China
Africa
Explore chapters and articles related to this topic
Intelligent Sensor Systems
Published in David C. Swanson, ®, 2011
It can be clearly seen in Equation 17.38 that the phases are coupled between the ω1 and 2ω1 terms, the ω2 and 2ω2 terms, and the sum and difference frequency terms. The “phase coupling” is very interesting and clearly shows how the bispectrum in Equation 17.35 can detect such coherence between different frequencies in the spectrum. Normally (i.e., for linear time invariant systems), we expect the phase relationship between Fourier harmonics to be independent, and even orthogonal. Thus, we would expect no “coherence” between different frequencies in a linear signal spectrum. But we do expect bispectral coherence between the phase-coupled frequencies for a signal generated using a nonlinearity. Also note that Gaussian noise added to the signal but not part of the nonlinear filtering will average to zero in the bispectrum. The bispectrum is the feature detector of choice for nonlinear signals.
Some Aspects of Large Deviation Theory
Published in Harish Parthasarathy, Advanced Probability and Statistics: Applications to Physics and Engineering, 2023
We model the signal dynamics as an ARMA process with unknown parameters and cast this dynamics in state variable form. The parameters are assumed to be slowly time varying and hence we use the EKF to estimate both the state and the ARMA parameters over each time slot from noisy signal measurements. From the ARMA parameters over each time slot, we construct an estimate of the slowly time varying spectrum and bispectrum using our knowledge of the variance and skewness of the process noise. The spectrum gives us the set of dominant frequencies present in the signal along with their amplitudes/intensity while the bispectrum yield the relative time delay/phase shift of the signal in each time slot.
Higher-Order Spectrum Coherent Receivers
Published in Le Nguyen Binh, Advanced Digital, 2017
The power spectrum is the Fourier transform of the autocorrelation of a signal. The bispectrum is the Fourier transform of the triple correlation of a signal. Thus, both the phase and amplitude information of the signals are embedded in the triple-correlated product.
Detection and Quantification of Non-Linear Structural Behavior Using Frequency Domain Methods
Published in Research in Nondestructive Evaluation, 2020
The bispectrum appears to be a most useful tool among the frequency domain techniques presented in this paper. The bispectrum provides information regarding the type of nonlinearity (i.e. Asymmetric nonlinearity) present in the structure and also gives the clear-cut information about the cross-coupling of various frequencies. It is also found to be less sensitive to measurement noise. Conversely, a higher order spectrum, such as trispectrum is helpful to investigate symmetric non-linearity in the system. Even though coherence also gives this frequency information it is difficult to read directly from the coherence plot, unlike bispectrum plots and may require further analysis. The Quadratic nonlinearity index based on bispectrum is used to quantify the severity of nonlinearity in the system. Further, Bispectrum can work with ambient vibration data and requires only a single sensor data, can be used as an effective nonlinear indicator in the case of systems with limited measurement.
A time-varying wavelet phase extraction method using the wavelet amplitude spectra
Published in Systems Science & Control Engineering, 2018
Peng Zhang, Yong-shou Dai, Yong-cheng Tan, Hongqian Zhang, Chunxian Wang
The bispectrum is the Fourier transform of the third-order cumulant of the signal. The third-order cumulants of the seismogram can be expressed as follows: where the symbol E represents the mathematical expectation. Then, is processed by Fourier transformation, and the bispectrum of the seismogram can be expressed as follows: can also be described by equation (16) according to the relationship among the seismogram, the reflection coefficient sequence and the seismic wavelet: where and are the bispectra of the reflection coefficient sequence and the seismic wavelet, respectively. According to the literature (Matsuoka & Ulrych, 1984),, so equation (16) can also be expressed as follows: where and are the amplitude and phase spectra of the bispectrum of the seismogram, respectively, and , where , and are the frequency spectrum, the amplitude spectrum and the phase spectrum of the seismic wavelet, respectively. Thus, the relationship between the phase spectrum of the bispectrum of the seismogram and the phase spectrum of the seismic wavelet can be expressed as follows: By using equation (18), the initial phase spectrum of the wavelet can be estimated from the bispectrum of the seismogram.