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Sample-Rate Selection
Published in William S. Levine, Control System Fundamentals, 2019
Mohammed S. Santina, Allen R. Stubberud, Gene H. Hostetter
In digital signal processing applications, selection of the sampling period also depends on the reconstruction method used to recover the bandlimited signal from its samples [1]. Another statement of the sampling theorem related to signal reconstruction states that when a bandlimited continuous-time signal is sampled at a rate higher than twice the bandlimit frequency, the samples can be used to reconstruct uniquely the original continuous-time signal.
Sample-Rate Selection
Published in William S. Levine, The Control Handbook: Control System Fundamentals, 2017
Michael Santina, Allen R. Stubberud
In digital signal processing applications, selection of the sampling period also depends on the reconstruction method used to recover the bandlimited signal from its samples [1]. Another statement of the sampling theorem related to signal reconstruction states that when a bandlimited continuous-time signal is sampled at a rate higher than twice the bandlimit frequency, the samples can be used to reconstruct uniquely the original continuous-time signal.
Discrete-Time Signal Processing and Short-Time Fourier Analysis
Published in Philipos C. Loizou, Speech Enhancement, 2013
The reciprocal of Ts is known as the sampling frequency, Fs = 1/Ts, expressed in hertz. For perfect signal reconstruction [from discrete x(n) to continuous xa(t)], the Nyquist–Shannon sampling theorem [1] requires that the sampling frequency must be at least twice the highest frequency in the signal.
A new integrated analytics approach for wind turbine fault detection using wavelet, RLS filter and random forest
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2023
Shiyao Qin, Mengzhou Zhang, Xiaojing Ma, Mei Li
In the process of noise reduction, the threshold value of the high-frequency coefficient is selected, and the hard threshold and the soft threshold are given in two forms of Donoho. Usually, the hard threshold denoising will cause the loss of available information, so the analysis of engineering signal is mostly based on the soft threshold denoising technique. The method described in this paper is also soft thresholding. Common wavelet bases are Haar, Daubechies (dbN), Symlets. Compared with Haar and Symlets, the dbN wavelet has better regularity, that is, the smooth error introduced by the wavelet as a sparse basis is not easy to be detected thus makes the process of signal reconstruction smoother. The characteristic of dbN wavelet is that the larger the order (sequence N), the higher the order of vanishing moment and the higher the vanishing moment, the better the smoothness. After some comparison experiments, N = 3 is chosen because the denoising result is good enough and larger N can add computational complexity and or even get a signal that is too smooth. The decomposition layers L is set to 5 for the same consideration. Noise reduction result is shown in Section 2.4.2.
Covid-19 diagnosis by WE-SAJ
Published in Systems Science & Control Engineering, 2022
Wei Wang, Xin Zhang, Shui-Hua Wang, Yu-Dong Zhang
However, most of the research on Shannon's entropy has been on engineering applications, and its physical meaning and principles have not been discussed in depth. Moreover, the shortcomings of Shannon entropy make it prone to wavelet mixing and energy leakage when dealing with non-stationary signals, which may lead to inaccurate or even incorrect results. Given this, many new solutions to these problems have emerged, such as relative wavelet entropy (Rosso et al., 2001) and Tsallis Wavelet Entropy (Chen & Li, 2014). Our research uses a 4-level decomposition of biorthogonal wavelets. Compared to orthogonal wavelet bases, biorthogonal wavelet bases resolve the incompatibility of symmetry and exact signal reconstruction. Biorthogonal wavelets consist of two wavelets called dyads, which decompose and reconstruct the signal separately. Bi-orthogonal wavelets resolve the contradiction between linear phase and orthogonality requirements and are widely used in signal and image reconstruction. In this research, wavelet entropy is used for feature extraction. And then, the extracted features are fed into a two-layer Feedforward Neural Network for classification.
Methodology for data-driven predictive maintenance models design, development and implementation on manufacturing guided by domain knowledge
Published in International Journal of Computer Integrated Manufacturing, 2022
Oscar Serradilla, Ekhi Zugasti, Julian Ramirez de Okariz, Jon Rodriguez, Urko Zurutuza
According to the Nyquist-Shannon sampling theorem, a signal of unknown frequency locations has to be sampled at least at 2 times its frequency in order to enable signal reconstruction, thus maintaining enough information to avoid nonreversible information loss by the aliasing effect, presented by Mishali and Eldar (2009). Anyway, collecting more data than needed is preferable to collecting less than that stated, given that in oversampled data, downscaling is possible, but under-sampled data cannot reconstruct original data correctly. However, big data collection and storage result in higher costs, so the collection strategy should be correctly designed to fit use-cases requirements to reduce costs and computational time. The use of signal processing techniques is encouraged to design a suitable data collection strategy that addresses the use-case’s PdM characteristics. Signal processing techniques can help to determine a suitable sampling frequency. Moreover, signal processing techniques include filters such as IIR Filters, Chebysev, Butterworth or Bessel as stated by Almaged and Hale (2019), which can be used to reduce the bandwidth of a signal that has a higher sampling frequency than required. When the sampling rate of the variables is different, in order to enable data analysis in any timestep for all available variables, timestep by imputation such as repeating last value or interpolation can be useful.