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Fourier Transform
Published in Nassir H. Sabah, Electric Circuits and Signals, 2017
The bandwidth of a signal is the frequency range over which frequencies present in the signal have significant values. Although plausible, this is not a precise definition, as it does not specify a criterion for significance. In discussing frequency responses in Chapter 10, the 3-dB bandwidth was defined as the frequency range over which the signal power is not less than one-half of its maximum value. In the case of a frequency spectrum that has one main lobe and several smaller ones, as for a rectangular pulse (Figure 16.1.1c), the bandwidth may be considered to be from zero to the frequency 2π /t of the first zero. In this case, only the frequencies in the first lobe are considered significant, as they account for more than 90% of the energy of the signal (Example SE16.2). Nevertheless, it is generally true that: Concept: The faster a signal changes in time, the wider is its bandwidth.
The Place of Measurement, Instrumentation, and Laboratory
Published in Francis S. Tse, Ivan E. Morse, Measurement and Instrumentation in Engineering, 2018
The data are valid if they give the desired information, which may be only a part of the information of an event under observation. Alternatively, the data may have been modified by means of signal conditioning, to get the desired information. It was stated in Sec. 1-3B that an instrument generally measures only a specific item. It is neither possible nor necessary to have “all” the information of a source. A digital voltmeter indicates only the magnitude of the input voltage. A frequency spectrum is a plot of the amplitude of the harmonic components of a periodic signal versus frequency. Some spectrum analyzers on the market do not give the phase angle of the harmonic components. Yet the phase information is pertinent for some related analysis.
Robotic Laser Measurement Technique for Solid Sound Field Intensity
Published in Chunguang Xu, Robotic Nondestructive Testing Technology, 2022
The laser virometer converts the detected vibration velocity change into an electrical signal. The change of vibration velocity with time, namely the time-domain signal of vibration velocity, can be observed on the display. The purpose of our experiment is to obtain the natural frequency of the transducer, so the frequency spectrum of vibration velocity signal needs to be analyzed. Frequency spectrum analysis is to transfer a signal from the time domain to the frequency domain. Each frequency in the obtained frequency spectrum corresponds to a periodic harmonic component of the signal. The most commonly used transformation method is fast Fourier transform (FFT).
Intelligent fault diagnosis of rolling bearings based on clustering algorithm of fast search and find of density peaks
Published in Quality Engineering, 2023
Jun Wu, Manxi Lin, Yaqiong Lv, Yiwei Cheng
Twelve time domain statistical features and eleven frequency domain statistical features are extracted from the raw signals of rolling bearings. All the statistical features are shown in Table 1, where is sampling value at time, is the number of the sampling times. is the frequency spectrum of monitoring signal transformed by fast Fourier transform algorithm, where and is the number of spectrum lines. is the frequency value of -th spectrum line.
Milky translucent haze of a large-scale topological defect array in nematic liquid crystal
Published in Liquid Crystals, 2023
The optical microscopic (OM) picture of a defect array is shown in Figure 2(c). The dark spots are the defects, where and are 0. The bright area is the nematic liquid crystal, where is maximum and is , which is . The transmittance distribution can be directly converted to a 2D step function , of which the bright area is and the dark spots are the 0’s. The 2D Fourier transform of is the spatial frequency spectrum of the defects,
Aero-thermo-elastic analysis of nonlinear isotropic cracked plate in supersonic flow
Published in Mechanics Based Design of Structures and Machines, 2023
Seyed Saeed Mozafareiyan, Jalil Rezaeepazhand
As can be seen in Figure 7, before reaching the critical aerodynamic pressure the plate motion is damped. For the plate motion increases with time until a LCO is reached (Figure 8). Figure 9 shows frequency spectrum (power spectrum) of time history of using Fast Fourier Transform (FFT). This spectrum was calculated for the time responses given in Figure 8. In this figure, the peak amplitude presents the dominant frequency of oscillations. The phase plot of the cracked plate around zero point of equilibrium is presented in Figure 10. As can be seen in Figure 11, in post-flutter with increasing aerodynamic pressure, the amplitude of the limited cycle oscillations increases.