A technique for the cross spectrum analysis of pairs of complex-valued time series, with emphasis on properties of polarized components and rotational invariants

1973 ◽  
Vol 20 (12) ◽  
pp. 1129-1141 ◽  
Author(s):  
Christopher N.K. Mooers
1995 ◽  
Vol 88 (6) ◽  
pp. 651-655 ◽  
Author(s):  
Michel Ducher ◽  
Jean Pierre Fauvel ◽  
Marie Paule Gustin ◽  
Catherine Cerutti ◽  
Robert Najem ◽  
...  

1. A new method was developed to evaluate cardiac baroreflex sensitivity. The association of a high systolic blood pressure with a low heart rate or the converse is considered to be under the influence of cardiac baroreflex activity. This method is based on the determination of the statistical dependence between systolic blood pressure and heart rate values obtained non-invasively by a Finapres device. Our computerized analysis selects the associations with the highest statistical dependence. A ‘Z-coefficient’ quantifies the strength of the statistical dependence. The slope of the linear regression, computed on these selected associations, is used to estimate baroreflex sensitivity. 2. The present study was carried out in 11 healthy resting male subjects. The results obtained by the ‘Z-coefficient’ method were compared with those obtained by cross-spectrum analysis, which has already been validated in humans. Furthermore, the reproducibility of both methods was checked after 1 week. 3. The results obtained by the two methods were significantly correlated (r = 0.78 for the first and r = 0.76 for the second experiment, P < 0.01). When repeated after 1 week, the average results were not significantly different. Considering individual results, test—retest correlation coefficients were higher with the Z-analysis (r = 0.79, P < 0.01) than with the cross-spectrum analysis (r = 0.61, P < 0.05). 4. In conclusion, as the Z-method gives results similar to but more reproducible than the cross-spectrum method, it might be a powerful and reliable tool to assess baroreflex sensitivity in humans.


2012 ◽  
Vol 2 (3) ◽  
pp. 214-237 ◽  
Author(s):  
M. A. A. Bakar ◽  
D. A. Green ◽  
A. V. Metcalfe

AbstractWe compare spectral and wavelet estimators of the response amplitude operator (RAO) of a linear system, with various input signals and added noise scenarios. The comparison is based on a model of a heaving buoy wave energy device (HBWED), which oscillates vertically as a single mode of vibration linear system. HBWEDs and other single degree of freedom wave energy devices such as oscillating wave surge convertors (OWSC) are currently deployed in the ocean, making such devices important systems to both model and analyse in some detail. The results of the comparison relate to any linear system. It was found that the wavelet estimator of the RAO offers no advantage over the spectral estimators if both input and response time series data are noise free and long time series are available. If there is noise on only the response time series, only the wavelet estimator or the spectral estimator that uses the cross-spectrum of the input and response signals in the numerator should be used. For the case of noise on only the input time series, only the spectral estimator that uses the cross-spectrum in the denominator gives a sensible estimate of the RAO. If both the input and response signals are corrupted with noise, a modification to both the input and response spectrum estimates can provide a good estimator of the RAO. A combination of wavelet and spectral methods is introduced as an alternative RAO estimator. The conclusions apply for autoregressive emulators of sea surface elevation, impulse, and pseudorandom binary sequences (PRBS) inputs. However, a wavelet estimator is needed in the special case of a chirp input where the signal has a continuously varying frequency.


1967 ◽  
Vol 47 (5) ◽  
pp. 477-491
Author(s):  
R. L. Desjardins

This paper reviews the principles and use of spectrum analysis and discusses the effectiveness of combining multiple regression techniques with cross-spectrum analysis in time series studies. This method is useful in comparing the variations of an empirical index or the response of different instruments to environmental factors as a function of time. The variability of daily latent-evaporation estimates from a regression technique is examined and compared with evaporation readings from atmometers. A comparison is made of the variation in evaporation from two types of small atmometers and two types of tank evaporimeters. All four instruments appear to respond to meteorological parameters similarly at Swift Current and Ottawa.


Sensors ◽  
2021 ◽  
Vol 21 (14) ◽  
pp. 4638
Author(s):  
Bummo Koo ◽  
Jongman Kim ◽  
Yejin Nam ◽  
Youngho Kim

In this study, algorithms to detect post-falls were evaluated using the cross-dataset according to feature vectors (time-series and discrete data), classifiers (ANN and SVM), and four different processing conditions (normalization, equalization, increase in the number of training data, and additional training with external data). Three-axis acceleration and angular velocity data were obtained from 30 healthy male subjects by attaching an IMU to the middle of the left and right anterior superior iliac spines (ASIS). Internal and external tests were performed using our lab dataset and SisFall public dataset, respectively. The results showed that ANN and SVM were suitable for the time-series and discrete data, respectively. The classification performance generally decreased, and thus, specific feature vectors from the raw data were necessary when untrained motions were tested using a public dataset. Normalization made SVM and ANN more and less effective, respectively. Equalization increased the sensitivity, even though it did not improve the overall performance. The increase in the number of training data also improved the classification performance. Machine learning was vulnerable to untrained motions, and data of various movements were needed for the training.


2020 ◽  
Vol 14 (3) ◽  
pp. 295-302
Author(s):  
Chuandong Zhu ◽  
Wei Zhan ◽  
Jinzhao Liu ◽  
Ming Chen

AbstractThe mixture effect of the long-term variations is a main challenge in single channel singular spectrum analysis (SSA) for the reconstruction of the annual signal from GRACE data. In this paper, a nonlinear long-term variations deduction method is used to improve the accuracy of annual signal reconstructed from GRACE data using SSA. Our method can identify and eliminate the nonlinear long-term variations of the equivalent water height time series recovered from GRACE. Therefore the mixture effect of the long-term variations can be avoided in the annual modes of SSA. For the global terrestrial water recovered from GRACE, the peak to peak value of the annual signal is between 1.4 cm and 126.9 cm, with an average of 11.7 cm. After the long-term and the annual term have been deducted, the standard deviation of residual time series is between 0.9 cm and 9.9 cm, with an average of 2.1 cm. Compared with the traditional least squares fitting method, our method can reflect the dynamic change of the annual signal in global terrestrial water, more accurately with an uncertainty of between 0.3 cm and 2.9 cm.


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