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Window Functions and Their Applications in Signal Processing
21 Oct 2013-
TL;DR: In this paper, the authors present a review of window functions for signal processing, and their performance comparison of data windows and their figures of merit, as well as applications of windows in spectral analysis.
Abstract: 1. Fourier analysis techniques for signal processing -- 2. Pitfalls in the computation of DFT -- 3. Review of window functions -- 4. Performance comparison of data windows -- 5. Discrete-time windows and their figures of merit -- 6. Time-domain and frequency-domain implementations of windows -- 7. FIR filter design using windows -- 8. Application of windows in spectral analysis -- 9. Applications of windows.
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TL;DR: In this paper, the power spectral density (PSD) of the surface topography of real-world surfaces has been used for tuning functional properties of surfaces, such as adhesion, friction, and contact conductance.
Abstract: Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from knowledge of the power spectral density (PSD) of the surface topography. The utility of the PSD is that it contains statistical information that is unbiased by the particular scan size and pixel resolution chosen by the researcher. In this article, we first review the mathematical definition of the PSD, including the one- and two-dimensional cases, and common variations of each. We then discuss strategies for reconstructing an accurate PSD of a surface using topography measurements at different size scales. Finally, we discuss detecting and mitigating artifacts at the smallest scales, and computing upper/lower bounds on functional properties obtained from models. We accompany our discussion with virtual measurements on computer-generated surfaces. This discussion summarizes how to analyze topography measurements to reconstruct a reliable PSD. Analytical models demonstrate the potential for tuning functional properties by rationally tailoring surface topography - however, this potential can only be achieved through the accurate, quantitative reconstruction of the power spectral density of real-world surfaces.
272 citations
TL;DR: In this article, the authors observed that waves propagating on the surface of water can be amplified after being scattered by a draining vortex, and the maximum amplification was 14% ± 8, obtained for 3.70 Hz waves, in a 6.25 cm-deep fluid.
Abstract: When an incident wave scatters off of an obstacle, it is partially reflected and partially transmitted. In theory, if the obstacle is rotating, waves can be amplified in the process, extracting energy from the scatterer. Here we describe in detail the first laboratory detection of this phenomenon, known as superradiance 1, 2, 3, 4. We observed that waves propagating on the surface of water can be amplified after being scattered by a draining vortex. The maximum amplification measured was 14% ± 8%, obtained for 3.70 Hz waves, in a 6.25-cm-deep fluid, consistent with the superradiant scattering caused by rapid rotation. We expect our experimental findings to be relevant to black-hole physics, since shallow water waves scattering on a draining fluid constitute an analogue of a black hole 5, 6, 7, 8, 9, 10, as well as to hydrodynamics, due to the close relation to over-reflection instabilities 11, 12, 13.
212 citations
27 Jan 2017
TL;DR: In this article, the power spectral density (PSD) of the surface topography has been used to predict surface properties, such as adhesion, friction, and contact conductance.
Abstract: Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from knowledge of the power spectral density (PSD) of the surface topography. The utility of the PSD is that it contains statistical information that is unbiased by the particular scan size and pixel resolution chosen by the researcher. In this article, we first review the mathematical definition of the PSD, including the one- and two-dimensional cases, and common variations of each. We then discuss strategies for reconstructing an accurate PSD of a surface using topography measurements at different size scales. Finally, we discuss detecting and mitigating artifacts at the smallest scales, and computing upper/lower bounds on functional properties obtained from models. We accompany our discussion with virtual measurements on computer-generated surfaces. This discussion summarizes how to analyze topography measurements to reconstruct a reliable PSD. Analytical models demonstrate the potential for tuning functional properties by rationally tailoring surface topography—however, this potential can only be achieved through the accurate, quantitative reconstruction of the PSDs of real-world surfaces.
201 citations
TL;DR: The power spectrum and two-point correlation function for the randomly fluctuating free surface on the downstream side of a stationary flow with a maximum Froude number F_{max}≈0.85 and the noise show a clear correlation between pairs of modes of opposite energies.
Abstract: We measured the power spectrum and two-point correlation function for the randomly fluctuating free surface on the downstream side of a stationary flow with a maximum Froude number ${F}_{\mathrm{max}}\ensuremath{\approx}0.85$ reached above a localized obstacle. On such a flow the scattering of incident long wavelength modes is analogous to that responsible for black hole radiation (the Hawking effect). Our measurements of the noise show a clear correlation between pairs of modes of opposite energies. We also measure the scattering coefficients by applying the same analysis of correlations to waves produced by a wave maker.
172 citations
Cites methods from "Window Functions and Their Applicat..."
...The Fourier transform in time is computed using a rectangular window, while we used a Hamming window function [31] with support x ∈ [0....
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TL;DR: A time-window-variation technique is developed for fast acquisition of HR from short-period time windows and measuring HR variation using CSD that achieves the smallest average error among the three techniques.
Abstract: The fast acquisition of heart rate (HR) is a challenge in noncontact vital sign detection using a Doppler radar system. Most of the previous studies use long-period time windows to guarantee a sufficient frequency spectrum resolution for HR measurement using the peak searching method on the frequency spectrum. For fast acquisition of HR, the length of the time window is less than 5 s and the accuracy is significantly degraded due to insufficient spectrum resolution. For vital sign detection using complex signal demodulation (CSD), measuring HR variation becomes a difficult job due to respiration harmonic interference and insufficient frequency spectrum resolution. In this paper, a time-window-variation technique is developed for fast acquisition of HR from short-period time windows and measuring HR variation using CSD. Experiments are performed on four human subjects under controlled laboratory conditions by a 5.8-GHz continuous-wave Doppler radar vital sign detection system. The HR measurement results within 2–5-s time windows are compared by applying a simple fast Fourier transform (FFT) and peak searching method, a 10-s sliding-time-window FFT method, and the proposed method. The proposed method achieves the smallest average error among the three techniques. The proposed method has also proved to be able to measure HR variation using CSD.
111 citations