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While the generalized Mexican-hat wavelets are constructed from the standard Mexican-hat function by utilizing a polynomial series with the admissible condition imposed, the signal matching characteristics are achieved by minimizing the spectral differences between the reference signal and the generalized Mexican-hat wavelet via even and odd symmetry decomposition.
But in practice, for arbitrary combination of unknown and reference signal, the pulse width of the signals can modify the method application; In this work a criterion for choosing the optimal pulse width values is defined, by investigating the relationships between the reference signal's period and the pulse width.
Around 6 s, there is a delay between the reference signal and the longitudinal speed.
The LMS algorithm estimates implicitly the phase differences between the reference signal and the input signals.
The DOA is estimated by computing the phase shift between the reference signal and its phase-shifted version.
Third, a suitable metric for performing the calibration has to be identified and fourth, the offset between the reference signal and the signals received by the devices has to be computed.
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MCCA with reference (MCCAR) imposes an additional constraint to maximize not only the covariations among loadings of each modality, but also the column-wise correlations between Ak and the reference signal, as shown in Eq. (3).
Feedback controllers require a 'subtractor' that is able to compute the error between the process output and the reference signal.
The proposed algorithm ensures required accuracy of difference between the plant output and the reference signal, which significantly depends on external disturbances.
It is proved that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are bounded and the tracking error between the system output and the reference signal converges to a small neighborhood of zero by appropriate choice of the design parameters.
It is found by Kuo et al. [12] that the convergence of this direct-form ANC system is dependent on the frequency separation between two adjacent sinusoids in the reference signal.
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