Rectangular Window Function Research Articles

Global field synchronization in gamma range of the sleep EEG tracks sleep depth: Artifact introduced by a rectangular analysis window

BackgroundInvestigating functional connectivity between brain networks has become an area of interest in neuroscience. Several methods for investigating connectivity have recently been developed, however, these techniques need to be applied with care. We demonstrate that global field synchronization (GFS), a global measure of phase alignment in the EEG as a function of frequency, must be applied considering signal processing principles in order to yield valid results. New methodMultichannel EEG (27 derivations) was analyzed for GFS based on the complex spectrum derived by the fast Fourier transform (FFT). We examined the effect of window functions on GFS, in particular of non-rectangular windows. ResultsApplying a rectangular window when calculating the FFT revealed high GFS values for high frequencies (>15Hz) that were highly correlated (r=0.9) with spectral power in the lower frequency range (0.75–4.5Hz) and tracked the depth of sleep. This turned out to be spurious synchronization. With a non-rectangular window (Tukey or Hanning window) these high frequency synchronization vanished. Both, GFS and power density spectra significantly differed for rectangular and non-rectangular windows. Comparison with existing method(s)Previous papers using GFS typically did not specify the applied window and may have used a rectangular window function. However, the demonstrated impact of the window function raises the question of the validity of some previous findings at higher frequencies. ConclusionsWe demonstrated that it is crucial to apply an appropriate window function for determining synchronization measures based on a spectral approach to avoid spurious synchronization in the beta/gamma range.

PERFORMANCE IMPROVEMENT OF INDOOR DS-UWB COMMUNICATION USING PSD ESTIMATION AND PULSE SHAPE OPTIMIZATION

Ultra-wideband system offers a great substitution for short-range, high-speed Personal Wireless Area Network, as well as for detection and ranging applications. IR-UWB technology can also be used in the military for radar and image sensing as well as localization of objects. In spite of this tremendous usefulness of UWB, some bandwidth interfering issues with the coexisting narrowband system can also be arises due to the huge bandwidth of UWB (> 500 MHz). This spectrum interference makes a huge pressure and lot of regulations to restrict the use of UWB in different environment. Consequently, the trait of UWB is not fully utilized. In this paper, we proposed the modified seventh order derivative of Gaussian monocycle and presented the performance analysis of pulse in an indoor environment with AWGN and the Rayleigh noise distributions. The aim of pulse shape optimization is for detection and ranging application of UWB to spectral interference. We recommended that higher order derivative of the Gaussian monocycle pulse offers an excellent reliability for the detection and ranging purpose in an indoor environment with co-existing narrowband communication. The pulse is windowed with a rectangular window function in the time domain to bind the pulse into the finite time interval. The pulse is analyzed for the interference with co-existing narrowband communication by fulfilling the power spectral density (PSD) masks provided by regulatory bodies of different countries.

Estimating observation error covariance matrix of seismic data from a perspective of image denoising

Estimating observation error covariance matrix properly is a key step towards successful seismic history matching. Typically, observation errors of seismic data are spatially correlated; therefore, the observation error covariance matrix is non-diagonal. Estimating such a non-diagonal covariance matrix is the focus of the current study. We decompose the estimation into two steps: (1) estimate observation errors and (2) construct covariance matrix based on the estimated observation errors. Our focus is on step (1), whereas at step (2) we use a procedure similar to that in Aanonsen et al. 2003. In Aanonsen et al. 2003, step (1) is carried out using a local moving average algorithm. By treating seismic data as an image, this algorithm can be interpreted as a discrete convolution between an image and a rectangular window function. Following the perspective of image processing, we consider three types of image denoising methods, namely, local moving average with different window functions (as an extension of the method in Aanonsen et al. 2003), non-local means denoising and wavelet denoising. The performance of these three algorithms is compared using both synthetic and field seismic data. It is found that, in our investigated cases, the wavelet denoising method leads to the best performance in most of the time.

Automatic data extrapolation to zero offset along local slope

Velocity-independent seismic data processing requires information about the local slope in the data. From estimates of local time and space derivatives of the data, a total least-squares algorithm gives an estimate of the local slope at each data point. Total least squares minimizes the orthogonal distance from the data points (the local time and space derivatives) to the fitted straight line defining the local slope. This gives a more consistent estimate of the local slope than standard least squares because it takes into account uncertainty in the temporal and spatial derivatives. The total least-squares slope estimate is the same as the one obtained from using the structure tensor with a rectangular window function. The estimate of the local slope field is used to extrapolate all traces in a seismic gather to the smallest recorded offset without using velocity information. Extrapolation to zero offset is done using a hyperbolic traveltime function in which slope information replaces the knowledge of the normal moveout (NMO) velocity. The new data processing method requires no velocity analysis and there is little stretch effect. All major reflections and diffractions that are present at zero offset will be reproduced in the output zero-offset section. Therefore, if multiple reflections are undesired in the output, they should be removed before data extrapolation to zero offset. The automatic method is sensitive to noise, so for poor signal-to-noise ratios, standard NMO velocities for primary reflections can be used to compute the slope field. Synthetic and field data examples indicate that compared with standard seismic data processing (velocity analysis, mute, NMO correction, and stack), our method provides an improved zero-offset section in complex data areas.

Low-Complexity Adaptive Sonar Imaging

We have studied the low-complexity adaptive (LCA) beamformer in active sonar imaging. LCA can be viewed as either a simplification of the minimum variance distortionless response (MVDR) beamformer, or as an adaptive extension to the delay-and-sum (DAS) beamformer. While both LCA and MVDR attempt to minimize the power of noise and interference in the image, MVDR achieves this by computing optimal array weights from the spatial statistics of the wavefield, while LCA selects the best performing weights out of a predefined set. To build confidence in the LCA method, we show that a robust MVDR implementation typically creates weight sets with shapes spanning between a rectangular and Hamming window function. We let LCA select from a set of Kaiser windows with responses in this span, and add some steered variations of each. We limit the steering to roughly half the − $3$ -dB width of the window's amplitude response. Using experimental data from the Kongsberg Maritime HISAS1030 sonar we find that LCA and MVDR produce nearly identical images of large scenes, both being superior to DAS. On point targets LCA is able to double the resolution compared to DAS, or provide half that of MVDR. This performance is achieved with a total of six windows: the rectangular window and the Kaiser window with $\beta =5$ , in an unsteered version, and versions that are left and right steered to the steering limit. Slightly smoother images are produced if the window count is increased to 15, but past this we observe minimal difference. Finally, we show that LCA works just as well if Kaiser windows are substituted with trigonometric ones. All our observations and experiences point to LCA being very easy to understand and manage. It simply works, and is surprisingly insensitive to the exact type of window function, steering amount, or number of windows. It can be efficiently implemented on parallel hardware, and handles any scene without the need for parameter adjustments.

Dual-/tri-apodization techniques for high frequency ultrasound imaging: a simulation study.

BackgroundIn the ultrasound B-mode (Brightness-mode) imaging, high side-lobe level reduces contrast to noise ratio (CNR). A linear apodization scheme by using the window function can suppress the side-lobe level while the main-lobe width is increased resulting in degraded lateral resolution. In order to reduce the side-lobe level without sacrificing the main-lobe width, a non-linear apodization method has been suggested.MethodsIn this paper, we computationally evaluated the performance of the non-linear apodization method such as dual-/tri-apodization focusing on the high frequency ultrasound image. The rectangular, Dolph-Chebyshev, and Kaiser window functions were employed to implement dual-/tri-apodization algorithms. The point and cyst target simulations were conducted by using a dedicated ultrasound simulation tool called Field-II. The center frequency of the simulated linear array transducer was 40 MHz and the total number of elements was 128. The performance of dual-/tri-apodization was compared with that of the rectangular window function focusing on the side-lobe level and the main-lobe widths (at -6 dB and -35 dB).ResultsIn the point target simulation, the main-lobe widths of the dual-/tri-apodization were very similar to that of the rectangular window, and the side-lobe levels of the dual-/tri-apodization were more suppressed by 9 ~ 10 dB. In the cyst target simulation, CNR values of the dual-/tri-apodization were improved by 41% and 51%, respectively.ConclusionsThe performance of the non-linear apodization was numerically investigated. In comparison with the rectangular window function, the non-linear apodization method such as dual- and tri-apodization had low side-lobe level without sacrificing the main-lobe width. Thus, it can be a potential way to increase CNR maintaining the main-lobe width in the high frequency ultrasound imaging.

SU-E-T-558: Photon Fluence Model for Distributed Radiation Sources Using the Convolution Method

Purpose: Sophisticated dose calculation algorithms based on principles of convolution theory are commonly used in commercial treatment planning systems for calculating photon dose from point‐like radiation sources. However, not much has been studied regarding the modeling of distributed sources such as a Cobalt‐60 (Co‐60) source of 2 cm diameter. In this work, we present a convolution based photon fluence model that can be used for dose calculations for any finite size source. Methods: The photon fluence model proposed in this work is based on two key functions: the source distribution function and the aperture function. The source distribution function, which models primary and scatter radiation independently, was determined using a one‐time Monte Carlo (MC) simulation. Since the focus of this work is on Co‐60 delivery, the MC modeling was based on a Theratronics T780 Co‐60 unit (Best Theratronics). The validity of the MC model was verified with the ion chamber measurements made in a water phantom. The aperture function is a rectangular window function representing the field size. The fluence model was evaluated by comparing the calculated photon fluence to the MC simulated fluence. Results: The comparisons between the photon fluence calculated using the proposed model and the MC simulation fluences show good agreement, better than 2% in the in‐field region of all large and small fields. In the tail and sharp dose gradient regions, this agreement is better than 5% for the large field sizes and 1.5% for the small field sizes. The primary and scatter fluence output factors are within 2% of those obtained with the MC simulations. Conclusion: The results of our investigations indicate that the proposed photon fluence model can accurately determine fluence for large and small radiation beams from finite size sources. This model has the potential of playing an integral role in Co‐60 based IMRT treatment planning.

Doppler Information Optimization through Fusion Algorithms

ABSTRACT This paper analyses the velocity estimation of a target, from the Doppler filter using 1) Kalman filter 2) Adaptive Kalman filter 3) Kalman filter with state vector fusion 4) Adaptive Kalman filter with state vector fusion 5) State vector fused adaptive Kalman filter. Simulation through MATLAB gave good response for 4 th and 5 th algorithms under low signal to noise ratio. 2 nd and 3 rd algorithms gave better results in intensive maneuvers. But 1 st algorithm even though it is low cost and faster, fails due to the delay in response. Keywords Adaptive Doppler Kalman filter, state vector fusion, intensive maneuver. 1. INTRODUCTION For tracking the velocity of a target, required Doppler frequency shift of the received echo signal is obtained using short time Fourier transformation (STFT) [4] on a rectangular window function. Then quadratic interpolation is used to find better frequency shift. This estimated velocity is optimized using fusion technique. The integration or fusion of redundant information can reduce overall uncertainty and thus serve to increase the accuracy with which the features are perceived by the system [10]. Multiple sensors providing redundant information can also serve to increase reliability in the case of sensor error or failure [5]. Papic

Entropy-Based Time Window for Artifact Removal in UWB Imaging of Breast Cancer Detection

In this letter, we propose an entropy-based time window function for artifact removal in ultra-wideband (UWB) imaging of breast cancer detection. The artifact is due to the incident and skin-breast backscattered signal in such an imaging system. Observing that artifacts at different antennas are very similar, we define an entropy function in the antenna domain to measure the similarity of different antenna signals and design a rectangular window function to eliminate the artifacts. This window function is applied to the computed finite-difference time-domain (FDTD) data of the breast model with a tumor embedded. Compared with the Wiener filtering algorithm, this entropy-based algorithm is computationally simple. In addition, it requires no prior knowledge about the breast and the tumor and brings no distortion to the tumor reflection

Discrete iterative optical computed tomography algorithm for reconstructions comprising opaque objects

A new approach combining a discrete iterative reconstruction- reprojection algorithm DIRR with a finite impulse response FIR low- pass filter is proposed for reconstructing images comprising opaque ob- jects in optical computed tomography CT. This filter, employing a rectangular window function and various bandwidths, is adopted to smooth the reprojection data between iterative reconstruction and re- projection stages. Compared reconstruction results of the traditional it- erative reconstruction-reprojection IRR algorithm, projection space it- eration reconstruction-reprojection PSIRR algorithm, and the new DIRR algorithm for an asymmetrical four-peak and a single-peak test image, including a circle round opaque object, are studied. The results show that the reconstruction precision of the new algorithm is related to the value of the bandwidth of the finite impulse response FIR filter, and the optimal bandwidth increases when the space frequency of the recon- structed image ascends. Furthermore, the DIRR algorithm with an opti- mal bandwidth has an obviously higher reconstruction precision than IRR and PSIRR algorithms, and has a potential application of recon- structing images, including obstacle objects with limited views. © 2005

A generalised model of milling forces

This paper presents the development of a generalised cutting force model for both end-milling and face-milling operations. The model specifies the interaction between workpiece and multiple cutter flutes by the convolution of cutting-edge geometry function with a train of impulses having the period equivalent to tooth spacing. Meanwhile, the effect of radial and axial depths of cut are represented by the modulation of the cutting-edge geometry function with a rectangular window function. This formulation leads to the development of an expression of end/face-milling forces in explicit terms of material properties, tool geometry, cutting parameters and process configuration. The explicitness of the resulting model provides a unique alternative to other studies in the literature commonly based on numerical integrations. The closed-form nature of the cutting force expression can facilitate the planning, optimisation, monitoring, and control of milling operations with complicated tool—work interactions. Experiments were performed over various cutting conditions and results are presented, in verification of the model fidelity, in both the angle and frequency domains.

Window function influence on phase error in phase-shifting algorithms

We present five different eight-point phase-shifting algorithms, each with a different window function. The window function plays a crucial role in determining the phase (wavefront) because it significantly influences phase error. We begin with a simple eight-point algorithm that uses a rectangular window function. We then present alternative algorithms with triangular and bell-shaped window functions that were derived from a new error-reducing multiple-averaging technique. The algorithms with simple (rectangular and triangular) window functions show a large phase error, whereas the algorithms with bell-shaped window functions are considerably less sensitive to different phase-error sources. We demonstrate that the shape of the window function significantly influences phase error.

An improved Force-Response Window Function for Impact Vibration Testing.

In this paper, the authors propose a drastic improvement with regard to the force-response window function, which is commonly used on impact vibration testing. The customary force-response window function pairs a rectangular window function for impulsive force signals and an exponential function for vibration response signals. The three dynamic characteristics : inertia, damping and stiffness, are measured with distortion since neither is an actual force signal an exact impulse, nor is data acquisition triggered at t=0 for the exponential window function. Consequently, modal parameters are necessarily identified with bias errors that cannot be ignored in the measured data. Bias errors cannot be removed by any post-treatment techniques because an actual force is never an exact impulse. An improved force-response window function frees the experimental results obtained by impact vibration testing from the problem of the bias error.