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Sampling
Published in Jerry D. Gibson, The Communications Handbook, 2018
The situation shown in Fig. 2.1 (j) corresponds to the case where f < 2fM. In this case, there is an overlap between M(c) and M(c - coM). This overlap of the spectra is known as aliasing or foldover. When this aliasing occurs, the signal is distorted and it is impossible to recover the original signal m(t) from the sampled signal. To avoid aliasing, in practice, the signal is sampled at a rate slightly higher than the Nyquist rate. Iff > 2fM, then, as shown in Fig. 2.1(f), there is a gap between the upper limit coM of M(c) and the lower limit cos - wM of M(c - cs). This range from coM to cos - wM is called a guard band. As an example, speech transmitted via telephone is generally limited to fM = 3.3 kHz (by passing the sampled signal through a low-pass filter). The Nyquist rate is, thus, 6.6 kHz. For digital transmission, the speech is normally sampled at the rate f = 8 kHz. The guard band is then f - 2fM = 1.4 kHz. The use of a sampling rate higher than the Nyquist rate also has the desirable effect of making it somewhat easier to design the low-pass reconstruction filter so as to recover the original signal from the sampled signal.
Signal Processing
Published in Bogdan M. Wilamowski, J. David Irwin, Fundamentals of Industrial Electronics, 2018
James A. Heinen, Russell J. Niederjohn
Several comments are in order regarding the use of an FFT for spectral analysis. Prior to sampling, it is often beneficial to pass the original signal through a continuous-time lowpass filter. Such an “anti-aliasing” filter helps to ensure that the signal to be sampled is bandlimited and free of high-frequency noise.
Generalizations of Shannon Sampling Theorem
Published in Ahmed I. Zayed, Advances in Shannon’s Sampling Theory, 2018
The choice of Γ is arbitrary, but it must be in such a way that the replications of the spectral support Ω do not overlap and hence alias. The geometry of the sampling lattice depends on the choice of Γ and a sensible choice of the latter will be the one that minimizes the sampling rate. The lowest rate at which a multidimensional band-limited signal can be sampled without aliasing is the Nyquist rate. Unlike in one-dimensional sampling, in multidimensional sampling there may be more than one sampling geometry that can achieve the Nyquist rate.
S-Transform Based Kurtosis Analysis for Detection of LG and LL Faults in 14 Bus Microgrid System
Published in IETE Journal of Research, 2022
Sagnik Datta, Aveek Chattopadhyaya, Surajit Chattopadhayay, Arabinda Das
LG fault is made to occur between phase “C” and ground on load bus B10 (Non-linear load bus) and B6 (furnace bus), one at a time; while leaving the other load buses healthy. Similarly, LL fault is also made to occur between phase “B” and phase “C” of load bus B10 (Non-linear load bus) and B6 (furnace bus), one at a time; while leaving the other load buses healthy. Outgoing currents from Bulk generator and PV Cell bus are monitored from phase “C”. Total simulation time is of 0.5 s. Fault duration is taken to be within 0.15–0.35 s. Sampling frequency is set at 1000 Hz. Very high sampling frequency is considered to avoid any chance of aliasing. When fault occurs the current waveform undergoes a transition from steady state to transient state and after the fault is cleared the current waveform once again goes back to its steady state. To analyse the total transition of the waveform from steady state to transient state and again back to steady state, the fault duration is kept to be within 0.15–0.35 s where the total fault simulation time is 0.5 s. Simulation time is set to be small to keep the data size small.
Gender and Age Classification Enabled Blockschain Security Mechanism for Assisting Mobile Application
Published in IETE Journal of Research, 2021
Sapna Juneja, Sourav Jain, Aparna Suneja, Gurminder Kaur, Yasser Alharbi, Ali Alferaidi, Abdullah Alharbi, Wattana Viriyasitavat, Gaurav Dhiman
The steps of SURF are Key point Detection – SURF uses a fast Hessian Detector for this purpose. The value of the determinant of the Hessian matrix is computed for each pixel in constant time using integral images. where x is pixel location, P is scale, H(x,P) is the Hessian matrix, Lxx is the second-order derivative with respect to x, Lxy and Lyx are second-order derivative with respect to both x and y, and Lyy is second-order derivative with respect to y. Gaussian is considered ideal for scale-space analysis. Continuous Gaussian functions are cropped and converted into discrete. Aliasing still occurs when images are sub-sampled. Aliasing is a condition, which occurs when a signal is sampled at less than twice the highest frequency present in the signal. So to overcome this, box filters are used [28]. Initially, for finding Gaussian derivative response, Convolution of the input image and Gaussian derivative was done due to which the complexity was of the order of O(N∧2).
Adaptive phasor estimation technique during off-nominal frequency for numerical relays
Published in Journal of Information and Telecommunication, 2018
Omar Sami Thiab, Łukasz Nogal, Ryszard Kowalik
Converting analog signals to sequences of numerical values passes through below steps. Surge filter: The large inrush in the input analog signals will be suppressed using surge filter for the safety of the digital relay.Anti-aliasing filter: To avoid possible errors in the evaluation of input signal, anti-aliasing filter is used according to the Nyquist criterion.Analog/digital sample and hold: To convert the input signal from analog to digital. To scan the whole signal, a data window of limited length is applied to acquire information on part of the signal. Within the section of the signals that are scanned by the data window, a limited number of points of the waveform are sampled. While the window moving forward, more samples are obtained at different snapshots of time. The sampling window length, numbers of samples in the window, as well as the shape of the sampling window are dependent on the relay algorithm.