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In infrared spectroscopy of thin film samples, interference introduces distortions in spectra, commonly referred to as fringes. Fringes may alter absorbance peak ratios, which hampers the spectral analysis. We have previously introduced extended multiplicative signal correction (EMSC) for fringes correction. In the current article, we provide a robust open-source algorithm for fringe correction in infrared spectroscopy and propose several improvements to the Fringe EMSC model. The suggested algorithm achieves a more precise fringe frequency estimation by mean centering of the measured spectrum and applying a window function prior to the Fourier transform. It selects two frequencies from a user defined number of maxima in the Fourier domain. The improved Fringe EMSC algorithm is validated on two experimental datasets, one of them being a hyperspectral image. Techniques for separating sample spectra from background spectra in hyperspectral images, and techniques to identify spectra affected by fringes are also provided. publishedVersion

PURPOSE To improve the SNR efficiency and reduce the T2 blurring of 3D rapid acquisition with relaxation enhancement stack-of-spiral arterial spin labeling imaging by using variable refocusing flip angles and k-space filtering. METHODS An algorithm for determining the optimal combination of variable flip angles and filtering correction is proposed. The flip angles are designed using extended phase graph physical simulations in an analytical and global optimization framework, with an optional constraint on deposited power. Optimal designs for correcting to Hann and Fermi window functions were compared with conventional constant amplitude or variable flip angle only designs on 6 volunteers. RESULTS With the Fermi window correction, the proposed optimal designs provided 39.8 and 27.3% higher SNR (P

The transient electromagnetic method has a wide range of depth of exploration in the ground. The transient-electromagnetic-method-based shallow sounding is becoming popular in engineering geophysics such as grounding grid measurement, pipeline detection, and mine exploration. It is useful for shallow sounding to raise the transmitting frequency, improve the spectral resolution, and enhance the power of withstanding all kinds of near-surface noise. Therefore, a well-designed transmitter current waveform should not only induce more effective geoelectric information at a low energy cost but also prevent external interferences during transient electromagnetic method prospecting. For this purpose, the frequency-domain characteristics of single-pulse waveforms and multipulse sequences are analysed, on the basis of three fundamental waveforms—rectangular, triangular, and half-sine shapes. The energy efficiency ratio, high-frequency energy percentage, and frequency resolution are introduced to evaluate the performance of the transmitter current source, in a numerical or graphical manner. Furthermore, six window functions are used to modulate the rectangular pulse sequence. The analysis and simulation results prove that the pulse current source modulated by the Blackman window is advantageous in terms of energy efficiency, high-frequency content, and frequency resolution. In addition, the Blackman modulating sequence has many blank frequency bands (also called identifiable bands) where the noise is completely exposed and easy to remove. This work is useful for the design, optimisation, and selection of transmitter current waveforms for different applications, especially for near-surface geophysical prospecting.

Two-dimensional (2D) data are typically truncated in both dimensions, but invariably and severely so in the indirect dimension. These truncated FIDs and/or interferograms are extensively zero filled, and Fourier transformation of such zero-filled data is always preceded by a rapidly decaying apodization function. Hence, the frequency line width in the spectrum (at least parallel to the evolution dimension) is almost always dominated by the apodization function. Such apodization-driven line broadening in the indirect (t1 ) dimension leads to the lack of clear resolution of cross peaks in the 2D spectrum. Time-domain analysis (i.e. extraction of frequency, amplitudes, line width, and phase parameters directly from the FID, in this case via Bayesian modeling into a tabular format) of NMR data is another approach for spectral resonance characterization and quantification. The recently published complete reduction to amplitude frequency table (CRAFT) technique converts the raw FID data (i.e. time-domain data) into a table of frequencies, amplitudes, decay rate constants, and phases. CRAFT analyses of time-domain data require minimal or no apodization prior to extraction of the four parameters. We used the CRAFT processing approach for the decimation of the interferograms and compared the results from a variety of 2D spectra against conventional processing with and without linear prediction. The results show that use of the CRAFT technique to decimate the t1 interferograms yields much narrower spectral line width of the resonances, circumventing the loss of resolution due to apodization. Copyright © 2016 John Wiley & Sons, Ltd.

Summary A common approach to model memristive systems is to include empirical window functions to describe edge effects and nonlinearities in the change of the memristance. We demonstrate that under quite general conditions, each window function can be associated with a sigmoidal curve relating the normalised time-dependent memristance to the time integral of the input. Conversely, this explicit relation allows us to derive window functions suitable for the mesoscopic modelling of memristive systems from a variety of well-known sigmoidals. Such sigmoidal curves are defined in terms of measured variables and can thus be extracted from input and output signals of a device and then transformed to its corresponding window. We also introduce a new generalised window function that allows the flexible modelling of asymmetric edge effects in a simple manner. Copyright © 2016 John Wiley & Sons, Ltd.

Rationale Absorption mode Fourier transform ion cyclotron resonance (FTICR) mass spectra offer significant benefits in terms of spectral resolution, signal-to-noise (S/N) ratio and measured mass accuracy. However, to date, methods for producing absorption mode spectra have created an undesirable baseline deviation as a consequence of FFT artifacts, resulting in interference of the frequency side-lobes of intense peaks. Methods for fitting and removing this deviation have been developed, but these are computationally intensive, slow and can be unreliable in practice. Methods We have developed an approach for producing FTICR mass spectra which uses a new apodization approach to produce spectra which do not exhibit baseline deviation, whilst maintaining all the normal absorption mode benefits. This method involves the use of 'full' apodization function, replacing the more common Hann or half Hann functions, and where the user can control the position of the function maximum expressed as a fraction (F) of the transient length. Results Absorption mode spectra produced using the new apodization function we propose provide all the normal benefits but do not exhibit baseline deviation that must be corrected prior to spectral interpretation. Additionally, varying the value of the F parameter allows users additional control over the compromise between the spectral resolving power and the S/N ratio. This is particularly beneficial in spectra with pronounced amplitude changes during the recording of the transient (detection). Conclusions The use of a 'full' apodization function, which may be asymmetric, prior to zero-padding and Fourier transformation, allows the production of absorption mode spectra which do not suffer from baseline deviation. Hence, it is no longer necessary to apply a baseline deviation correction in post processing, providing a significant performance advantage. Copyright © 2015 John Wiley & Sons, Ltd.

The finite-difference method has been widely utilized in seismic wave numerical modeling, seismic imaging, and full waveform inversion; the accuracy of finite-difference numerical solution directly affects the result of seismic imaging and inversion. We can truncate spatial convolutional counterpart of the pseudo-spectral method to get finite-difference operators using truncated windows, and the properties of truncated windows in their amplitude responses play a major role in finite-difference approximation. In specific, the accuracy of finite-difference approximation can be determined by the properties of main lobe and side lobe in the amplitude response of window functions, narrower main lobe and larger attenuation of side lobe bring higher accuracy of finite-difference approximation, and significantly suppress numerical dispersion. According to it, we propose an optimized method based on Chebyshev auto-convolution combined window function which has narrow main lobe and large attenuation of side lobe. Through adjusting three parameters of the Chebyshev auto-convolution combined window function, we visually and more intuitively control the properties of main lobe and side lobe to adjust the accuracy of finite-difference approximation. The optimized explicit finite-difference operator increases the accurate wave number coverage range and reduces the volatility of accuracy error, which indicates that the accuracy of low-order operators can reach that of high-order operators. In respect of economics, it effectively reduces the computational cost and improves the computational efficiency.

Memristor is introduced as the fourth basic circuit element. In this paper, we show that piecewise linear function can be used to model memristor. Piecewise linear function is used as a window function to model the memristor device. The piecewise linear window function is linear at each subregion of the domain. Because of this good character, explicit relation between the thickness of the doped region and the charge can be delivered, together with the explicit memristance expression. Models using a general nonlinear window function may not have these explicit results. The piecewise linear window function is also more flexible than the existing window functions. Piecewise linear function can also be used to model the more general memristive systems. Copyright © 2014 John Wiley & Sons, Ltd.

The pulse radar method is one of the fault location methods for power cables. It locates the breakdown point by measuring the delay time of the echo or the discharge signal coming from the breakdown point. The equipment for the pulse radar method is more compact compared to the Murray loop bridge, and its operation is simpler because sensitive adjustments to the proportions are not needed. However, the signal propagating through the cable may be distorted, depending on the distance and frequency, leading to poor location accuracy. In this report, signal processing in the time–frequency domain is proposed to resolve this problem. The pulse waveforms received at two different terminals of the cable were extracted by a window function, and subsequently Fourier-transformed in order to calculate the phase difference at an appropriate frequency. Special care was taken for unwrapping the folded phase spectrum. The phase difference was interpreted as the time lag at an identical frequency. The technique was applied to fault location for a full-size XPLE cable line. © 2012 Wiley Periodicals, Inc. Electr Eng Jpn, 182(1): 10–17, 2013; Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/eej.22323

Purpose: The goal of this paper is to extend our recently developed FBP (filtered backprojection) algorithm, which has the same characteristics of an iterative Landweber algorithm, to an FBP algorithm with the same characteristics of an iterative MAP (maximum a posteriori) algorithm. The newly developed FBP algorithm also works when the angular sampling interval is not uniform. The projection noise variance can be modeled using a view-based weighting scheme. Methods: The new objective function contains projection noise model dependent weighting factors and image dependent prior (i.e., a Bayesian term). The noise weighting is view-by-view based. For the first time, the FBP algorithm is able to model the projection noise. Based on the formulation of the iterative Landweber MAP algorithm, a frequency-domain window function is derived for each iteration of the Landweber MAP algorithm. As a result, the ramp filter and the windowing function are both modified by the Bayesian component. This new FBP algorithm can be applied to a projection data set that is not uniformly sampled. Results: Computer simulations show that the new FBP-MAP algorithm with window function index k and the iterative Landweber MAP algorithm with iteration number k give similar reconstructions in terms of resolution and noise texture. An example of transmission x-ray CT shows that the noise modeling method is able to significantly reduce the streaking artifacts associated with low-dose CT. Conclusions: View-based noise weighting scheme can be introduced to the FBP algorithm as a weighting factor in the window function. The new FBP algorithm is able to provide similar results to the iterative MAP algorithm if the ramp filter is modified with a additive term. Nonuniform sampling and sensitivity can be accommodated by proper backprojection weighting.

Purpose: In order to eventually develop an analytical algorithm with noise characteristics of an iterative algorithm, this technical note develops a window function for the filtered backprojection (FBP) algorithm in tomography that behaves as an iterative Landweber algorithm. Methods: Based on the formulation of the iterative Landweber algorithm, a frequency domain window function is derived for each iteration of the Landweber algorithm. The resultant window function has an index k, emulating the characteristics of the Landweber algorithm at the kth iteration. The window function is used to modify the ramp filter in the FBP algorithm. Results: Computer simulations show that the windowed FBP algorithm with window function index k and the iterative Landweber algorithm iteration number k give similar reconstructions in terms of resolution and noise. Conclusions: Analytical FBP algorithms are able to provide similar results to the iterative Landweber algorithm if the ramp filter in the FBP algorithm is modified by a set of specially designed window functions.

This appendix contains sections titled: Spectrums The Spectrum Analyzer The Window Function Density and Discrete Spurs Control Parameters Frequency Conversion in an Analyzer Displaying L, FPSD, and PPSD Spectral Overlaps Anomalous Spurs

Extracting effective signals from bit in noises from rigs and machines on ground is a key step in SWD (Seismic while drilling) pilot data preprocessing. Source signals from bit, because of the broad range of frequencies and short time duration, can be easily affected by the noises from rigs and machines. Cepstrum analysis is a nonlinear filtering technology, which can change the convoluted signals in time domain into added signals in frequency domain. This method can remove the structural reverberation to extract the source signals by selecting a window function. In this paper, we discuss the cepstral filtering and extract the transient source signals according to the simulation data of drill string. Furthermore, SWD pilot data are processed by using this method in order to realize the intensifying of bit signals.

A cone-angle-based window function is defined in this manuscript for image reconstruction using helical cone beam filtered backprojection (CB-FBP) algorithms. Rather than defining the window boundaries in a two-dimensional detector acquiring projection data for computed tomographic imaging, the cone-angle-based window function deals with data redundancy by selecting rays with the smallest cone angle relative to the reconstruction plane. To be computationally efficient, an asymptotic approximation of the cone-angle-based window function is also given and analyzed in this paper. The benefit of using such an asymptotic approximation also includes the avoidance of functional discontinuities that cause artifacts in reconstructed tomographic images. The cone-angle-based window function and its asymptotic approximation provide a way, equivalent to the Tam-Danielsson-window, for helical CB-FBP reconstruction algorithms to deal with data redundancy, regardless of where the helical pitch is constant or dynamically variable during a scan. By taking the cone-parallel geometry as an example, a computer simulation study is conducted to evaluate the proposed window function and its asymptotic approximation for helical CB-FBP reconstruction algorithm to handle data redundancy. The computer simulated Forbild head and thorax phantoms are utilized in the performance evaluation, showing that the proposed cone-angle-based window function and its asymptotic approximation can deal with data redundancy very well in cone beam image reconstruction from projection data acquired along helical source trajectories. Moreover, a numerical study carried out in this paper reveals that the proposed cone-angle-based window function is actually equivalent to the Tam-Danielsson-window, and rigorous mathematical proofs are being investigated.

For sidelobe suppression design of antennas, weighting with window functions has been traditionally used. The antenna gain is degraded if a low sidelobe level is sought, so that expansion of the antenna beamwidth is inevitable. Also, there have been discussions of using the convergent calculation in the derivation of a window function that realizes desired characteristics such as sidelobe-free conditions, but it has not been clear whether the theoretically maximum antenna gain is realized. This paper presents a method of analytical derivation of a weight vector satisfying the maximum achievable antenna gain while the desired beamwidth is obtained under the null sidelobe constraint for the sidelobe region output. In addition, we demonstrate the effectiveness of the method by simulation examples. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 90(9): 35–44, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.20370

We consider pilot symbol assisted modulation (PSAM) implemented with a sinc interpolator. The sensitivity of the error rate performance to different window functions applied to the sinc interpolator is investigated. The bit error rates (BERs) for diversity M-ary quadrature amplitude modulation (MQAM) with different window functions applied to the sinc interpolator are compared. The Kaiser window is found superior to the other windows considered. A thorough discussion of the dependency of the BER performance on the symbol location is also given. Copyright © 2007 John Wiley & Sons, Ltd.

The transfer function (TF) is a comparative method to monitor the mechanical condition of transformer windings. To perform on-site diagnosis a high reproducibility of TF results is required. Consequently, there are certain restrictions for the determination of the TF using time domain records. This paper describes the effect of different signal processing procedures on the results of TF calculations. Window functions, digital filters, length and treatment of pre-trigger samples are aspects of special interest for the application of the TF method. Additionally, condition parameters of the device under test affect the results of TF measurements. The correlation of transformer temperatures and TF characteristics has been investigated as well as the dielectric effect of the insulating oil and the position of the tap changer. Finally, the effect of different test set-up concepts is presented. Copyright © 2005 John Wiley & Sons, Ltd.

For pulse compression processing, a range sidelobe suppression method previously reported for the derivation of a pulse compression filter window function realizes a zero range sidelobe on the time constraint points and simultaneously minimizes the S/N loss corresponding to the signal loss. The present paper presents an evaluation by simulation of the pulse compression processing performance based on this design method. It is found that filter design by about fourfold oversampling is adequate and that characteristics better than those achieved by the conventional window function scheme can be obtained in terms of the peak sidelobe level, S/N loss, and compressed pulse width, indicating that the present design procedure is effective. The performance deterioration due to the Doppler shift is similar to that in the conventional method and thus is acceptable for practical purposes. © 2005 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 89(1): 45–53, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.20233

A discontinuous reproducing kernel element approximation is proposed in the case where weak discontinuity exists over an interface in the physical domain. The proposed method can effectively take care of the discontinuity of the derivative by truncating the window function and global partition polynomials. This new approximation keeps the advantage of both finite element methods and meshfree methods as in the reproducing kernel element method. The approximation has the interpolation property if the support of the window function is contained in the union of the elements associated with the corresponding node; therefore, the continuity of the primitive variables at nodes on the interface is ensured. Furthermore, it is smooth on each subregion (or each material) separated by the interface. The major advantage of the method is its simplicity in implementation and it is computationally efficient compared to other methods treating discontinuity. The convergence of the numerical solution is validated through calculations of some material discontinuity problems. Copyright © 2005 John Wiley & Sons, Ltd.

It is known that OFDM transmission systems give better performance than single-carrier systems in a multipath environment. However, the communication quality degrades rapidly when the delayed wave arrives beyond the guard interval. In order to solve this problem, various systems that try to suppress the undesired wave by using an adaptive array have been proposed. This paper considers fixed reception and investigates an MMSE adaptive array for OFDM that does not suppress waves arriving within the guard interval, only waves arriving beyond the guard interval. More precisely, the SMI optimization method is proposed in which a window function is used to extract only the wave components beyond the guard interval. In order to demonstrate the effectiveness of the proposed system, an evaluation is made by computer simulation. It is shown that the system operates well as an MMSE adaptive array in a fixed reception environment, exhibiting high suppression power for delayed waves beyond the guard interval. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 87(9): 1–8, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.10221

This paper studies the optimum design of a multistage synchronous rate converter consisting of cascaded interpolation circuits by the window method. Two design approaches are proposed. One is a “simple design method” with a good perspective but a limited applicable range. The other is a “general-purpose design method” that can be applied widely. In this paper, the former is mainly used. The signals are assumed to have a flat spectrum. As the cumulative product rule of the conversion error, the power sum is assumed. By providing the signal bandwidth, required conversion error, and total interpolation rate, optimum values are derived for the half width of the window in each stage and the interpolation rate that minimizes the number of multiplications and the interpolation coefficients. In the range where the “simple design method” is valid (where the signal bandwidth is relatively narrow), the optimum conditions for the number of calculations and for the total number of interpolation coefficients are the same. Then, the dependence of the number of calculations and the total number of interpolation coefficients as well as of the total interpolation rate and the total number of interpolation coefficients is found. A design example is presented. It is shown that highly accurate rate conversion is possible with few calculations. Further, according to the “general-purpose design method,” it is possible to treat signals with a broad bandwidth (such as 0.92ϕ). © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(4): 26–37, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.10015

Since the introduction of Fourier transform NMR spectroscopy, free induction decay (FID) has been available in a binary format, which is required to apply several mathematical treatments on the raw data. Those mathematical procedures are the application of window functions on the FID, baseline correction of the time domain data, and finally the Fourier transformation. Nevertheless, it took a long time until digital filtering was applied on NMR raw data. Digital filtering can be done as either a postprocessing procedure or on the fly. The on the fly concept is preferable, but it requires specialized and very fast processors. With the common availability of such processors, called digital signal processors (DSP), digital filtering on NMR raw data became a routine method. The application of digital filters allows us to overcome problems such as baseline distortion in the NMR spectrum due to nonperfect phase response of any common analog antialiasing filter, distortion of the signal amplitude due to a nonperfect amplitude response of any common analog antialiasing filter, a limited dynamic range due to aliased noise by nonoversampling techniques, reduced dynamic range due to quantization noise, and folded signals due to folded signals outside of the spectral window. The manner in which digital filters are used in a NMR spectrometer is the same as audio applications; it just requires stronger processors to apply high-performance digital filters on the fly. This article is an introduction to the concept of digital filters. Therefore, the description is strongly simplified and the ideal case is assumed. © 2002 Wiley Periodicals, Inc. Concepts in Magnetic Resonance (Magn Reson Engineering) 15: 164–176, 2002

In order to carry out high-precision measurement of the radiation characteristics of antennas and to evaluate the reflection characteristics of microwave anechoic chamber used for antenna measurement, it is important to recognize the location and intensity of the unwanted reflection sources caused by the ambient environment. In this paper, the radiation pattern measurement proposed by the authors is applied for estimating the location of the reflection sources and their effects on the radiation pattern. In the proposed radiation pattern measurement method, the reflected waves are eliminated by the Fourier transform of the measured reflected electric field data obtained on varying the measurement distance. First, a method for estimating the locations of the reflected wave sources and their effects is theoretically shown from the radiation pattern of the reflected wave. This pattern is obtained after the direct radiation pattern obtained from the radiation pattern with the reflected wave suppressed is eliminated from the measured radiation pattern. From a verification experiment using a standard L-band horn, the effectiveness of the method is verified. Second, a window function is applied to the measurement distance range so that the sidelobes of the Fourier transform spectrum are reduced. From the radiation pattern of the reflected wave obtained by applying a gating process to this Fourier spectrum at each angle, the effect of several reflection sources is estimated individually. From the results of computer simulation, the effectiveness of the proposed method is verified. Further, the range of applicability of the method is discussed. © 2001 Scripta Technica, Electron Comm Jpn Pt 1, 85(4): 33–43, 2002

The circle-plus-arc orbit possesses advantages over other "circle-plus" orbits for the application of x-ray cone beam (CB) volume CT in image-guided interventional procedures requiring intraoperative imaging, in which movement of the patient table is to be avoided. A CB circle-plus-two-arc orbit satisfying the data sufficiency condition and a filtered backprojection (FBP) algorithm to reconstruct longitudinally unbounded objects is presented here. In the circle suborbit, the algorithm employs Feldkamp's formula and another FBP implementation. In the arc suborbits, an FBP solution is obtained originating from Grangeat's formula, and the reconstruction computation is significantly reduced using a window function to exclude redundancy in Radon domain. The performance of the algorithm has been thoroughly evaluated through computer-simulated phantoms and preliminarily evaluated through experimental data, revealing that the algorithm can regionally reconstruct longitudinally unbounded objects exactly and efficiently, is insensitive to the variation of the angle sampling interval along the arc suborbits, and is robust over practical x-ray quantum noise. The algorithm's merits include: only 1D filtering is implemented even in a 3D reconstruction, only separable 2D interpolation is required to accomplish the CB backprojection, and the algorithm structure is appropriate for parallel computation.

The local cosine/sine basis is a localized version of the cosine/sine basis with a window function which can have arbitrary smoothness. It has orthogonality and good time and frequency localization properties. The adaptive local cosine/sine basis is a best-basis obtained from an overabundant library of cosine/sine packets based on a cost-functional. We propose a 2D semi-adaptive (time-adaptive or space-adaptive) local cosine transform (referred to as a 2D semi-ALCT) and apply it to the SEG–EAEG salt model synthetic data set for compression. From the numerical results, we see that most of the important features of the data set can be well preserved even in the high compression ratio (CR=40:1) case. Using reconstructed data from the highly compressed ALCT coefficients (CR=40:1) for migration, we can still obtain a high-quality image including subsalt structures. Furthermore, we find that the window partition, generated by the 2D semi-ALCT, is well adapted to the characteristics of the seismic data set, and the compression capability of the 2D semi-ALCT is greater than that of the 2D uniform local cosine transform (2D ULCT). We find also that a (32, 32) or (32, 64) minimum (time, space) window size can generate the best compression results for the SEG–EAEG salt data set.

The Krichevsky–Trofimov estimator can be implemented as an arithmetic data compressor based on a finite window. We analyze the redundancy of this estimator for the Markov source of finite order. The per-letter redundancy behaves with near certainty as (the number of effective states) × (alphabet size)/2 (window size) when the window size is large. Our analysis applies the renewal theory. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(11): 56–62, 2000

The reproducing kernel particle method (RKPM) has many attractive properties that make it ideal for treating a broad class of physical problems. RKPM may be implemented in a ‘mesh-full’ or a ‘mesh-free’ manner and provides the ability to tune the method, via the selection of a window function and its associated dilation parameter, in order to achieve the requisite numerical performance. RKPM also provides a framework for performing hierarchical computations making it an ideal candidate for simulating multi-scale problems. Although the method has many appealing attributes, it is quite new and its numerical performance is still being quantified with respect to more traditional discretization techniques. In order to assess the numerical performance of RKPM, detailed studies of the method on a series of model partial differential equations has been undertaken. The results of von Neumann analyses for RKPM semi-discretizations of one and two-dimensional, first- and second-order wave equations are presented in the form of phase and group errors. Excellent dispersion characteristics are found for the consistent mass matrix with the proper choice of dilation parameter. In contrast, row-sum lumping the mass matrix is demonstrated to introduce severe lagging phase errors. A ‘higher-order’ mass matrix improves the dispersion characteristics relative to the lumped mass matrix but also yields significant lagging phase errors relative to the fully integrated, consistent mass matrix. Published in 2000 by John Wiley & Sons, Ltd.

Density-weighted k-space sampling with spiral trajectories is used to reduce spatial side lobes in chemical-shift imaging (CSI). In this method, more time is spent collecting data at the center of k space and less time at the edges of k space in order to make the sampling density proportional to a given apodization function, subject to constraints imposed by gradient performance and Nyquist sampling. The efficient k-space coverage of spiral-based trajectories enables good control over the sampling density within practical in vivo scan times. The density-weighted acquisition is compared to a conventional, nonweighted spiral sampling without the application of a window function. For a fixed voxel size and imaging time, the noise variance is observed to be the same for both cases, while spatial side lobes are greatly reduced with the variable-density sampling. This method is demonstrated on a normal volunteer by imaging of brain metabolites at 1.5 T with both single slice CSI and volumetric CSI. Magn Reson Med 42:314-323, 1999.

The use of modulated B 0 projection gradient waveforms is proposed for magnetic resonance Imaging (MRI) and magnetic resonance spectroscopic Imaging (MRSI) to shape the k-space sampling density function to match the profile of an applied reconstruction window function. This allows for a time-efficient means of maximizing the signal-to-noise ratio when, for example, a low-pass spatial filter, designed to reduce k-space truncation artifacts and corresponding point-spread function sidelobe energies, is implemented. Both the two-dimensional (2D) and 3D cases are investigated. To create the projection gradient waveforms, a design method is developed that uses nonlinear constrained optimization (NLCO) to minimize the variance of the reconstruction noise. The design is subject to both equality and inequality constraints, which include the maximum gradient magnitude and slew rate. It Is shown that NLCO can also be applied to twisting the projection trajectories for purposes of reducing the data acquisition time while still maintaining the desired sampling density. Applications to 1 H MRSI are investigated via simulations. Advantages and limitations of the new sampling schemes are discussed.

This paper describes a novel and simple design technique for windows in the form of a weighted sum of cosine terms. First, it is made clear that not only does there not exist a basic difference between the Blackman–Harris windows and the Z-window proposed by Zhong and colleagues, there is just a difference in mathematical expression, because the coefficients of both window families can be interconverted easily. Next, by focusing on the limitation of the duration time which is the essential property of windows, a novel and simple windows design technique based on the frequency domain sampling theorem is explained. Windows designed using most conventional design techniques have as a parameter the sample number N, because these conventional design techniques basically use the discrete Fourier transform (DFT). On the other hand, the design technique proposed in this paper can realize windows for an arbitrary purpose, which need not include N as a parameter. © 1999 Scripta Technica, Electron Comm Jpn Pt 2, 82(1): 43–48, 1999

A study of an analogue transmultiplexer element of an on-board multicarrier demodulator (MCD) using a surface acoustic wave (SAW) processor is made in this paper. The theoretical analysis and simulation results applying various windowing techniques on a convolve-multiply-convolve (CMC) SAW processor are presented. The primary objective of this analysis/simulation is to study the effect of windowing on the side-lobe rejection ratio (SLRR) of the analogue transmultiplexer.

In this paper, we present a technique, based on the principle of the frequency-domain convolution of a time-domain signature and a truncation window function, to process the electromagnetic field solution in a resonant structure derived by using the finite-difference time-domain (FDTD) algorithm. We show that the use of this technique enables us to substantially reduce the total number of iterations provided that certain criteria are imposed on the time and frequency resolutions, as well as on the Nyquist sampling rate. The conventional approach to terminating the time iteration is to employ a rectangular windowing (RGW), which induces the unwanted Gibbs phenomenon in the frequency domain. To avoid this, we apply the Blackman–Harris window (BHW) function which modulates as well as truncates the computed time-domain electromagnetic signals. We demonstrate via a numerical experiment that the BHW modulation and truncation yield excellent results with only a small number of iterations, often only one-tenth of that needed in the RGW method. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 15: 389–392, 1997.

Box splines are a multivariate extension of uniform univariate B-splines. Direct evaluation of box spline basis function can be difficult, but they have a relatively simple Fourier transform and can therefore be evaluated with an inverse FFT. Symmetry, recursive evaluation of the coefficients, and parallelization can be used to improve absolute performance. A windowing function can also be used to reduce truncation artifacts. We explore all these options in the context of a high-performance parallel implementation. Our goal is the provision of an empirical touchstone for the inverse FFT evaluation of box spline basis functions, for eventual application to forward projection (splat-based) volume rendering.

Multiple scale methods based on reproducing kernel and wavelet analysis are developed. These permit the response of a system to be separated into different scales. These scales can be either the wave numbers corresponding to spatial variables or the frequencies corresponding to temporal variables, and each scale response can be examined separately. This complete characterization of the unknown response is performed through the integral window transform, and a space-scale and time-frequency localization process is achieved by dilating the flexible multiple scale window function. An error estimation technique based on this decomposition algorithm is developed which is especially useful for local mesh refinement and convergence studies. This flexible space-scale window function can be constructed to resemble the well-known unstructured multigrid and hp-adaptive finite element methods. However, the multiple scale adaptive refinements are performed simply by inserting nodes into the highest wavelet scale solution region and at the same time narrowing the window function. Hence hp-like adaptive refinements can be performed without a mesh.

This paper describes a new design algorithm for finite impulse response (FIR) digital filters, which approximates constant passband amplitude and linear phase characteristics. The algorithm converts a filter's specification characteristic into a continuous impulse response by using the frequency response of a window function. The continuous impulse response is translated into discrete values to calculate tap-gain coefficients of an FIR filter. In this design algorithm, window functions belonging to the Hanning window series (such as the Harris' window whose characteristics are already known) are used. This design algorithm is an analytical design technique, featuring a filter length that can be decided when the specification is decided and does not require iterative numerical calculations to calculate tap-gain coefficients.

Summary In this paper, we propose a flexible memristive model with simplex basis function. In the memristive model, a piecewise window function is applied to limit the physical range of the state variable, and a piecewise linear model (called simplex basis function model) is applied to describe the integral function of the current and charge. The expression of the state variable and the memristance can be almost analytically obtained. Thus, some serious errors occurring in the simulations of some existing memristive models can be avoided. The proposed memristive model shows great flexibility due to the good approximation capability of the simplex basis function model. Copyright © 2016 John Wiley & Sons, Ltd.

This paper explores a Reproducing Kernel Particle Method (RKPM) which incorporates several attractive features. The emphasis is away from classical mesh generated elements in favour of a mesh free system which only requires a set of nodes or particles in space. Using a Gaussian function or a cubic spline function, flexible window functions are implemented to provide refinement in the solution process. It also creates the ability to analyse a specific frequency range in dynamic problems reducing the computer time required. This advantage is achieved through an increase in the critical time step when the frequency range is low and a large window is used. The stability of the window function as well as the critical time step formula are investigated to provide insight into RKPMs. The predictions of the theories are confirmed through numerical experiments by performing reconstructions of given functions and solving elastic and elastic–plastic one-dimensional (1-D) bar problems for both small and large deformation as well as three 2-D large deformation non-linear elastic problems. Numerical and theoretical results show the proposed reproducing kernel interpolation functions satisfy the consistency conditions and the critical time step prediction; furthermore, the RKPM provides better stability than Smooth Particle Hydrodynamics (SPH) methods. In contrast with what has been reported in SPH literature, we do not find any tensile instability with RKPMs.

A new continuous reproducing kernel interpolation function which explores the attractive features of the flexible time-frequency and space-wave number localization of a window function is developed. This method is motivated by the theory of wavelets and also has the desirable attributes of the recently proposed smooth particle hydrodynamics (SPH) methods, moving least squares methods (MLSM), diffuse element methods (DEM) and element-free Galerkin methods (EFGM). The proposed method maintains the advantages of the free Lagrange or SPH methods; however, because of the addition of a correction function, it gives much more accurate results. Therefore it is called the reproducing kernel particle method (RKPM). In computer implementation RKPM is shown to be more efficient than DEM and EFGM. Moreover, if the window function is C∞, the solution and its derivatives are also C∞ in the entire domain. Theoretical analysis and numerical experiments on the 1D diffusion equation reveal the stability conditions and the effect of the dilation parameter on the unusually high convergence rates of the proposed method. Two-dimensional examples of advection-diffusion equations and compressible Euler equations are also presented together with 2D multiple-scale decompositions.

The complex dielectric permittivity (CDP) of soils is used in moisture and salinity measurements. We have developed a CDP spectra determination method based on Fourier analysis of electrical signals reflected in probes of various lengths. The S 11 parameters of the probes placed in samples under test were measured using a vector network analyzer, and the results were transformed into the time domain using transient-state analysis and a simulated needle pulse. The pulses reflected from the ends of the probes’ rods were extracted using a windowing function and transformed into the frequency domain. The CDP was then calculated independently at each frequency using an analytical expression. In contrast to time-domain spectroscopy techniques, knowledge of the incident signal in the soil sample is not needed. Also, no assumptions on a dielectric relaxation model of the tested materials are necessary. The method was tested on six reference materials and samples of two soils at various water contents. The accuracy of the obtained results was assessed and a rod length combination of 4 and 10 cm was selected for further use. The measurement errors for the tested reference media were determined. The method performed the best in the frequency range 0.2 to 1.0 GHz for the real part of the CDP and 0.20 to 0.85 GHz for the imaginary part. This approach may be adapted for use with a time domain reflectometry needle pulse device.

Publisher Summary This chapter discusses the computer processing techniques in high-resolution nuclear magnetic resonance (NMR). The standard processing techniques discussed include—the Fourier transform, spectral folding and aliasing, window functions, and artefact reduction techniques. Violation of the Nyquist condition, giving rise to signal folding or aliasing into excessively small spectral windows, enables the saving of acquisition points for any given resolution. In one-dimensional spectroscopy, this is obsolete for two reasons. Firstly, the widely used digital filtering very efficiently eliminates any signal falling outside the chosen spectral window. Secondly, the memory capacity makes any saving in the number of acquisition data points quite futile. Also called “apodization functions,” the window functions consist in giving different weights to different parts of time domain data. They are routinely used to diminish truncation artefacts, and have a strong influence on data resolution and signal-to-noise (S/N) ratio. The chapter also discusses the specialized processing techniques. Some of these techniques include deconvolution methods, linear prediction, least-squares fit, and Bayesian analysis.

This paper introduces a new method to reveal the spectral information hidden in highly resolved microwave maps locally dominated by localized scattering centers. The method first partitions the map, i.e. it localizes these centers by suitable window function. It then transforms each segment containing a localized scattering center into frequency-aspect angle space. The method is tested for a simulated scenario of two localized scatterers. Its superiority over previous exploitation schemes is borne out by applying it to experimental data on the edge scattering of a metal plate.

This paper derives a design method for an ARMA 4-line lattice filter using a sliding rectangular window. The adaptive ARMA 4-line lattice filter already proposed uses a forgetting factor, which is one of the weighting functions to estimate coefficients of a time-varying system in which system coefficients vary with sufficient smoothness. Therefore, the effect of past observed signal over the estimated coefficients decreases exponentially. The filter presented here is realized using a rectangular window because the concern is over the effects of past observation signal rather than window length. Using this filter, an input signal is estimated when designing; furthermore, a system can be identified in which an arbitrary section in the frequency domain is weighted. Thus, by not only analyzing voice signal which is considered a model whose input signal is unknown and EEG data but also by weighting the frequency domain, for example, the holmant in the low-frequency domain can be estimated in low degree with very high precision and a specific wave (such as a α activities) in EEG data can also be detected. Moreover, in this paper the algorithm is verified by model experiments.

Sampled counting processes are often studied using methods for the analysis of stationary time series. We express some time series parameters as smoothed versions of corresponding point process parameters and use these relations to suggest estimates of the point process parameters. In addition, we propose a reconstructive approach to the estimation problem. We derive some properties of the estimators and apply them to data from meteorology, entomology and particle physics

The effect of the number of significant digits on the demodulator output noise is analyzed and examined by a simulation in relation to the FM broadcasting system specification. The quantization noise Nq generated at A-D conversion of IF signals is regarded as a white Gaussian noise similar to the thermal noise Nz fed to a receiver input. From the condition of C/Nz satisfying the broadcasting specification, Nq such that Nq Ni- 10 [dB] is obtained and then the quantization precision satisfying this condition (being translated into the precision at the output of a digital signal processing demodulator) is obtained. As a numerical example, it is shown that only 6- and 9-bit precisions are necessary for monophonic and stereophonic reception, respectively. The simulation result agrees with the numerical result. Reduction in the number of filter taps at the demodulator with the introduction of a window function is also studied. Given the system specification, the obtained result is also applicable for digital FM demodulators of any use.

For registration between images, algorithms of point correspondence searching type and deformation field analyzing type have been proposed in the past. The former had a problem of increasing processing quantity and the latter had a problem of assuming small displacement or deformation. This paper proposes a cooperative image registration technique which absorbs finite displacement and nonrigid body deformation by iteratively applying affine transformations from coarse to fine for binary images expressed by sets of loci vectors of characteristic points. The process consists of four steps: (1) for each characteristic point of a reference image, a local affine transformation (LAT) weighted by Gaussian window functions is applied; (2) based on the least-squares method, LAT is optimized for each characteristic point of the reference image so that overlapping for a group of characteristic points of input images becomes best; (3) optimized LAT is applied for each characteristic point of the reference image and deformed reference image is generated; (4) iterating steps (1) through (3) while gradually decreasing the spreads of the Gaussian window functions, when the deformed image coincides with the input image, displacement between images is determined. We have applied this method to binary character images including large deformation and random-dot stereograms and obtained good results. Also, we evaluated the processing quantity by this method and showed that extension to gray scale images is easily formulated.

This paper proposes a reconstruction method for the 3-D distributional image of the absorption coefficient of the object. In the method, a cone-beam X-ray source and a 2-D detector array are placed in confronting positions on the opposite sides of the object. By rotating them 360 deg., the projection data are acquired, and then the inverse filtering is applied. This is a reconstruction problem from an incomplete projection data. In this paper, the compound image is constructed by backprojecting the projection image directly along the locus of projection. The inverse filtering is applied to the result to determine the 3-D distribution image of the absorption coefficient of the object. In the defined geometrical system for the measurement, the inverse filtering cannot essentially be applied since the impulse response is space variant. Consequently, a nonuniform sampling coordinate system is defined to make the impulse response space invariant. The inverse filter function is derived from the Hankel function by utilizing the symmetry of the impulse response in regard to the axis of rotation. Furthermore, to stabilize the inverse filtering, a window function is employed which considers the space-dependence of the incompleteness of the projection image in the frequency domain. Finally, the usefulness of the proposed reconstruction method is verified by a computer simulation.

The factors that determine the resolution of monochromators operating in both the non-diffraction-limited and diffraction-limited modes are discussed. The instrument line shape function of a monochromator (often called the spectral slit function) operating above the diffraction limit is a triangle, whereas in the diffraction-limited case it is sinc2 ([sin x]2/x2) function. For Fourier transform infrared (FT-IR) spectrometers, the instrument line shape function is a sinc ([sin x]/x) function unless the interferogram is multiplied by an apodization function. In this case, the instrument line shape function is the Fourier transform of the apodization function. Common apodization functions that are discussed include the triangular function and the three Norton–Beer functions. The effect of a diverging (noncollimated) beam, passing through the interferometer of a FT-IR spectrometer, on the resolution and instrument line shape function is discussed at the end of the article. Keywords: resolution; instrument line shape function; spectral slit function; monochromator; non-diffraction-limited resolution; diffraction-limited resolution; sinc function; sin c2 function; Fourier transform infrared spectrometers; apodization function; triangular apodization; Norton–Beer apodization functions; effect of a diverging beam

This paper deals with some approximations by the generalized Shannon sampling series, which are defined by the Blackman-Harris (or cosine-sum) window functions. In the case of certain (m + 1)-term cosine-sum window functions the order of approximation can be estimated via the 2m -th modulus of continuity. Some choices of parameters in Blackman-Harris window function generate interpolating generalized Shannon sampling series. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)