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Time series analysis and forecasting
Published in Amithirigala Widhanelage Jayawardena, Fluid Mechanics, Hydraulics, Hydrology and Water Resources for Civil Engineers, 2021
Amithirigala Widhanelage Jayawardena
Cross correlation is used to determine the dependence between two series xt and yt, not only at the same time level but also for one series leading or lagging the other. For xt and yt with zero mean, the cross-covariance cxy(τ) is defined as cxy(τ)=E[xtyt+τ]cyx(τ)=cxy(−τ)=E[xt+τyt]
Discrete Fourier Transform and Discrete Systems
Published in Taan ElAli, ®, 2020
Correlation is often used in the detection of a target in a radar signal. It can also be used in the estimation of the frequency content of a certain signal. Cross-correlation is the correlation between two different signals and auto-correlation is the correlation with the signal itself. The cross-correlation is given by the relation Rx1x2(p)=∑n=−∞+∞x1(n)x2(p+n)
Ultra-Wideband Radar Receivers
Published in James D. Taylor, Introduction to Ultra-Wideband Radar Systems, 2020
James D. Taylor, Elizabeth C. Kisenwether
Cross-correlation is the correlation of a received signal with some reference signal waveform. The best place to start is through the work of P. M. Woodward on information theory.24 Woodward’s work from 40 years ago is relevant to UWB signal detection and processing and introduces some correlation detection concepts and objectives. Woodward points out that the signal receiver should extract wanted signal information that is received with unwanted noise. The reception problem is to eliminate as much unwanted noise as possible without destroying the signal-of-interest information. In addition, Woodward discusses the fact that most reception methods are aimed at maximizing output signal to noise. Noise is viewed as the limiting factor in sensitivity; the less noise, the better.24 Some caution is needed because there is no general theorem which shows that maximum output signal to noise ensures maximum informátion gain, although the concept is intuitively appealing and looks like a practical place to start.
Perception of rhythmic agency for conversational labeling
Published in Human–Computer Interaction, 2023
Christine Guo Yu, Alan F. Blackwell, Ian Cross
The rhythmic behavior of the system in the four conditions was varied as follows: In the CA condition, the time intervals between stimulus presentations were randomized. In the CR condition, all stimuli were presented periodically, appearing at regular intervals (using the “comfortable” rate observed during the practice task). In the UR condition, the user sets the rhythm (period) in all stages, by choosing the speed at which they click. In the UC condition, the system observes the period of the user clicks in the presentation stage, and then imitates the same period in the recall stage. The order of these four conditions was randomized across participants. In conditions CA, UC and UR,3In CR condition, the system intervals were strictly periodic, of which the standard deviation was 0, hence the cross-correlation formula (see Boker et al., 2002) was not applicable to CR condition. the intervals between events are compared, testing for cross-correlation coefficients between the series of user click intervals and the series of visual stimuli presentation intervals. Cross-correlation is a measure for the “similarity of two interacting series as a function of the displacement of one relative to the other” (Boker et al., 2002), with its value ranging between 0 and 1. Increased value of the cross-correlation coefficients between user intervals and system intervals provides a measure of rhythmic entrainment between the two.
Development of operation policy for dry season reservoirs in tropical partially gauged river basins
Published in International Journal of River Basin Management, 2022
C. Chandre Gowda, Amai Mahesha, S. G. Mayya
Correlation functions attain the selection of input for streamflow modelling information, low streamflow achieved. The cross-correlations are generally adopted to select the particular input models in many studies. The cross-correlation methods represent the most popular analytical techniques for choosing appropriate inputs. The cross-correlation, autocorrelation, and partial autocorrelation have been adopted to determine the information for time series analysis of rainfall-runoff models (Sudheer et al., 2002). The autocorrelation is the linear dependence of a variable with itself at two points in time. The partial autocorrelation function of a stationary time series gives the correlation between the lagged variable after accounting for the correlations with other variables. The cross-correlation is a measure of similarity of two sequences as a function of the lag of one relative to the other. To model streamflow in the present work, lag time precipitations and run-off are used as the input to model, since it was found that the effect of other parameters is negligible. In the present study, correlation analysis is carried for lag 0 to lag12 (the correlation coefficient is less than 0.3 after 12 d lags, so only 12 days are considered), the lag duration is in days. In correlation analysis, the partial autocorrelation and autocorrelation of the streamflows are plotted with 95% confidence interval band.
Demonstration of Temperature-Dependent Analysis of GAA – β-(AlGa)2O3/Ga2O3 High Electron Mobility Transistor
Published in IETE Journal of Research, 2022
Ravi Ranjan, Nitesh Kashyap, Ashish Raman
All the simulation of noise is performed up to 1000 GHz frequency for all the temperatures. The NFmin is approximate 10 dB in the frequency range of 1 GHz 100 GHz for the entire temp, and it denotes that little noise is added by the network shown in Figure 7(a). At lower temperature, the perpendicular (vertical) field increases because of which the NFmin of the device is larger. Since noise is a random phenomenon, some statistical analysis is essential. Due to this autocorrelation and cross-correlation of the two-port devices are analyzed. From the analysis, it can be analyzed that the mean free path (λ) of electrons crossing the channel is the function of temperature and frequency. At higher temperatures, the scattering mechanisms are not much impressive to disturb the correlation between the gate and drain current, and it performs the higher cross-correlation and is plotted in Figure 7(b) and 7(c). Autocorrelation is related to the cross-correlation of a signal with itself. Figure 7(d) and 7(e) display the graph of autocorrelation, which shows higher autocorrelation between input and output voltages. Lower noise conductance is responsible for lower DIBL and at a higher temperature, lower noise conductance is achieved, as shown in Figure 7(f).