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Reconstruction of Varying Bandwidth Signals from Event-Triggered Samples
Published in Marek Miskowicz, Event-Based Control and Signal Processing, 2018
Dominik Rzepka, Miroslaw Pawlak, Dariusz Koscielnik, Marek Miśkowicz
The Shannon theorem introduced to engineering community in 1949 is a fundamental result used for digital signal processing of analog signals [1]. The main assumption under which a signal can be reconstructed from its discrete-time representation is that sampling rate is twice higher than the highest frequency component in the signal spectrum (Nyquist frequency), or twice the signal bandwidth. The class of signals with a finite bandwidth is often referred to as bandlimited. The concept of bandwidth is defined using the Fourier transform of the infinitely long signal, that is, the signal that is not vanishing in any finite time interval of (—TO, TO). Furthermore, according to the uncertainty principle, only signals defined over infinite time interval can be exactly bandlimited. As it is known, real physical signals are always time limited, so they cannot be perfectly bandlimited and the bandlimited model is only the convenient approximation [2]. Moreover, in practice, the Nyquist frequency is determined on the basis of the finite record of signal measurements as the frequency for which higher spectral components are weak enough to be neglected. Therefore, the evaluation of the Nyquist frequency is referred not to the global but to the local signal behavior.
Oscilloscope Voltage Measurement
Published in John G. Webster, Halit Eren, Measurement, Instrumentation, and Sensors Handbook, 2017
All digital scopes are capable of producing an aliased display. Some models are more prone to this problem than others, but even the best will alias under the right conditions. An alias is a lower-frequency false reproduction of the input signal resulting from undersampling, that is, sampling less than the Nyquist frequency. The display of the digital scope is based on computer display technology. This results in a display that is very bright and easy to see, even under conditions where an analog scope would have difficulty in producing a viewable display. The disadvantage of the digital scope’s display is its lower horizontal resolution. Most of the scopes on the market have a raster scan display with a resolution of 500 lines, less than half the resolution of an analog scope’s display. This is not a problem in most applications. It could become a factor where very complex waveforms, such as those found in TV systems, are being analyzed. Many digital scopes have display systems that exhibit large dead or blind times. Scopes based on a single CPU will be able to display their waveform data only after the CPU has finished all of its operations. This can result in a display that is unresponsive to front-panel control inputs as well as not being able to follow changes in the input signal.
Discrete Transforms
Published in Scott E. Umbaugh, Digital Image Processing and Analysis, 2017
Figure 5.2-12 illustrates the concept of aliasing. For simplicity, we will look at two periods and only consider the frequencies in the horizontal direction. By applying the periodicity of the Fourier transform, which says it is periodic with period of N×N for an N×N image, if there is information in the signal at frequencies greater than N/2, overlap will occur. This overlap causes the aliasing, which manifests itself as false information in the high frequencies. In Figure 5.2-12a, we show the spectrum of two periods where the Nyquist criteria have been met. Figure 5.2-12b shows what happens if the original signal actually contains frequencies greater than N/2 in the horizontal direction—adjacent periods overlap and aliasing occurs. Note that one method to avoid aliasing is to bandlimit the original signal with a low-pass filter so that it does not contain any frequencies above the Nyquist frequency.
Vibration safety evaluation model and sensor network-based monitoring system for coke drums in operation
Published in Journal of Asian Architecture and Building Engineering, 2023
Jewoo Choi, Deok Shin Kang, Min Gyu Lee, Sang Geun Bae, Taehoon Hong, Dong-Eun Lee, Hyo Seon Park
Figure 5 shows a wiring diagram of the accelerometer, a photograph of the control room and system installation on site, and a real-time monitoring screen for vibration safety of coke drums using the accelerometers. The accelerometer was wired to the datalogger of the monitoring server in the on-site control room using a Bayonet Neill–Concelman (BNC) cable. Six BNC cables with a length of 30 m, four BNC cables with a length of 50 m, and two BNC cables with a length of 80 m (50 m + 30 m) were used, and in this study, there was little noise or safety change in data due to the difference in the length of the cables used. The datalogger used here was Scada III 310 by SIEMENS; its detailed specifications are presented in Table 2. The LMS test lab of SIEMENS was used for real-time monitoring analysis and checking for sensor and data abnormalities. In order to secure the reliability of the measured data and reduce the aliasing and spectral leakage, a sampling rate considering the Nyquist frequency and a sufficiently long measurement time are required. In general, it has been reported that the extraction of modal parameters becomes more stable and accurate with increasing the sampling rate and measurement time (Yun et al. 2021). In consideration of these points, the horizontal vibration of the coke drums and the structure was measured for a total of 30 days at a sampling rate of 512 Hz, and data were collected for approximately 25 cycles.
Monitoring of Induced Groundborne Vibrations in Cultural Heritage Buildings: Miscellaneous Errors and Aliasing through Integration and Filtering
Published in International Journal of Architectural Heritage, 2021
Georgios Karanikoloudis, Paulo B. Lourenço, Nuno Mendes, João B. Serra, Rubén Boroschek
A representative number of cycles should be monitored in order for the obtained ppv values to be representative of at least 16 h at daytime or 8 h of night-time operational period (BS 5228-2 2009). The sampling frequency of the acquisition data needs to be high enough, in order to eliminate any aliasing effects, especially for post-processing purposes. According to Shannon’s theorem, the sampling frequency should be at least twice the highest frequency of interest, for the acquired data, i.e. the Nyquist frequency (Rouphael 2009). Still, when a signal is subjected to integration and/or differentiation, non-smooth transitions between sample points can highly reflect on aliasing and miscellaneous errors. Thus, the sampling frequency should be relatively high, i.e. at least 500 Hz. According to Worden 1990, a sampling frequency of 10 times the highest frequency of the signal is advised (Worden 1990).
Enhanced Seismic Response Prediction of Critical Structures via 3D Regional Scale Physics-Based Earthquake Simulation
Published in Journal of Earthquake Engineering, 2023
M. Korres, F. Lopez-Caballero, V. Alves Fernandes, F. Gatti, I. Zentner, F. Voldoire, D. Clouteau, D. Castro-Cruz
In the decimation/downsampling procedure in digital signal processing (DSP), the Nyquist frequency, , plays a crucial role in aliasing effect. More specifically, any frequency component above the Nyquist frequency will cause aliasing of the final signal. In order to avoid aliasing, special anti-aliasing filters need to be applied before re-sampling the signal.