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Biomolecular Processing and Molecular Electronics
Published in Sergey Edward Lyshevski, Molecular Electronics, Circuits, and Processing Platforms, 2018
A high-performance interactive software has been developed in the MATLAB environment to support the frequency-domain analysis. We utilize the power spectral density (PSD) analysis applying different methods of PSD estimation (covariance, multiplier, periodogram, etc.). For example, the Welch method is based on dividing the sequence of data into (possibly overlapping) segments, computing a modified periodogram of each segment and averaging the PSD estimates. That is, we consider xm[n] = x[(N/M)m — (L/2)+n], n = 0,1,…, L — 1 to be the mth segment of the sequence x ϵ CN divided into M segments of length L. The Welch PSD estimate is given as Rx={|Xm[k]|2}m, where {·}m denotes averaging across the data segments.
Power Spectrum
Published in Afshin Samani, An Introduction to Signal Processing for Non-Engineers, 2019
One way to reduce this relatively high estimation variance is to apply an averaging filter on the estimated PSD (Daniel periodogram) (Manilo and Nemirko, 2016). Other algorithms have also been developed to reduce the estimation variance in periodograms. A very commonly used algorithm is called the Welch method. The Welch method splits the signal into smaller overlapping epochs and then estimates the PSD for each of the epochs. Finally, the overall estimation of PSD is obtained by averaging the estimated PSD from each of the epochs.
® Applications in Behavior Analysis of Systems Consisting of Carbon Nanotubes through Molecular Dynamics Simulation
Published in Sarhan M. Musa, ®, 2018
Masumeh Foroutan, Sepideh Khoee
Figure 7.4 shows the spectrum the C60 oscillating inside a nanotube (15, 15) obtained from molecular dynamics simulation. This spectrum has been obtained from Welch’s method using MATLAB software. Welch’s method is used for estimating the power of a signal versus frequency. There are some syntaxes for pwelch in MATLAB toolbox like including [Pxx, w] = pwelch(x).
Measurement of the Gas Velocity in a Water-Air Mixture in CROCUS Using Neutron Noise Techniques
Published in Nuclear Technology, 2020
Mathieu Hursin, Oskari Pakari, Gregory Perret, Pavel Frajtag, Vincent Lamirand, Imre Pázsit, Victor Dykin, Gabor Por, Henrik Nylén, Andreas Pautz
Next, an attempt was made to determine the uncertainty due to the length of the time series used to estimate the transit time. The Welch’s method used for the estimation of the PSD is based on the average of FFTs performed over various segments of the time series. All segments have the same length determined by the window size. The uncertainty related to the length of the time series can be estimated using a block bootstrap approach.34,35 Segments of a given acquisition are randomly selected with replacement to produce repetitions of the same signal. No overlap between segments is considered in the Welch’s method so that each segment can be considered independent. The four methods to estimate the transit time were applied to the time series. This process was repeated 100 times to estimate the uncertainty related to the signal length for each method. The “Absolute Standard Deviation” value quoted in Table IV is the standard deviation of the transit times determined for each one of the 100 repetitions. The variations observed in the CPSD phase are illustrated in Fig. 14 for the long acquisition at 20 L · min air injection rate.
Experimental investigation of biodynamic human body models subjected to whole-body vibration during a vehicle ride
Published in International Journal of Occupational Safety and Ergonomics, 2019
Yener Taskin, Yuksel Hacioglu, Faruk Ortes, Derya Karabulut, Yunus Ziya Arslan
PSD diagrams were estimated using Welch’s method, which is an improved method of periodograms [45]. In Welch’s method, data sets are segmented into overlapping or non-overlapping smaller pieces. Each piece of data is multiplied by a windowing function and their spectrums are then calculated and averaged in order to obtain the estimated PSD. In our case, 4096 data points for each segment with a Hamming window and 50% overlapping segments were used. The estimated PSD () of experimentally measured and theoretical calculated accelerations was obtained from the following equation: where = estimated power spectral density; L= length of segments; K = total number of segments; W(j) = related windowing function; Xk(j) = kth segmented data; fn = normalized frequency; i = imaginary unit; n = number of samples.
Characterization of timber masonry walls with dynamic tests
Published in International Journal of Architectural Heritage, 2019
Ana Maria Gonçalves, Paulo Candeias, Luís Guerreiro, João Gomes Ferreira, Alfredo Campos Costa
The dynamic identification tests aim at estimating the dynamic properties, namely the vibration frequencies, mode shapes, and damping ratios of the model. In these tests, the input and output accelerations were measured in the shaking table and in the model, respectively, with a sampling rate of 250 Hz. The recorded signals were first processed by removing the direct current (DC) components (0 Hz) and by filtering using a lowpass Fourier filter with a cutoff frequency of 40 Hz (Bendat and Piersol 2000; Carvalho et al. 1998). The Welch method was used to estimate the Power Spectral Density (PSD). In order to smoothen it and reduce the dispersion of the PSD, 210 (1024) samples per frame were used with a minimum number of zeros (padding) and a Hanning window with an overlap of 2/3. This set of operations was carried out in the software MATLAB (MathWorks 2014). The functions used for this calculation are part of the MATLAB routines for post-processing: pwelch (Welch’s Power Spectral Density Estimate), cpsd (Cross Power Spectral Density), and mscohere (Magnitude Squared Coherence).