Design Of Window Function Research Articles

A new window function for the spectral analysis of effect of celestial body on Taiji mission below 0.1 mHz

The Taiji project is a space gravitational wave detection mission consisting of three satellites that form a large equilateral triangle with a side length of approximately 3×109 m in heliocentric orbit. It may have the potential to detect gravitational waves below 0.1 mHz. Gravitational wave signals in the μHz range have a strain sensitivity as large as 2.9×10-14, or approximately 8.7×10-5 m variation in inter-satellite distance. However, inter-satellite distances are affected by the celestial bodies in the solar system, introducing changes that may reach magnitudes of 3×107 m; thus, the effect of celestial bodies on these distances may exceed the gravitational signals below 0.1 mHz. Therefore, it is necessary to accurately estimate the effect of the gravity of celestial bodies below 0.1 mHz. In this study, based on the inter-satellite distances in the Taiji mission, a window function design method is proposed and a six-term cosine window function is designed. It has a high decay rate of h-12 and a good peak sidelobe level of −88 dB. It improves the attenuation of spectral leakage while maintaining an acceptable minimum number of signal periods, which is beneficial for signals where it is difficult to obtain more periods, such as for the Taiji mission. Based on the analytical results of the states of satellites in cases when the satellites move only in the gravitational field of the Sun, the ability of the new window function is validated.

Statistical Analysis and EEG Signal Filtering Using Design of Window Function Based on Optimization Methods

The window functions, which are widely used in Finite Impulse Response (FIR) digital filter design with the Fourier Series Methods, aim to eliminate the oscillations adversely affecting the filter performance that occur during the filter design. Window functions, which were developed with different methods in the literature, were designed with three different optimization techniques in this study. By using Particle Swarm Optimization (PSO), Grey Wolf Colony Optimization (GWCO), Cuckoo Search Optimization (CSO) algorithms, which are among current metaheuristic optimization methods, new window functions are designed for FIR digital filter design such that the designed new window functions have different window coefficients and design parameters. The difference of the designed window functions was analyzed with the Friedman and Wilcoxon tests, which are statistical data analysis methods, and the originality of the designed window functions was proven. FIR digital filters that can perform the same operation as the designed window functions have been produced and the results obtained by performing the filtering application of the EEG signal with the produced filters are presented in the study.

Window Function Design for Asymmetric Beampattern Synthesis and Applications

This letter proposes a novel window function design to synthesize asymmetric beampatterns while minimizing the gain loss for clutter/interference suppression as required in practical applications, such as airborne phased array radar (APAR). Compared with beampattern synthesis in terms of designing the weight vector directly, the proposed method can achieve asymmetric sidelobes for multiple steering directions resort to designing one window while circumventing repetitive computations. To tackle the resultant non-convex optimization problem, an iterative alternating optimization (IAO) algorithm is introduced where each iteration involves multiple subproblems that can be solved via either convex approximation (CA) approach or closed-form solutions. Finally, numerical simulations are provided to verify the effectiveness of the proposed method comparing with the classical adjustable window functions (CAWFs).

Optimization Approach in Window Function Design for Real-Time Filter Applications

Eliminating the Gibbs oscillations that occur during the Finite Impulse Response (FIR) digital filter design with the Fourier Series method will ensure correct filtering. For this reason, the development of the window improves the performance of the filter and, therefore, the system. In this study, the cosh window function is designed using Particle Swarm Optimization, which is a preferred optimization method in many areas. Thus, alternatives to the standard results obtained from the existing traditional calculations will be produced, and different windows that perform the same function will be obtained. In addition, exponential and cosh window functions were designed in LabVIEW environment, which is a graphical programming language-based program, and the designed windows were analyzed at different parameter values. LabVIEW provides a fast and easy programming environment, and it provides the opportunity to realize real-time applications with its external hardware. Utilizing this feature, the amplitude spectrum of cosh window designed in LabVIEW is displayed in real time for different window parameter values. As a result, FIR digital filters were designed using cosh window based on optimization and the cosh window designed in LabVIEW, and the distorted EEG signal was filtered using these filters and displayed in real time.

Distortionless 1/2 Overlap Windowing in Frequency Domain Anti-Jamming of Satellite Navigation Receivers

Frequency-domain anti-jamming technology is a common anti-jamming method for satellite navigation receivers. 1/2 overlapping windowing can effectively solve the spectrum leakage in the frequency domain conversion process, but the traditional window function will cause the loss of signal energy. This paper proposes a window function design method with no loss of signal energy, which can effectively solve the signal energy loss caused by the window function. The feasibility of the proposed method is theoretically deduced, and the effectiveness of the proposed method is verified by simulation and measured data. Compared with the traditional window function, the signal-to-noise ratio improvement of the method proposed in this paper is better than 0.5 dB. The frequency domain anti-jamming processing is optimized, the signal-to-noise ratio loss caused by the anti-jamming processing is reduced, and the anti-jamming performance is indirectly improved. This plays an important role in the performance optimization of satellite navigation system links.

A novel design of window function modulated meander-line-coils EMATs for unidirectional Rayleigh waves generation and sidelobes suppression

A new design of Window Function modulated electromagnetic acoustic transducers (EMATs) to generate unidirectional Rayleigh waves is proposed. The novel EMATs, Rectangular-Window-Meander-Line-Coil EMATs (RWMLC-EMATs) and Kaiser-Window-Meander-Line-Coil EMATs (KWMLC-EMATs), contain two variable length meander line coils with a spacing of one quarter of Rayleigh waves’ wavelength; the excitation signals for these two coils have a phase difference of 900. The structure of the variable wire length determines the level of the sidelobes suppression; the structure of two meander line coils combined with the excitation signals with a phase difference of 900 determine that Rayleigh waves only propagate along one direction. RWMLC-EMATs and KWMLC-EMATs are analyzed via a wholly analytical method and are validated with experiments, which proves the feasibility of the proposed EMATs structure. In addition, the effect of the wire step and the longest wire length are investigated analytically and experimentally. Results indicate that, wire step mainly affects the suppressed level of sidelobes – a large wire step leads to a small suppressed level of sidelobes. This work can be used for Rayleigh waves EMATs design and optimization to improve their defect detection capability.

Optimal design of window functions for filter window bank

This paper considers the designs of the periodic window functions in the filter window banks. First, the filter window bank with the constant synthesis periodic window functions is considered. The total number of the nonzero coefficients in the impulse responses of the analysis periodic window functions is minimized subject to the near perfect reconstruction condition. This is an $ L_0 $ norm optimization problem. To find its solution, the $ L_0 $ norm optimization problem is approximated by the $ L_1 $ norm optimization problem. Then, the column of the constraint matrix corresponding to the element in the solution with the smallest magnitude is removed. Next, it is tested whether the feasible set corresponding to the new $ L_0 $ norm optimization problem is empty or not. By repeating the above procedures, a solution of the $ L_0 $ norm optimization problem is obtained. Second, the filter window bank with the time varying synthesis periodic window functions is considered. Likewise, the design of the periodic window functions in both the analysis periodic window functions and the synthesis periodic window functions is formulated as an $ L_0 $ optimization problem. However, this $ L_0 $ norm optimization problem is subject to a quadratic matrix inequality constraint. To find its solution, the set of the synthesis periodic window functions is initialized. Then, the set of the analysis periodic window functions is optimized based on the initialized set of the synthesis periodic window functions. Next, the set of the synthesis periodic window functions is optimized based on the found set of the analysis periodic window functions. Finally, these two procedures are iterated. It is shown that the iterative algorithm converges. A design example of a filter window bank with the constant synthesis periodic window functions and a design example of a filter window bank with the time varying synthesis periodic window functions are illustrated. It is shown that the near perfect reconstruction condition is satisfied, whereas this is not the cases for the nonuniform filter banks with the conventional samplers and the conventional block samplers.

Eliminating the Effect of Image Border with Image Periodic Decomposition for Phase Correlation Based Remote Sensing Image Registration.

In the remote sensing community, accurate image registration is the prerequisite of the subsequent application of remote sensing images. Phase correlation based image registration has drawn extensive attention due to its high accuracy and high efficiency. However, when the Discrete Fourier Transform (DFT) of an image is computed, the image is implicitly assumed to be periodic. In practical application, it is impossible to meet the periodic condition that opposite borders of an image are alike, and image always shows strong discontinuities across the frame border. The discontinuities cause a severe artifact in the Fourier Transform, namely the known cross structure composed of high energy coefficients along the axes. Here, this phenomenon was referred to as effect of image border. Even worse, the effect of image border corrupted its registration accuracy and success rate. Currently, the main solution is blurring out the border of the image by weighting window function on the reference and sensed image. However, the approach also inevitably filters out non-border information of an image. The existing understanding is that the design of window function should filter as little information as possible, which can improve the registration success rate and accuracy of methods based on phase correlation. In this paper, another approach of eliminating the effect of image border is proposed, namely decomposing the image into two images: one being the periodic image and the other the smooth image. Replacing the original image by the periodic one does not suffer from the effect on the image border when applying Fourier Transform. The smooth image is analogous to an error image, which has little information except at the border. Extensive experiments were carried out and showed that the novel algorithm of eliminating the image border can improve the success rate and accuracy of phase correlation based image registration in some certain cases. Additionally, we obtained a new understanding of the role of window function in eliminating the effect of image border, which is helpful for researchers to select the optimal method of eliminating the effect of image border to improve the registration success rate and accuracy.

Conforming window functions for meshfree methods

Window functions provide a base for the construction of approximation functions in many meshfree methods. They control the smoothness and extent of the approximation functions and are commonly defined using Euclidean distances which helps eliminate the need for a meshed discretization, simplifying model development for some classes of problems. However, for problems with complicated geometries such as nonconvex or multi-body domains, poor solution accuracy and convergence can occur unless the extents of the window functions, and thus approximation functions, are carefully controlled, often a time consuming or intractable task. In this paper, we present a method to provide more control in window function design, allowing efficient and systematic handling of complex geometries. “Conforming” window functions are constructed using Bernstein–Bézier splines defined on local triangulations with constraints imposed to control smoothness. Graph distances are used in conjunction with Euclidean metrics to provide adequate information for shaping the window functions. The conforming window functions are demonstrated using the Reproducing Kernel Particle Method showing improved accuracy and convergence rates for problems with challenging geometries. Conforming window functions are also demonstrated as a means to simplify the imposition of essential boundary conditions.

Band-Pass Digital Filter Window Function Method Design and Spectrum Leak Analysis Based on MATLAB

In the digital signal processing process, the length of signal that we can get is limited, so should be infinite long time sequence limit in a certain interval, only choose one of the segment signal to carry on the analysis, namely cut off the signal, and this process is equivalent to add a window function to the signal is, using the window function truncation infinite unit sampling response sequence. This article in accordance with the principles of window function design method, based on analysis spectrum of the measured signal, design and analysis that add different window function on filter performance effect while signal intercept, and ultimately chose a suitable window function for the measured signal to the design of filter. Through the MATLAB simulation shows that the choice of window function can meet the measured signal filtering.

Application of modified Wigner distribution method to voltage flicker-generated signal studies

With the time–frequency localization characteristics embedded in Wigner distribution, the time and frequency information of a waveform can be both integrally presented. Yet, due to the cross-term problem, the inspection performance is often affected. Therefore, in this study, with the assistance of a window function design, we have proposed a modified Wigner distribution method and applied to voltage flicker-generated signal analysis. This approach not only effectively reserves the merits of Wigner distribution and short-time Fourier transform, but also highly decreases the probability of cross-term occurrence. In order to confirm the feasibility of the method, it has been tested to inspect several voltage flicker-generated signals collected from both simulated waveforms and field measurements. Test results support the feasibility of the method for the application investigated.