Time delay estimation using the cross bispectrum

The cross bispectrum phase can be effectively used to estimate the time required for a nonGaussian signal to propagate between a pair of spatially separated sensors in the presence of highly correlated Gaussian noise. The authors present a consistent estimator of the phase of the cross bispectrum, derive the exact distribution of the phase of a complex Gaussian sample bispectrum, and show that in most cases the exact distribution can be approximated by a Gaussian distribution. Using this Gaussian approximation, the authors derive the variance of the time delay estimate computed from the sample cross bispectrum of a signal in additive correlated noise. These results allow the performance of time delay estimators based on the cross bispectrum phase to be quantified as a function of the sample size, the skewness of the signal, the signal-to-noise ratio (SNR), and the noise correlation     

Bearing estimation in the bispectrum domain

A new array processing method is presented for bearing estimation based on the cross bispectrum of the array output data. The method is based on the asymptotic distribution of cross-bispectrum estimates and uses maximum likelihood theory. It is demonstrated that, when the noise additive sources are spatially correlated Gaussian with unknown cross-spectral matrix (CSM), the cross-bispectrum method provides better bearing estimates than the stochastic maximum likelihood method with known CSM. Analytical studies and simulations are given to document the performance of the new method     

Feasibility study of parameter estimation of random sampling jitter using the bispectrum

An actual sampling process can be modeled as a random process, which consists of the regular (uniform) deterministic sampling process plus an error in the sampling times which constitutes a zero-mean noise (the jitter). In this paper we discuss the problem of estimating the jitter process. By assuming that the jitter process is an i.i.d. one, with standard deviation that is small compared to the regular sampling time, we show that the variance of the jitter process can be estimated from thenth order spectrum of the sampled data,n=2, 3, i.e., the jitter variance can be extracted from the 2nd-order spectrum or the 3rd-order spectrum (the bispectrum) of the sampled data, provided the continuous signal spectrum is known. However when the signal skewness exceeds a certain level, the potential performance of the bispectrum-based estimation is better than that of the spectrum-based estimation. Moreover, the former can also provide jitter variance estimates when the continuous signal spectrum is unknown while the latter cannot. This suggests that the bispectrum of the sampled data is potentially better for estimating any parameter of the sampling jitter process, once the signal skewness is sufficiently large.     

Improved bispectrum estimation based on modified group delay

This article proposes an improved estimation method for the bispectrum of a system or signal, by applying the modified group delay (MMGD) in the bispectrum domain. To achieve a higher frequency resolution, the bispectrum is computed in frequency domain and further to reduce the variance preserving the frequency resolution, MMGD is applied in the bispectrum domain. The proposed method due to its better frequency resolution not only properly detects the phase coupled frequencies but also reduces the bispectrum magnitude estimate’s variance significantly compared to that of biperiodogram. Compared to the proposed method, though the windowed bispectrum (WB) provides a better reduction in variance, it is unable to detect the coupled frequencies due to its poor frequency resolution. For an AR process in the presence of noise (SNR = 4 dB), the system magnitude estimate by the proposed method has a 27.63% lower normalized sum sample mean square error (NSSMSE) than that by the WB. Also for a non-minimum phase system in presence of noise (SNR = 7 dB), the phase estimation by the new approach has 8.6% lower NSSMSE than that by WB and also it is marginally better than that obtained by applying MMGD in system group delay domain.     

Waveform estimation from noisy signals with variable signal delayusing bispectrum averaging

A technique based on bispectrum averaging is described for generally recovering the signal waveform from a set of noisy signals with variable signal delay. The technique does not require explicit time alignment of signals and any initial estimate of signal. The technique, however, does not yield estimates of the signal position. A comparison is made of two algorithms for recovering the Fourier amplitude and the Fourier phase from an averaged bispectrum. These algorithms are the recursive method and the least squares method. The methods are numerically investigated using computer-generated data and a physiological signal and noise. The advantages and disadvantages of these different algorithms are discussed. Some experimental results for the evoked potential studies that demonstrate the technique are given. The results show the effectiveness of the technique: various potential applications of the technique might be expected     

Improved phase estimation based on complete bispectrum and modified group delay

In this paper, a new method for extracting the system phase from the bispectrum of the system output has been proposed. This is based on the complete bispectral data computed in the frequency domain and modified group delay. The frequency domain bispectrum computation improves the frequency resolution and the modified group delay reduces the variance preserving the frequency resolution. The use of full bispectral data also reduces the variance as it is used for averaging. For the proposed method at a signal to noise ratio of 5dB, the reduction in root mean square error is in the range of 1.5–7 times over the other methods considered.     

双谱估计在导引头信号检测与处理中的应用

双谱估计是一种应用广泛的高阶谱估计。将双谱估计应用于超宽带导引头信号检测与处理系统中,为导引头信号处理中的平滑和滤波增添了一种新的方法。仿真结果表明该方法是有效的。     

A Robust hierarchical motion estimation algorithm in noisy image sequences in the bispectrum domain

The present study describes a robust hierarchical motion estimation algorithm in noisy image sequences using the bispectrum. The motion can be characterized by an affine model and the parameters of an affine motion model are estimated by means third-order auto-bispectrum and cross-bispectrum measures. The basic components of this framework to obtain motion vectors are (i) pyramid construction, (ii) motion estimation and (iii) coarse-to-fine refinement. The entire motion is decomposed as a global and a local motion field, which helps accurately obtain high resolution estimates for the local motion field. Simulation results are presented and compared to those obtained from the phase correlation algorithm. The results demonstrate that the proposed method is more suited than the phase correlation algorithm to analyses complex noisy image sequences. On the other hand, our method produces smoother displacement vector field with a more accurate measure of object motion in different signal-to-noise ratio scenarios.     

Statistical approach to quantify the presence of phase coupling using the bispectrum

The bispectrum is a method to detect the presence of phase coupling between different components in a signal. The traditional way to quantify phase coupling is by means of the bicoherence index, which is essentially a normalized bispectrum. The major drawback of the bicoherence index (BCI) is that determination of significant phase coupling becomes compromised with noise and low coupling strength. To overcome this limitation, a statistical approach that combines the bispectrum with a surrogate data method to determine the statistical significance of the phase coupling is introduced. Our method does not rely on the use of the BCI, where the normalization procedure of the BCI is the major culprit in its poor specificity. We demonstrate the accuracy of the proposed approach using simulation examples that are designed to test its robustness against noise contamination as well as varying levels of phase coupling. Our results show that the proposed approach outperforms the bicoherence index in both sensitivity and specificity and provides an unbiased and statistical approach to determining the presence of quadratic phase coupling. Application of this new method to renal hemodynamic data was applied to renal stop flow pressure data obtained from normotensive (N = 7) and hypertensive (N = 7) rats. We found significant nonlinear interactions in both strains of rats with a greater magnitude of coupling and smaller number of interaction peaks in normotensive rats than hypertensive rats.     

Phase spectrum method for time delay estimation using twin-plane electrical capacitance tomography

Flow velocity distribution can be measured by means of a twin-plane tomography system and cross-correlation techniques. However, the use of these techniques based on finding the argument that maximises an estimated cross-correlation function (CCF) of corresponding pixels from two planes, in practice is limited by their low accuracy in reconstructed concentration. Presented is a method permitting the time delay to be measured with higher accuracy. The method is based on utilising the phase of the cross-spectral density of the CCF to estimate a time delay. The method is found to be more promising than the classical correlation method.     

The bispectrum of sampled data. II. Monte-Carlo simulations ofdetection and estimation of the sampling jitter

For pt.I see IEEE Trans. Acoust. Speech, Signal Process., vol.41, no.1, p.296-312 (1993). The effect of jitter in sampling on the spectrum and bispectrum of the sampled data has been considered previously. Methods of detecting the presence of jitter in a uniform sampling process and of estimating its variance based on a test statistic calculated from the bispectrum estimates have been proposed. The present authors demonstrate, by means of Monte-Carlo simulations, how these results can be applied in an actual case. For this purpose, samples taken from a stationary band-limited process in sampling times given by a random jitter process are generated by computer. The authors then apply the jitter detection and estimation methods that have been developed in previous work and study how their performance depends on signal duration and on jitter variance. They examine the actual simulation results concerning detection probability, estimation bias, and estimation variance in comparison with the theoretical results. This comparison indicates that the bispectrum is a domain where jitter detection and estimation with high performance can be achieved, provided that a signal with sufficiently long duration and high skewness is available     

Phase estimation of visual evoked responses

The phase of visual evoked responses (VERs) is one of the basic parameters in functional diagnostics of the visual system. A new method for phase estimation of VERs based on the observer model in system identification is introduced. Simulated data show significantly less variance of estimation than actual estimators do. By means of the new estimator, the dynamics of the visual system according to selected optical stimuli has been analyzed.     

Signal reconstruction from the phase of the bispectrum

The authors present a simple procedure, the bispectrum signal reconstruction (BSR) algorithm, to recover the Fourier phase of a signal from the phase of its bispectrum. By simple analogy, a procedure that recovers the Fourier magnitude of a signal from the magnitude of its bispectrum is also presented. In addition, the authors propose an iterative scheme, the bicepstrum iterative reconstruction algorithm (BIRA), for the reconstruction of a finite impulse response (FIR) sequence from only the phase of its bispectrum, and they demonstrate how some a priori information on the energy of the cepstra coefficients can improve significantly the convergence rate of the algorithm. Both schemes are based on the key observation that the differences of the bispectrum coefficients contain all the information concerning the Fourier phase of the signal, whereas their sums contain the Fourier-magnitude information     

Modified Wigner bispectrum and its generalizations

The Wigner bispectrum of multicomponent signals is studied, and its modified and reduced forms are introduced. A generalization of the presented forms to the Wigner higher-order spectra (WHOS), in the case of multicomponent signals, is provided. From our previous work it is known that cross terms removal (reduction) is possible for odd-order spectra with equal numbers of conjugated and nonconjugated terms. Here, we extend the analysis to even-order spectra. The theory is illustrated by examples.     

Phase estimation characteristics of ultra-wideband quasi-radio signal

Synthesis and analysis of the maximum likelihood algorithm for estimating the phase of ultra-wideband quasi-radio signal with unknown amplitude and phase are performed. Duration of the specified signal may amount to several periods or a fraction of the period of harmonic oscillation. Characteristics of the classical maximum likelihood phase estimate of a narrow-band radio signal are found when receiving an ultra-wideband quasi-radio signal. Applicability conditions of narrow-band radio signal model are defined for solving the problem of phase estimation with the specified accuracy.     

Phase estimation in data channelization for video transmitting

Channelization is one of the important techniques for sharing a single physical channel among the multiple videos. In channelization, the videos are partitioned into segments and the bandwidth of the physical channel is partitioned into logical channels. The first segment of each video is transmitted through the first logical channel, the second segment of each video is transmitted through the second logical channel, and so forth. The segments are transmitted periodically through the logical channels. In this paper, the video signals to be transmitted through the logical channels are estimated. Furthermore, the phase is estimated in terms of jitter delays that occur among the video segments, while transmitting them through the logical channels. The phase is an important parameter in video communication latency. Using the phase, the group delay can be estimated and based on the group delay, the storage space required at the client’s site can be determined so that the continuous and jerk-free delivery of the videos is provided to the users.     

Natural scene-illuminant estimation using the sensor correlation

This paper describes practical algorithms and experimental results concerning illuminant classification. Specifically, we review the sensor correlation algorithm for illuminant classification and we discuss four changes that improve the algorithm's estimation accuracy and broaden its applicability. First, we space the classification illuminants evenly along the reciprocal scale of color temperature, called "mired," rather than the original color-temperature scale. This improves the perceptual uniformity of the illuminant classification set. Second, we calculate correlation values between the image color gamut and the reference illuminant gamut, rather than between the image pixels and the illuminant gamuts. This change makes the algorithm more reliable. Third, we introduce a new image scaling operation to adjust for overall intensity differences between images. Fourth, we develop the three-dimensional classification algorithms using all three-color channels and compare this with the original two algorithms from the viewpoint of accuracy and computational efficiency. The image processing algorithms incorporating these changes are evaluated using a real image database with calibrated scene illuminants     

An empirical bispectrum model for sea surface scattering

The properties of a surface bispectrum are found by generating a skewed surface on a digital computer and then evaluating its correlation function, bicoherence function, power spectrum, and bispectrum. The bispectrum is defined to be the Fourier transform of the bicoherence function. It is found that the surface bicoherence function and its first and second derivatives must all vanish at the origin. In general, the surface bispectrum is a complex function. Its real part is centrosymmetric, just like the surface spectrum, and its imaginary part is antisymmetric. A function with the above-stated properties is introduced to represent the imaginary part of the sea surface bispectrum. The unknown parameter in this function is calibrated using a data set from the FASINEX experiment. The sea surface backscattering model is based on an integral equation model which accounts for frequency, polarization, incident angle, azimuthal angle, and wind speed. It is found that the proposed bispectrum can be used to account for the up/down wind asymmetry