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Aerial Cranes
Published in Jie Huang, Nonlinear Dynamics and Vibration Control of Flexible Systems, 2023
The frequency sensitivity curves are shown in Figure 5.43 designed for zero damping. The normalized frequency is defined as the ratio of the real frequency to the design frequency. The MEI shaper limits the residual vibrations to the tolerable level at the design frequency. Meanwhile, the residual vibrations at two modified frequencies are suppressed to zero by the MEI shaper. The insensitivity, which provides a quantitative measure of robustness, is defined as the range of each curve that lies below the tolerable vibration level. The 5% insensitivity ranges from 0.798 to 1.205, and the 10% insensitivity ranges from 0.715 to 1.298. Increasing the tolerable level increases distance between the modified frequencies, and then widens the range of the frequency insensitivity. The MEI shaper exhibits a notch filtering effect, and suppresses a wide range of system frequencies.
Preprocessing
Published in Kaushik Majumdar, A Brief Survey of Quantitative EEG, 2017
Figure 2.1 elaborates how a low-pass filter can be implemented. It depicts the graph of the complex function H(z), where z = F, F is the normalized frequency. It is about an FIR filter. There are only a finite number of time points i, such that h(i) ≠ 0. The total of the frequencies is equal to the sample frequency. The normalized frequency is obtained by dividing the actual frequency by the sample frequency (multiplied by π radian/sample), where 0.5 denotes the Nyquist frequency.
Multi-Dimensional Photonic Processing by Discrete-Domain Approach
Published in Le Nguyen Binh, Photonic Signal Processing, 2019
In discrete-time signal processing, the term normalized frequency is used to describe a frequency independent of the system sampling frequency. The concept is applied in 2-D processing with a straightforward extension to spatial frequency.
Actively controllable size-dependent elastic wave band gaps in planar functionally graded micro-lattice
Published in Mechanics of Advanced Materials and Structures, 2022
The interested normalized frequency range is assumed as 10–20 with interval 0.05 at first. The population size in each generation is assumed as 600 and the termination criterion is satisfied as soon as the max difference of the design variable in the two consecutive iterations is less than a prescribed small value, which is designed as 1e-5 in this work. According to the presented GA optimization setting, Figure 22 shows the iteration history of the individual possessing the best fitness as well as the average estimation of each population. As evident from the convergence history plots, the optimization process converges steadily for all complex wave vectors from ΓX, XM, and ΓM directions. Table 4 gives the optimized design variables and the final objective.