate is guaranteed. Counterexamples are presented for higher dimensions which yield invalid covariance estimates.

Activity detection in a multi-user environment

The detection of a weak stochastic signal in multi-variate impulsive noise is investigated. The signal is that of a new user in a Code-Division Multiple-Access multi-user system. A particular type of transformation noise is considered: the trasmitted signal vector is modified by a linear transformation prior to signal detection thereby yielding a signal process and noise process that are dependent from component to component of the recieved vector. The linear operator is designed to combat multiple-access interference. The effect of such a transformation is studied by deriving the efficacies and asymptotic relative efficiencies of several detectors. Both linear and non-linear cross-correlator detector structures are examined. The performance of the detectors is determined for two types of non-Gaussian noise: additive channel noise and residual multiple-access interference noise. The numerical results are consistent with previous findings and motivate the investigation of a hybrid detector which is composed of a combination of the linear correlator and the polarity coincidence correlator. The asymptotic normality of the test statistics under study is also investigated.

Nonparametric Hard Limiting and Sign Detection of Narrow-Band Deterministic and Random Signals

Hard limiting or sign detection schemes for low-pass known and random signals in additive noise are popular as very simple signal detectors maintaining constant values for their false-alarm probabilities under the rather weak assumption that the sampled noise observations have zero median values. For nonparametric detection of narrow-band signals the natural extension of the zero medians assumption is the zero marginal medians assumption on the in-phase and quadrature noise components. Nonparametric detectors operating under this assumption are developed here for narrow-baud signals; these can be taken to be the logical counterparts of the low-pass sign correlator and polarity coincidence correlator detectors of low-pass theory. The concept of conditional testing, which has been applied previously to obtain efficient multilevel versions of low-pass sign detection schemes, is shown to enter quite naturally in the definition of narrow-band counterparts of the sign correlator and the polarity coincidence correlator detectors. It is also shown that under the diagonal symmetry extension of the low-pass univariate symmetry condition on the noise probability density function, multilevel extensions of these conditional test narrow-hand detectors may also be defined as counterparts of the multilevel conditional test schemes for low-pass signals.

The polarity coincidence correlator: Significance testing and other issues

The polarity coincidence correlator (PCC) is a useful nonparametric measure of correlation. In this paper, an error is pointed out in the significance test given by Cochran and Gibson (1977). Some further theoretical and practical issues are mentioned pertaining to the use of PCC with physiological waveforms; in particular, problems relating to autocorrelation and the definition of the sampling unit are discussed.

On a fast digital method of estimating the autocorrelation of a gaussian stationary process

The zero-mean stationary Gaussian processes have the property that if they are input into an instantaneous nonlinear device, the cross correlation of input and output is proportional to the auto-correlation of the input. This suggests an estimation procedure for the autocorrelation function based mainly on additions, which is a modified type of the PCC (polarity coincidence correlator). The object of this paper is to compute the bias and the variance of such an estimator and to discuss some fundamental properties. As a reference, some examples are provided which compare the behavior of the modified PPC estimator to the classical one based on products and additions.

Approximate expressions for the output signal-to-noise ratios for two types of cross correlators with correlated bandpass inputs

Thus far, analytical expressions have not been developed for the output signal-to-noise ratio of a polarity coincidence correlator when the noise is correlated between the input channels. Approximate expressions are developed here for the output signal-to-noise ratios for two types of cross-correlator systems- one being the polarity coincidence correlator with a hard limiter in each input channel and the other variation of this correlator having a hard limiter in only one input channel. The approximation scheme is based upon the known output signal-to-noise characteristics of a limiter and that of the standard analog correlator with no limiters. The derived expressions are applicable for the case of deterministic sine waves plus narrow-band Gaussian noise in each input channel, where the noise between channels may be correlated For the case of uncorrelated noise between input channels, good agreement is found between the approximate formulas and known exact results. Finally, asymptotic expressions are developed for certain limiting cases of input signal-to-noise ratios having extreme values in one or both input channels.

A theoretical and experimental comparison of output signal-to-noise ratios of three types of cross correlators

The output signal-to-noise ratio as a function of input signal-to-noise ratios is compared for three different types of cross-correlators: 1) the standard analog cross correlator consisting of bandpass filters, multiplier, and low-pass filter; 2) the polarity coincidence correlator (PCC) which incorporates hard limiters in each analog input channel; and 3) a modified type of PCC wherein only one of the analog channels utilizes a hard limiter. Some of the previous theoretical work on the PCC is extended to include new expressions for the output signal-to-noise ratio from which computations can more readily be made. In addition, discrete circuits were fabricated that closely approximate idealized elements so as to experimentally verify the theoretical results. In almost all cases tested, the experimental results were in close agreement with the math models.

High-speed digital cross-correlator design for multifrequency response analysis

Two new cross-correlator designs are presented capable of dealing with the requirements for multifrequency response analysis. One is a modified relay correlator, the other a modified polarity coincidence correlator.

Analysis of a cross correlator with a clipper in one channel (Corresp.)

General expressions are derived for the characteristic function and probability density function of the output of a cross crrelator utilizing a hard clipper in one input channel. The inputs are assumed to be <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_{1} \cos(\omega_{o}t)+n_{l}(t)</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A_{2} \cos(\omega_{o}t+\phi)+n_{2}(t)</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n_{1}</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n_{2}</tex> are independent narrowband Gaussian noises. From the characteristic function, which is expressed in the form of a Fourier series in the relative phase angle <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\phi</tex> , a double series involving cosines of multiples of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\phi</tex> and Hermite polynomials of all orders is obtained as the probability density function of the output. Both the characteristic function and the density function pertain to the output at only a single instant of time. The first and second moments of the output are also calculated from the characteristic function, and lead to a closed-form expression for the output signal-to-noise ratio as a function of the input signal-to-noise ratios. Limiting cases of the output signal-to-noise ratio are computed and compared with similar cases involving the more conventional analog correlator without clippers and with the polarity-coincidence correlator.

Three-level coincidence-correlator detectors

Nonparametric three-level coincidence-correlator (CC) detectors are considered for the detection of random signals in noise in two-input systems. Based on the maximum-efficacy criterion the structure of the optimum detector is obtained, together with the corresponding efficacy. The results allow the evaluation of practical detection schemes in this class of detectors, in terms of their performance relative to the constrained optimum and to the unconstrained optimum three-level CC detector. Some specific three-level CC detectors which are simple extensions of the polarity coincidence correlator are examined and a numerical comparison is made for Gaussian noise.

A Simple Nonparametric Test for Correlation

The polarity coincidence correlator (PCC), a nonparametric hypothesis testing procedure, is presented as an alternative to the Pearson product-moment correlation coefficient (r). Previous theoretical results indicate that the PCC statistic should be inferior to the correlation coefficient when the data are normal, but it may outperform r for non-normal data with a highly peaked probability density function. Application of the PCC to a human factors experiment is illustrated. For this particular application, the PCC performance compares favorably to the product-moment correlation test when the data are normal and exceeds that of the correlation test for non-normal data. The results, combined with the ease of PCC computation, support the PCC as a promising test for human factors experimentation.

Improved non-parametric coincidence detectors

Simple extensions of the polarity–coincidence correlator (PCC) for non-parametric detection of a common random signal in two-input systems are considered. The new detectors are based on conditional tests and are shown to be capable of a better performance than the PCC. For the case of Gaussian noise, substantial improvement in performance over that of the PCC is established.

Estimation and reduction of errors in flow measurements which use cross-correlation techniques

Propagation of inherent inhomogeneities or tracers in flowing liquids is used to measure flow. The peak value obtained from a cross-correlation analysis of downstream and upstream sensor signals is used to determine the tracer transit time and hence the flow. Performance of a “clamp-on” ultrasonic cross-correlation flowmeter developed by Canadian General Electric under contract from Atomic Energy of Canada Limited (AECL) was evaluated at the Chalk River Nuclear Laboratories of AECL. During this work, the effects of: (1) cross-correlation parameters, (2) filtering of correlator output and (3) use of an add-only polarity coincidence correlator on the standard deviation of transit time measurements were investigated both theoretically and experimentally. Comparison of ultrasonic cross-correlation flowmeter readings against gravimetric flow measurements gave a standard deviation of 2% of reading.

The Action of Dither in a Polarity Coincidence Correlator

An analysis has been made of how dither added to the input of a polarity coincidence correlator eliminates capture of a weak signal by an unwanted signal. For certain interfering environments the output signal-to-noise ratio of various correlators with three specific input dithers is analyzed. The correlators considered were a polarity coincidence correlator with: 1) no dither, 2) dither of random, amplitude uniformly distributed between the chosen plus-and-minus peak values, 3) sinusoidal dither, and 4) Gaussian dither. Each correlator was analyzed for the cases of Gaussian-noise, rectangular-wave, and sinusoidal interference and compared with the classical correlator. The choice of dither amplitude based upon the measured value of the noise power was studied. A uniformly distributed dither is shown to be slightly superior to sinusoidal dither, and both superior to Gaussian noise.

Sequential Phasemeters

The synthesis and the analysis of the sequential phasemeter based on the polarity-coincidence correlator is described. This phasemeter is devoted to harmonic signal phase-difference measurement in the presence of large random disturbances at the given-accuracy. The realization of the sequential phasemeter and some approximations that seem to be useful are presented as well.

Modified digital correlator and its estimation errors

The method of using auxiliary random noise to unbias the output of the multilevel digital correlator is investigated. It is shown that any random noise satisfying certain conditions may be used. The uniformly distributed noise that has been used previously in the polarity-coincidence correlator is a special case. Discretely distributed auxiliary noise, although not satisfying the conditions, has the same effect as quantizing the input signals more finely. The mean-square error of this modified digital correlator is analyzed.

Fluid flow measurements inside the reactor vessel of the 50 MWe Dodewaard nuclear power plant by cross-correlation of thermocouple signals

The determination of fluid flow velocities with conventional equipment is sometimes impossible owing to extreme environmental conditions or unacceptable disturbance of the flow pattern and increase in flow resistance. Transit time analysis of fluctuations in water temperature, pressure, radioactivity, etc., using suitable detecting elements can then still often be applied. In the downcomer region of the reactor system of the 50 MWe Dodewaard boiling water reactor with natural circulation, 30 pairs of fast response thermocouples are used to detect temperature fluctuations in the turbulent flowing water. After amplification and filtering, the signals of each thermocouple pair are fed into a multipoint polarity coincidence correlator to form the cross correlation function C12 (kΔτ). From this function the mean transit time τ1 of the temperature fluctuations to cover the distance l between the thermocouples is easily found. Then the local velocity follows from the simple relation VH2O = 1/τ1. The applied method has proved very useful in the determination of local fluid velocities in the range 0·15-1·50 m s−1. From these local measurements radial and axial velocity profiles and total recirculation flow can be derived.

Distance measures and asymptotic relative efficiency

The relationship between distance measures and asymptotic relative efficiency is discussed. It is shown that the ratio of the Bhattacharyya distance or <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">J</tex> divergences of two test statistics is equivalent to asymptotic relative efficiency. Two-input systems are discussed as examples, and the performances of the polarity coincidence correlator (PCC) and the correlator are discussed in terms of the distance measures of reduced data.