Unbiased expression of FRF with exponential window function in impact hammer testing

2004 ◽  
Vol 277 (4-5) ◽  
pp. 931-941 ◽  
Author(s):  
Se Jin Ahn ◽  
Weui Bong Jeong ◽  
Wan Suk Yoo
Keyword(s):  
Window Function ◽  
Exponential Window

scholarly journals DFT-Based Identification of Oscillation Modes from PMU Data Using an Exponential Window Function

Energies ◽  
2019 ◽  
Vol 12 (22) ◽  
pp. 4357
Author(s):  
Jin Kwon Hwang ◽  
Sangsoo Seo ◽  
Julian Sotelo Castanon ◽  
Ho-Chan Kim
Keyword(s):  
Power System ◽  
Conventional Method ◽  
Least Squares Method ◽  
Synthetic Data ◽  
Modal Identification ◽  
Window Function ◽  
Long Duration ◽  
Oscillation Modes ◽  
Transient Data ◽  
Exponential Window

The characteristics of oscillation modes, such as interarea, regional, and subsynchronous modes, can vary during a power system fault, which can cause switching and control actions in the power system. Transient data of the modal response due to such a fault can be acquired through phasor measurement units (PMUs). When the transient data have a long duration, it is desirable to perform modal identification separately on each segment of the transient data, so as to reflect the varying characteristics of oscillation modes. A conventional discrete Fourier transform (DFT)-based method for parametric modal identification cannot be efficiently applied to such a segment dataset. In this paper, a DFT-based method with an exponential window function is proposed to identify oscillation modes from each segment of transient data in PMUs. This window function allows the application of the least squares method (LSM) for modal identification in the same manner as the conventional method. The accuracy of identification of the proposed method is compared with those of the conventional method and a Prony method through synthetic data of transient responses. Its feasibility is also verified by identifying real-world oscillation modes from transient data in PMUs.

scholarly journals COMPARATIVE ANALYSIS OF EXPONENTIAL WINDOW FUNCTION FOR DESIGNING OF FIR FILTERS

2012 ◽  
Vol 3 (2) ◽  
pp. 329-334
Author(s):  
Susheel Kumar ◽  
Munish Verma ◽  
Vijay K. Lamba ◽  
Avinash Kumar ◽  
Sandeep Kumar
Keyword(s):  
Design Method ◽  
Stop Band ◽  
Fir Filter ◽  
Window Function ◽  
Signal Separation ◽  
Signal Restoration ◽  
Air Conditioners ◽  
Window Functions ◽  
Exponential Window ◽  
Kaiser Window

Filters are very commonly found in everyday life and include examples such as water filters for water purification, mosquito nets that filter out bugs, bouncers at bars filtering the incoming guests according to age (and other criteria), and air filters found in air conditioners that we are sometimes a bit too lazy to change/clean periodically. Filters have two uses: signal separation and signal restoration. Signal separation is needed when a signal has been contaminated with interference, noise, or other signals. For example, imagine a device for measuring the electrical activity of a baby's heart (EKG) while still in the womb. The raw signal will likely be corrupted by the breathing and heartbeat of the mother. A filter might be used to separate these signals so that they can be individually analyzed. Signal restoration is used when a signal has been distorted in some way. For example, an audio recording made with poor equipment may be filtered to better represent the sound as it actually occurred [1, 2]. The main goal of this work is to study the exponential  window function and analyze a digital low pass FIR filter using the same in MATLAB. Properties of window functions is studied and frequeny domain responses of  window functions is obtained. Then FIR filter is designed using widow design method and its characteristics have also been studied in frequency domain. The performace comparison between LPFs designed using other well known windows like Kaiser, Exponential, Cosh and modified kaiser window is done and it has been intuitively shown that for a given order and transition width, the filter designed using Exponential window provides the worse minimum stop band attenuation but better far end attenuation than filter designed by well known Kaiser Window.

Automatic Procedure for Automating the Analyzer Window Setting for Transient Vibration Data Capture

1999 ◽  
Author(s):  
Colin P. Ratcliffe ◽  
Roger M. Crane
Keyword(s):  
Composite Structures ◽  
Fourier Transforms ◽  
Optimization Procedure ◽  
Window Function ◽  
Impact Excitation ◽  
Transient Vibration ◽  
Vibration Data ◽  
Excitation Techniques ◽  
Exponential Window ◽  
Vibration Tests

Abstract When conducting experimental vibration tests on composite structures, one of the most important settings in the spectrum analyzer is the window function. This setting effects the performance of the Fourier analyzer, and can change the observed energy dissipation of the structure. For impact excitation techniques the window used for transient response signals is typically an exponential function. Traditionally, the window setting is chosen by what “looks right.” Too little windowing introduces errors during the Fourier transforms; too much degrades the signal. This paper presents an automatic procedure for optimizing the exponential window function when measuring transient, decaying signals. Initially, the natural attenuation of a signal is automatically determined, and this attenuation is then used to determine the optimum window parameters. The theory is developed for a single-degree-of-freedom system and demonstrated for theoretical and experimental multi-modal structures with poor signal-to-noise ratios. In all cases it is shown that the computationally inexpensive optimization procedure is highly satisfactory. There is also a side benefit in that almost identical numerical procedures can be used to automate the logarithmic decrement technique of estimating structural damping.

scholarly journals Abundance of Primordial Black Holes in Peak Theory for an Arbitrary Power Spectrum

2020 ◽  
Author(s):  
Chul-Moon Yoo ◽  
Tomohiro Harada ◽  
Shin’ichi Hirano ◽  
Kazunori Kohri
Keyword(s):  
Mass Spectrum ◽  
Power Spectrum ◽  
Environmental Effect ◽  
Window Function ◽  
Radial Coordinate ◽  
Primordial Black Holes ◽  
Scale Invariant ◽  
Curvature Perturbation ◽  
Arbitrary Power ◽  
Nonlinear Relation

Abstract We modify the procedure to estimate PBH abundance proposed in Ref. [1] so that it can be applied to a broad power spectrum such as the scale-invariant flat power spectrum. In the new procedure, we focus on peaks of the Laplacian of the curvature perturbation △ ζ and use the values of △ ζ and △ △ ζ at each peak to specify the profile of ζ as a function of the radial coordinate while the values of ζ and △ ζ are used in Ref. [1]. The new procedure decouples the larger-scale environmental effect from the estimate of PBH abundance. Because the redundant variance due to the environmental effect is eliminated, we obtain a narrower shape of the mass spectrum compared to the previous procedure in Ref. [1]. Furthermore, the new procedure allows us to estimate PBH abundance for the scale-invariant flat power spectrum by introducing a window function. Although the final result depends on the choice of the window function, we show that the k-space tophat window minimizes the extra reduction of the mass spectrum due to the window function. That is, the k-space tophat window has the minimum required property in the theoretical PBH estimation. Our procedure makes it possible to calculate the PBH mass spectrum for an arbitrary power spectrum by using a plausible PBH formation criterion with the nonlinear relation taken into account.

scholarly journals Continuous window functions for NFFT

2021 ◽  
Vol 47 (4) ◽  
Author(s):  
Daniel Potts ◽  
Manfred Tasche
Keyword(s):  
Fourier Transform ◽  
Shape Parameter ◽  
Optimal Choice ◽  
Approximate Algorithm ◽  
Window Function ◽  
Truncation Parameter ◽  
Error Constant ◽  
Window Functions ◽  
Nonequispaced Fast Fourier Transform ◽  
Error Behavior

AbstractIn this paper, we study the error behavior of the nonequispaced fast Fourier transform (NFFT). This approximate algorithm is mainly based on the convenient choice of a compactly supported window function. Here, we consider the continuous Kaiser–Bessel, continuous exp-type, sinh-type, and continuous cosh-type window functions with the same support and same shape parameter. We present novel explicit error estimates for NFFT with such a window function and derive rules for the optimal choice of the parameters involved in NFFT. The error constant of a window function depends mainly on the oversampling factor and the truncation parameter. For the considered continuous window functions, the error constants have an exponential decay with respect to the truncation parameter.

scholarly journals Spectral Domain Sparse Representation for DOA Estimation of Signals with Large Dynamic Range

Sensors ◽  
2021 ◽  
Vol 21 (15) ◽  
pp. 5164
Author(s):  
Jacob Compaleo ◽  
Inder J. Gupta
Keyword(s):  
Sparse Representation ◽  
Antenna Array ◽  
Dynamic Range ◽  
Direction Of Arrival ◽  
Doa Estimation ◽  
Single Step ◽  
Window Function ◽  
Spectral Domain ◽  
Low Sidelobe ◽  
Weighting Window

Recently, we proposed a Spectral Domain Sparse Representation (SDSR) approach for the direction-of-arrival estimation of signals incident to an antenna array. In the approach, sparse representation is applied to the conventional Bartlett spectra obtained from snapshots of the signals received by the antenna array to increase the direction-of-arrival (DOA) estimation resolution and accuracy. The conventional Bartlett spectra has limited dynamic range, meaning that one may not be able to identify the presence of weak signals in the presence of strong signals. This is because, in the conventional Bartlett spectra, uniform weighting (window) is applied to signals received by various antenna elements. Apodization can be used in the generation of Bartlett spectra to increase the dynamic range of the spectra. In Apodization, more than one window function is used to generate different portions of the spectra. In this paper, we extend the SDSR approach to include Bartlett spectra obtained with Apodization and to evaluate the performance of the extended SDSR approach. We compare its performance with a two-step SDSR approach and with an approach where Bartlett spectra is obtained using a low sidelobe window function. We show that an Apodization Bartlett-based SDSR approach leads to better performance with just single-step processing.

An analysis of the spectrum of a gravity anomaly over an inclined dike

Geophysics ◽  
1985 ◽  
Vol 50 (9) ◽  
pp. 1500-1501
Author(s):  
B. N. P. Agarwal ◽  
D. Sita Ramaiah
Keyword(s):  
Fourier Transform ◽  
Gravity Anomaly ◽  
Fourier Spectrum ◽  
Fourier Transforms ◽  
Weighted Average ◽  
Window Function ◽  
Average Spectrum ◽  
Amplitude Spectra ◽  
Distance Data ◽  
The Fourier Transform

Bhimasankaram et al. (1977) used Fourier spectrum analysis for a direct approach to the interpretation of gravity anomaly over a finite inclined dike. They derived several equations from the real and imaginary components and from the amplitude and phase spectra to relate various parameters of the dike. Because the width 2b of the dike (Figure 1) appears only in sin (ωb) term—ω being the angular frequency—they determined its value from the minima/zeroes of the amplitude spectra. The theoretical Fourier spectrum uses gravity field data over an infinite distance (length), whereas field observations are available only for a limited distance. Thus, a set of observational data is viewed as a product of infinite‐distance data with an appropriate window function. Usually, a rectangular window of appropriate distance (width) and of unit magnitude is chosen for this purpose. The Fourier transform of the finite‐distance and discrete data is thus represented by convolution operations between Fourier transforms of the infinite‐distance data, the window function, and the comb function. The combined effect gives a smooth, weighted average spectrum. Thus, the Fourier transform of actual observed data may differ substantially from theoretic data. The differences are apparent for low‐ and high‐frequency ranges. As a result, the minima of the amplitude spectra may change considerably, thereby rendering the estimate of the width of the dike unreliable from the roots of the equation sin (ωb) = 0.

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