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Linear optics measurement and correction - II
Published in Xiaobiao Huang, Beam-based Correction and Optimization for Accelerators, 2019
The precision of tune determination with NAFF is 1N2, which is a significant improvement over the simple approach of identifying the peak spectral line. The precision can be further improved by multiplying the raw data by a window function before applying Eq. (5.9) or (5.10). A commonly used window function is the Hanning window W(n)=sin2πnN−1.Theoretically, NAFF with Hanning window can achieve the tune precision of 1N4. But that is typically not the case with random noise in the data.
Fundamentals of Speech Processing
Published in Shaila Dinkar Apte, Random Signal Processing, 2017
The Hamming window is selected because the spectrum of it has the highest side lobe attenuation. When we multiply a signal in time domain by a rectangular window function, the frequency domain responses convolve. This convolution results in a ripple in passband and large oscillations in the stopband. The stopband oscillations are termed spectral leakage and the oscillations near the band edge of the filter are called the Gibbs phenomenon. The oscillations near the band edge get reduced by using a smooth window function. There are different window functions such as Hamming, Hanning, Blackman, and Bartlett. The spectrum of these window functions has a broader main lobe and smaller side lobes. Smooth windows reduce Gibbs phenomenon but lead to larger transition widths. If we go through the comparison of these window functions as shown in Table 5.4, we see that we have use compromise between the side lobe amplitude and transition width. M in Table 5.4 stands for the filter order. For the same transition width of 8π/M, the stopband attenuation is the highest for the Hamming window, and hence we selected it. The equation of the Hamming window is given by Equation 5.15.
Experimental investigation on the hydro-acoustic characteristics of tandem cylinders
Published in Selma Ergin, C. Guedes Soares, Sustainable Development and Innovations in Marine Technologies, 2022
The hydrophone was located at a distance of 5D down and 25D downward of the cylinder center. Fast Fourier Transform (FFT) functions were used to transform unsteady pressure fluctuations data obtained for the hydrophone position from time domain to frequency domain. Acoustic data in Pascal (Pa) unit was converted to decibel (dB) by using amplitude function (SPL function). The reference sound pressure was considered as 1.0×10-6 Pa for the water medium. The Hann (Hanning) function was employed as the window function. Acoustic spectrum was analyzed within the range of 1.6 kHz. The number of blocks was determined as 3200 in accordance with the required sensitivity in the experiments and a frequency resolution between 0.5 Hz was provided.
Evolutionary power spectrum density of earthquake-induced rail geometric irregularities
Published in Structure and Infrastructure Engineering, 2022
Jian Yu, Lizhong Jiang, Wangbao Zhou, Xiang Liu, Zhipeng Lai
For the convenience of expression, the ground motion number can be denoted as i, the data point number of irregularities as n, the irregularity signal as Ii(n), and the window function as w(n). Common window functions include the rectangular window, the Hanning window, and the Hamming window. This study adopted the Hamming window: where N denotes the length of the window function; R denotes the overlapping ratio of the window function; and m denotes the window function number. By subjecting the irregular signal to window function processing, Eqs. (4) and (5) can be obtained: where f denotes spatial frequency. By denoting the position where the point in the window function is located as x and replacing m with x, a space-frequency function Si(x, f) is obtained.
Novel frequency-based approach for detection of steady-state visual evoked potentials for realization of practical brain computer interfaces
Published in Brain-Computer Interfaces, 2022
Mehrnoosh Neghabi, Hamid Reza Marateb, Amin Mahnam
The aim of frequency detection algorithms in SSVEP BCI applications is to detect SSVEP responses that are intermingled with background EEG activity and noise. Generally, for high-frequency flickering stimuli, SSVEP response is low in amplitude, which makes SSVEP detection challenging. The main ideas behind the proposed SAoRS algorithm are to improve frequency detection performance by improving the signal-to-noise ratio and decreasing spectral leakage. When a finite length of a signal is used to estimate its frequency spectrum, the result would be the convolution of the actual spectrum and the spectrum of the window function, which results in spectral leakage. It is known that if the length of processing window for a periodic signal is selected to be a multiple of its period, then the leakage would be minimized [47]. Here, EEG was first resampled to a multiple of the targeted frequency and then divided into segments for averaging. This makes sure that the SSVEP response peak in the frequency domain remains sharp. Synchronous averaging is a well-known technique to improve the signal-to-noise ratio. However, in our application, the phase of the stimulus in the EEG signal is not known; therefore, the averaging was performed in the frequency domain.
Detection of a slant crack in a rotor bearing system during shut-down
Published in Mechanics Based Design of Structures and Machines, 2020
A slant-cracked rotor-bearing system decelerating through its critical speed has been considered in the present analysis. The shaft is discretized into ten finite beam elements and is supported on bearings at the ends. Data used for simulations are given in the Table 1. The slant angle of the crack is taken as 45° to the shaft axis, which is applicable to many cases. A harmonic torsional moment with an amplitude of 1.5 N-m is applied on the slant-cracked element. Time response has been simulated using the Houbolt time marching technique with a time step of 0.001 s. Time response in the vertical direction at the disc has been taken when the rotor shuts down above the critical speed at 63.7 Hz (400 rad/s), with a constant angular acceleration. The Hanning window function is used to multiply the time response to obtain better frequency components in the frequency domain (obtained by FFT).