Optimized staggered-grid finite-difference operators using window functions

The staggered-grid finite-difference （SGFD） method has been widely used in seismic forward modeling. The precision of the forward modeling results directly affects the results of the subsequent seismic inversion and migration. Numerical dispersion is one of the problems in this method. The window function method can reduce dispersion by replacing the finite-difference operators with window operators, obtained by truncating the spatial convolution series of the pseudospectral method. Although the window operators have high precision in the low-wavenumber domain, their precision decreases rapidly in the high-wavenumber domain. We develop a least squares optimization method to enhance the precision of operators obtained by the window function method. We transform the SGFD problem into a least squares problem and find the best solution iteratively. The window operator is chosen as the initial value and the optimized domain is set by the error threshold. The conjugate gradient method is also adopted to increase the stability of the solution. Approximation error analysis and numerical simulation results suggest that the proposed method increases the precision of the window function operators and decreases the numerical dispersion.

Windowing Techniques, the Welch Method for Improvement of Power Spectrum Estimation

This paper revisits the characteristics of windowing techniques with various window functions involved,and successively investigates spectral leakage mitigation utilizing the Welch method.The discrete Fourier transform(DFT)is ubiquitous in digital signal processing(DSP)for the spectrum analysis and can be efciently realized by the fast Fourier transform(FFT).The sampling signal will result in distortion and thus may cause unpredictable spectral leakage in discrete spectrum when the DFT is employed.Windowing is implemented by multiplying the input signal with a window function and windowing amplitude modulates the input signal so that the spectral leakage is evened out.Therefore,windowing processing reduces the amplitude of the samples at the beginning and end of the window.In addition to selecting appropriate window functions,a pretreatment method,such as the Welch method,is effective to mitigate the spectral leakage.Due to the noise caused by imperfect,nite data,the noise reduction from Welch’s method is a desired treatment.The nonparametric Welch method is an improvement on the periodogram spectrum estimation method where the signal-to-noise ratio(SNR)is high and mitigates noise in the estimated power spectra in exchange for frequency resolution reduction.The periodogram technique based on Welch method is capable of providing good resolution if data length samples are appropriately selected.The design of nite impulse response(FIR)digital lter using the window technique is rstly addressed.The inuence of various window functions on the Fourier transform spectrum of the signals is discussed.Comparison on spectral resolution based on the traditional power spectrum estimation and various window-function-based Welch power spectrum estimations is presented.

A NOVEL METHOD ON DESIGNING BISPECTRAL WINDOWS

A novel method on designing bispectral windows is proposed in this letter. Compound functions based on a function with binary quadric form, starting from the symmetry characteristic of three-order moments are used as the 2-D windowfunctions. Two approaches on how to find the expressions of the compound functions are discussed in detail. One is to approximate the compound function after being Taylor expanded under the Minimum Mean Square Error (MMSE) criteria. Another is to compound the hyperbolic secant function and the binary quadric function directly. According to theoretical analysis, the first type new windows have been proved as slightly better than the conventional ones, the second type new windows are much better than the conventional ones, and the bispectral estimation mean square error approximates to 0.

Cosine-modulated window function-based staggered-grid finite-difference forward modeling

The numerical dispersion and computational cost are high for conventional Taylor series expansion staggered-grid finite-difference forward modeling owing to the high frequency of the wavelets and the large grid intervals. In this study, the cosine-modulated binomial window function （CMBWF）-based staggered-grid finite-difference method is proposed. Two new parameters, the modulated time and modulated range are used in the new window function and by adjusting these two parameters we obtain different characteristics of the main and side lobes of the amplitude response. Numerical dispersion analysis and elastic wavefield forward modeling suggests that the CMBWF method is more precise and less computationally costly than the conventional Taylor series expansion staggered-grid finite-difference method.

Theoretical analysis of adaptive harmonic window and its application in frequency extraction of vibration signal

The goal of this paper is to find an excellent adaptive window function for extracting the weak vibration signal and high frequency vibration signal under strong noise.The relationship between windowing transform andfiltering is analyzed first in the paper.The advantage of adjustable time-frequency window of wavelet transform is introduced.Secondly the relationship between harmonic wavelet and multiple analytic band-pass filter is analyzed.The coherence of the multiple analytic band-pass filter and harmonic wavelet base function is discussed,and the characteristic that multiple analytic band-pass filter included in the harmonic wavelet transform is founded.Thirdly,by extending the harmonic wavelet transform,the concept of the adaptive harmonic window and its theoretical equation without decomposition are put forward in this paper.Then comparing with the Hanning window,the good performance of restraining side-lobe leakage possessed by adaptive harmonic window is shown,and the adaptive characteristics of window width changing and analytical center moving of the adaptive harmonic window are presented.Finally,the proposed adaptive harmonic window is applied to weak signal extraction and high frequency orbit extraction of high speed rotor under strong noise,and the satisfactory results are achieved.The application results show that the adaptive harmonic window function can be successfully applied to the actual engineering signal processing.

Performance analysis of fast GPS signal acquisition based on PMF and Window FFT

Combining the advantages of partial matched filter（PMF） and fast Fourier transform（FFT）,an improved fast acquisition method for GPS C/A code is proposed.According to PMF-FFT acquisition architecture,the greater the number of PMF will bring out the more slowly amplitude decreasing of the amplitude-frequency response,the smaller scale of the corresponding PMF,and the larger computation of the FFT.In order to compensate the frequency spectrum attenuation caused by spectrum leakage and fence effect,adding window function to PMF-FFT is presented.Through comparing the influences to the acquisition performance based on rectangular,Hamming,Blackman and Rife-Vincent（Ⅲ） window functions,an improved Rife-Vincent Ⅲ windowing algorithm is recommended for the fast acquisition based on PMF-FFT.

Parameter Estimation of Sub-/Super-synchronous Oscillation Based on Interpolated All-phase Fast Fourier Transform with Optimized Window Function

In recent years,with increasing amounts of renewable energy sources connecting to power grids,sub-/super-synchronous oscillations(SSOs)occurred more frequently.Due to the time-variant nature of SsO magnitudes and frequencies,as well as the mutual interferences among SsO modes with close frequencies,the accurate parameter estimation of SsO has become a particularly challenging topic.To solve this issue,this paper proposes an improved spectrum analysis method by improving the window function and a spectrum correction method to achieve higher precision.First,by aiming at the sidelobe characteristics of the window function as evaluation criteria,a combined cosine function is optimized using a genetic algorithm(GA).Furthermore,the obtained window function is self-convolved to extend its excellent characteristics,which have better performance in reducing mutual interference from other SSO modes.Subsequently,a new form of interpolated all-phase fast Fourier transform(IpApFFT)using the optimized window function is proposed to estimate the parameters of SsO.This method allows for phase-unbiased estimation while maintaining algorithmic simplicity and expedience.The performance of the pro-posed method is demonstrated under various conditions,com-pared with other estimation methods.Simulation results validate the effectiveness and superiority of the proposed method.

Beamlet prestack depth migration and illumination： A test based on the Marmousi model

Beamlet sources have strong local and directional character and can easily accomplish local illumination and migration. Besides, they provide better migration results than conventional migration methods. We introduce the basic principles of beamlet prestack depth migration that includes a windowed Fourier transform and frame theory. We explain the Gabor-Daubechies （G-D） frame based on a Gaussian function. Beamlet decomposition provides information on the local space and direction of wavefield. We synthesize the beamlet source and beamlet records in the wavelet domain using both rectangle and Gaussian windows and then extrapolate the synthesized data with a Fourier finite-difference operator. We test the method using the standard Marmousi model. By comparing and analyzing the migration results of single directional beamlet and beamlets with different windows and directions, we demonstrate the validity of the prestack depth migration with Gaussian beamlets method.

Threshold flux-controlled memristor model and its equivalent circuit implementation

Modeling a memristor is an effective way to explore the memristor properties due to the fact that the memristor devices are still not commercially available for common researchers. In this paper, a physical memristive device is assumed to exist whose ionic drift direction is perpendicular to the direction of the applied voltage, upon which, corresponding to the HP charge-controlled memristor model, a novel threshold flux-controlled memristor model with a window function is proposed. The fingerprints of the proposed model are analyzed. Especially, a practical equivalent circuit of the proposed model is realized, from which the corresponding experimental fingerprints are captured. The equivalent circuit of the threshold memristor model is appropriate for various memristors based breadboard experiments.

Accurate Analysis of Multi-Mode Interferometric Optical Fiber Sensor

In view of the problem that the sensing characteristics of the multi-mode interferometric fiber sensors cannot be accurately analyzed,an analysis method based on the fast Fourier transform(FFT)and inverse fast Fourier transform(IFFT)is proposed and demonstrated theoretically and experimentally.The suitabilities of the rectangular window function with the narrow main lobe(high spectrum resolution)and low side lobe(high main mode energy leakage)and the Hanning window function with the wide main lobe(low spectrum resolution)and high side lobe(high energy concentration)in this kind of sensor analysis are discussed,respectively.This method can not only realize the sensing performance analysis of the various modes,but also overcome the inconsistency of the different interference wavelength(dip)sensing characteristics in the conventional analysis methods.At the same time,this method is also beneficial to solve the repetitive problem of such sensors.

A new family of windows——convolution windows and their applications

A new family of windows is constructed by convolutions via a few rectangular windows with same time width and is thus referred to as convolution windows. The expressions of the second-order up to the eighth-order convolution windows in both the time and frequency domains are derived. Their applications in high accuracy harmonic analysis of periodic signals are investigated. Comparisons between the proposed windows and some known windows with the same width shows that, when the synchronous deviation of data sampling is slight, the proposed ones have the least effect of spectral leakage. Therefore, the new windows are well suited for high accuracy harmonic analysis and parameter estimation for periodic signals. The error analysis and computer simulations show that the estimation errors, corresponding to frequency, amplitude and phase of every harmonic component of a signal, are proportional to the pth power of the relative frequency deviation in case of the pth-order convolution window is applied to windowing signal of approximately p cycles. By introducing real time adjustment in sampling interval, the proposed algorithm can adaptively trace signal frequency and lead to less sampling synchronous deviation. The proposed approach has the advantages of easy implementation and high measure precision and can be used in harmonic analysis of quasi-periodic signals whose fundamental frequency drifts slowly with time.

Wavelet Variance Analysis of EEG Based on Window Function

A new wavelet variance analysis method based on window function is proposed to investigate the dynamical features of electroencephalogram(EEG).The exprienmental results show that the wavelet energy of epileptic EEGs are more discrete than normal EEGs, and the variation of wavelet variance is different between epileptic and normal EEGs with the increase of time-window width. Furthermore, it is found that the wavelet subband entropy (WSE) of the epileptic EEGs are lower than the normal EEGs.

Convergence of FBP Algorithm for Tomography

Filter back-projection （FBP） algorithms are available and extensively used methods for tomogra- phy. In this paper, we prove the convergence of FBP algorithms at any continuous point of image function, in L2-norm and L1-norm under the certain assumptions of image and window functions of FBP algorithms.

Comparative analysis of memristor models and memories design

The advent of the memristor breaks the scaling limitations of MOS technology and prevails over emerging semiconductor devices. In this paper, various memristor models including behaviour, spice, and experimental are investigated and compared with the memristor＇s characteristic equations and fingerprints. It has brought to light that most memristor models need a window function to resolve boundary conditions. Various challenges of availed window functions are discussed with matlab＇s simulated results. Biolek＇s window is a most acceptable window function for the memristor, since it limits boundaries growth as well as sticking of states at boundaries. Simmons tunnel model of a memristor is the most accepted model of a memristor till now. The memristor is exploited very frequently in memory designing and became a prominent candidate for futuristic memories. Here, several memory structures utilizing the memristor are discussed. It is seen that a memristor-transistor hybrid memory cell has fast read/write and low power operations. Whereas,a 1 T1 R structure provides very simple,nanoscale,and non-volatile memory that has capabilities to replace conventional Flash memories. Moreover, the memristor is frequently used in SRAM cell structures to make them have non-volatile memory. This paper contributes various aspects and recent developments in memristor based circuits, which can enhance the ongoing requirements of modern designing criterion.

Analysis and parameter extraction of memristive structures based on Strukov's non-linear model

Diverse models have been proposed for explaining the electrical performance of memristive devices. In principle, the behavior of internal variables associated to each one could be extracted from experimental results. In a former work, thermally grown TiOmemristive structures were built and characterized to obtain the constitutive relationship(magnetic flux versus charge). The aim of this work is to continue that analysis by determining the microscopic parameters within the frame of a simple model. We use the already obtained memristance dependence of time and the basic expressions from the non-linear model proposed by Strukov et al. to compute the state-variable,the mobility of the doping species, the speed of the boundary between the doped and the undoped regions, the voltages and the electric fields on the distinct regions. The power dissipation and its time evolution are also presented. Moreover, a quite different window function from those formerly proposed, which was estimated from experimental data, is also determined. This information provides a straightforward picture of the ionic transport during one cycle of a square voltage waveform within the framework of this simple model. Finally, a quality factor is proposed as the key parameter for actual memristors viewed under the same model.

Testing Jitter on PLL Clocks Based on Analysis of Instantaneous Phase

A novel method based on the analysis of instantaneous phase is proposed to extract the jitter on phase-locked loops output clock. The method utilizes the Hilbert transform to extend the real signal of PLLs output into an analytic signal, and the implementation of Hilbert transform is based on the Fourier transform windowed with Hamming window. Then, the jitter of clock is extracted from the instantaneous phase of analytic signal. The experimental results of simulations validate that the proposed method can effectively extract the jitter on PLL clock, and it has better performance by comparing the sinusoidal jitter extraction results with the other methods.

High-Speed Parallel Matched Filter Designing and FPGA Implementation

Matched filter is one of the key technologies to achieve high-speed data transmission. In this paper,a parallel finite-impulse response (FIR) filter structure based on polyphase filter-ing is used to achieve high-speed matched filter in quadrature phase-shift keying (QPSK) demodulation up to 800 Mb·s-1. First,a window function is employed of to obtain impulse response of matched filter. Second,the high-speed parallel FIR structure is presented based on polyphase filtering. Then,the filter with EP2S180F1020 on the Quartus II 7.2 platform is achieved. The final results show that the design is correct and can implement high-speed matched filtering,wherein the equivalent frequency of which is up to 2 037 MHz. In addition,this scheme is easy to real-ize,which brings great value to the application of this filter in high-speed matched filters design in demodulation systems.