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Since the beampattern has the characteristics of range-angle dependence, frequency diverse array multiple-input multiple-output (FDA-MIMO) radar has a good application prospect. There have been many studies to improve the performance of the beampattern by optimizing the frequency offset. However, on the basis of fully understanding the time parameters, the relationship between the array element frequency offset and the beampattern performance still needs to be clarified. Based on a new FDA-MIMO radar framework, this paper presents an analytical solution of the beampattern, which removes the influence of the time parameter. Taking the minimum main lobe as the objective function, an analytical method for solving a better frequency offset is given. Then, a method of using the window function was proposed to reduce the high side lobes of the range dimension. Comparing with the existing FDA radar beampattern design methods, it can achieve a more focusing beampattern. The simulation results verify the correctness of the theory.

In classical information processing, the windowed Fourier transform (WFT), or short-time Fourier transform, which is a variant of the Fourier transform by dividing a longer time signal into shorter segments of equal length and then computing the Fourier transform separately on each shorter segment, is proposed to provide a method of signal processing. Up to now the discrete Fourier transform has been successfully applied to the field of quantum information, but the related short-time discrete Fourier transform of this field has not been developed accordingly. To address this problem, we first introduce the concept of quantum window state, and further prove that the quantum Fourier transform of a quantum window state is also a quantum window state. Based on the definition of the quantum window state the local information of a quantum signal is extracted and the corresponding quantum circuits are also given. And then, by applying the quantum Fourier transform to the windowed quantum superposition states, we propose a novel concept called quantum windowed Fourier transform (QWFT). Finally, an application of quantum signal processing is given where QWFT is employed.

In order to overcome the problems of the traditional algorithm, such as the time-consuming execution of acquisition instructions, low signal tracking accuracy, and low signal capture accuracy, a global satellite positioning receiver acquisition and tracking algorithm based on UWB technology is designed in this study. On the basis of expounding the pulse generation method and working principle in UWB technology, this paper analyzes in detail the characteristics of UWB technology, such as antimultipath, low power consumption, and strong penetration. Then, on the basis of window function filtering, in the process of three-dimensional search of global satellite positioning signal, firstly, the satellite signal entering the GPS software receiver is processed by RF front-end mixing and AD sampling, and then, the signal tracking and navigation message solving are completed according to the relationship between the influence factor and Doppler frequency offset. The experimental results show that the execution time of the acquisition instruction of the proposed algorithm varies between 1129 ms and 1617 ms; the signal tracking accuracy ranges between 0.931 and 0.951, and the signal capture accuracy ranges between 93.3% and 95.6%, which proves that the proposed algorithm has achieved the design expectation.

Single-window discrete Gabor transform with an adaptive window width selection algorithm (AWWS-DGT) and multi-window discrete Gabor transform (M-DGT) are the current mainstream analysis and processing methods for multi-component signals. However, the time–frequency accuracy in the time–frequency plane obtained by the two algorithms is not very high, and not all components of the signals that contain complex and very different time–frequency components can be displayed accurately. The linear combination window algorithm based on the $$\ell_{1}$$ and $$\ell_{2}$$ norm constraints of the transform coefficients can accurately display all the components of the signal, but the algorithm has poor anti-noise performance. In this paper, an algorithm for finding the best linear combination window under the sparse solution constraint of discrete Gabor transform coefficients is proposed. First, the optimal window number adaptive selection method proposed in this paper is used to select a set of window functions with different window widths, and the goal is to obtain the sparse solution of the transform coefficient. Through the gradient descent method, the best linear combination coefficient is obtained. Second, according to the best linear combination coefficient obtained, the selected window is combined into an analysis window function. Finally, the influence of the parameters on the combined window is further studied, and the results show that the number of windows has a great influence on the result and that the influence of the regularization parameter is negligible. Experiments on two simulated non-stationary signals and real electrocardiogram signals show that the proposed algorithm can display all components of the signals, the time–frequency accuracy is improved by 3% to 10%, and the anti-noise performance is more than 20% higher than that of the existing linear combination window algorithm. These advantages are very important for the analysis and processing of practical signals.

Building on past work showing that the Hilbert transform can be used for edge feature enhancement, a new edge feature enhancement method is developed using a two‐dimensional (2D) isotropic Hilbert transform of the Cauchy distribution. First, both the shape of the Hilbert kernel and the Hilbert transform of edge feature models (step and delta) and various simulated signals result in edge feature enhancement, the properties of which are derived and confirmed. Second, Cauchy distribution as low‐pass filter is introduced in Hilbert transform to get new edge feature enhancement operator, and its efficiency under various criteria is comprehensively discussed. Third, a 2D isotropic extension is presented using a circularly symmetric window function. Finally, two experiments, including edge detection and image segmentation, are performed to validate the proposed edge feature enhancement method. The experimental results of the method applied to the Berkeley Segmentation Dataset and remote sensing images demonstrate that the new method is effective for edge detection and image segmentation.

The problem of synthesis of low-order polynomial window functions with an arbitrarily specified decay rate of spectral lobes (optimal with respect to minimization of the maximum side lobe on a specified segment of the frequency axis) is solved. A method for the synthesis of optimal functions with verification of the solution is developed. The window functions of orders 1–12 with side-lobe decay rates of 6, 12, 18, 24, and 30 dB/oct are synthesized and tables of the parameters are presented. The characteristics of the functions are analyzed and compared with the known ones. A simple algorithm for calculation of the synthesized functions is proposed.

The temporal resolution of conventional S transform (ST) is not sufficient for the separation of local coherent noise. We present a revised S transform (RST) which uses an analyzing window function with two control parameters of the scalar σ and the exponential factor γ. Selecting proper parameter values (say σ = 1.1, γ = 1.08), the time–frequency representation (TFR) acquired by our method exhibits a higher temporal resolution. Applying an appropriate filter in the time–frequency domain, we are able to remove specific local noise. Distributed acoustic sensing (DAS) VSP section may suffer from fiber cable coupling noise, hindering the subsequent data processing and geologic interpretation. The real data example shows the coupling noise occurred in the DAS VSP can be removed by the presented RST.

Spectral analysis of signals is used as one of the main methods for studying systems and objects of various physical natures. Under conditions of a priori statistical uncertainty, the signals are subject to random changes and noise. Spectral analysis of such signals involves the estimation of the power spectral density (PSD). One of the classical methods for estimating PSD is the periodogram method. The algorithms that implement this method in digital form are based on the discrete Fourier transform. Digital multiplication operations are mass operations in these algorithms. The use of window functions leads to an increase in the number of these operations. Multiplication operations are among the most time consuming operations. They are the dominant factor in determining the computational capabilities of an algorithm and determine its multiplicative complexity. The paper deals with the problem of reducing the multiplicative complexity of calculating the periodogram estimate of the PSD using window functions. The problem is solved based on the use of binary-sign stochastic quantization for converting a signal into digital form. This two-level signal quantization is carried out without systematic error. Based on the theory of discrete-event modeling, the result of a binary-sign stochastic quantization in time is considered as a chronological sequence of significant events determined by the change in its values. The use of a discrete-event model for the result of binary-sign stochastic quantization provided an analytical calculation of integration operations during the transition from the analog form of the periodogram estimation of the SPM to the mathematical procedures for calculating it in discrete form. These procedures became the basis for the development of a digital algorithm. The main computational operations of the algorithm are addition and subtraction arithmetic operations. Reducing the number of multiplication operations decreases the overall computational complexity of the PSD estimation. Numerical experiments were carried out to study the algorithm operation. They were carried out on the basis of simulation modeling of the discrete-event procedure of binary-sign stochastic quantization. The results of calculating the PSD estimates are presented using a number of the most famous window functions as an example. The results obtained indicate that the use of the developed algorithm allows calculating periodogram estimates of PSD with high accuracy and frequency resolution in the presence of additive white noise at a low signal-to-noise ratio. The practical implementation of the algorithm is carried out in the form of a functionally independent software module. This module can be used as a part of complex metrologically significant software for operational analysis of the frequency composition of complex signals.

Modal parameter identification is considered to be one of the most important tasks in structural health monitoring because it provides a reliable reference for structural vibration control, damage severity, and operational state. Moreover, at present, the combined deterministic-stochastic subspace algorithm is cogitated as one of the key algorithms in the modal parameter identification, which is why it is widely used in the modal parameter identification of bridge structures. In this paper, a novel method is proposed, which is a time-domain identification algorithm, based on sliding window-fuzzy C-means clustering algorithm-combined with deterministic-stochastic subspace identification (SC-CDSI), to achieve online intelligent tracking and identification of modal parameters for nonlinear time-varying structures. First of all, to realize the online tracking and identification process, it is necessary to divide the input and output signal of the nonlinear time-varying structure by windowing; for that, to determine the window function, window size and window step length according to the characteristics of the signal are analyzed. Secondly, in order to satisfy the intelligent identification of effective modals in stability diagram, the fuzzy C-means clustering algorithm is kept as a base, whereas frequency, damping ratio, and modal shapes serve as clustering elements, applied to fuzzy C-means clustering algorithm, and then the intelligent selection of effective modals is achieved. Finally, a shaking table test bridge is used as a modal parameter identification in lab, and its results are compared with the MIDAS finite element results. The compared results show that the proposed SC-CDSI identification algorithm can accurately achieve the intelligent identification of online tracking of the structural frequency, and the identification results are reliable to be used in real-life bridge structures.

This article presents a new fine Doppler frequency estimation method of complex sinusoidal signals for radar systems. The proposed method can work with nonrectangular window functions to suppress the interference signal caused by the undesired spectral leakage. This method is based on an interpolation curve that uses the sum and difference of two discrete Fourier transform (DFT) magnitudes, and can estimate an accurate frequency between the interpolation curve samples through precise linear approximation. The proposed method exhibits lower computational complexity than the conventional method, which compensates the bias of an arbitrary window function and exhibits high performance. Thus, the proposed method is applicable to radar systems requiring fast processing time. Furthermore, the simulation results show that the proposed method outperforms the conventional method for various window functions.

In this paper, the Cauchy mixture distribution is used for rigid and affine registration. The Cauchy function has a wider effective range than the general window function, so it has a greater information utilization ratio than most registration algorithms. This means that the method can quickly match point clouds without initial registration and corresponding points. On the other hand, the computational complexity of Cauchy mixture model is lower than that of widely used Gaussian mixture model. This means that the introduction of Cauchy mixture model will save computing resources. However, the log-likelihood function of the Cauchy mixture distribution is a nonlinear function that is difficult to solve. This paper proposes an optimization method for the Cauchy mixture model, and discusses the advantages of the Cauchy mixture model in rigid and affine registration. In the experiment, compared with several other algorithms, our method quickly and accurately registers point clouds.

Time–frequency (TF) analysis (TFA) provides an effective tool to characterize nonstationary signals with time-varying features. However, the TFA of gas turbine’s vibration signals is a challenging topic due to high complexity and strong nonstationarity. There is an obstacle to generate more accurate and sharper TF results for such multicomponent signals. This article proposes a novel TFA technique, named local maximum synchrosqueezing chirplet transform (LMSSCT), to deal with this problem. This method can not only well match window function and modulated frequency but produce an unbiased instantaneous frequency (IF) estimator to correct the deviation caused by strong frequency modulation (FM) in TF results. We give the theoretical analysis that this method is an improvement of classical local maximum synchrosqueezing transform (LMSST), and we also prove that it allows for perfect signal reconstruction. The numerical validation shows that the proposed method can be employed to effectively address the multicomponent signals with complex FM laws, even those with heavy noise. The experimental analysis on the test-bench signal and the vibration signal of a dual-rotor gas turbine validates that this method can capture more detailed features that are helpful to identify the origins of abnormal vibration of gas turbine.

This article proposes a method of phasor estimation called the Morlet wavelet-based two-point finite-impulse response (FIR) filter (MW-FIR), showing advantages on algorithm complexity, customizability, and zero overshoot. The method focuses on amplitude and frequency estimation, while phase and rate of frequency of change (ROCOF) estimation can be performed using the standard signal processing model with an FIR filter. The mathematical principle behind the method is presented. The causes of error are discussed, and the parameter selection procedure is introduced to minimize error and adjust algorithm performance according to different application requirements. The proposed method has been discussed and compared with the three-point interpolated discrete Fourier transform (ipDFT) method and the FIR method using a flat-top (FT) windowing function, under the static and dynamic situations given by the IEC/IEEE 60255-188-1 and noise immunity evaluation. Finally, the major advantages of the proposed frequency estimation method compared with the conventional FIR-based method using the derivative of angular position are discussed. It can be concluded that this method becomes a substitute for ipDFT in most cases and shows several advantages over the FIR-based method with an FT sequence.

The method of increase of productivity of estimation of spectral density of power (SDP) of random signals at the expense of reduction of computational complexity of procedures of digital processing of investigated signals is offered in the work. The choice and substantiation of the methodology of digital evaluation of SDP signals is performed. It is proved that the correlogram methodology of SDP estimation under the condition of the same volume of processed signal samples is characterized by higher quality factor in comparison with direct estimation methods. At the same time, the application of the fast Fourier transform (FFT) technique to calculate the autocorrelation function of the signal creates conditions for improving the performance of correlogram methods for estimating SDP. Therefore, the correlogram methodology of fast digital estimation of SDP of random signals is applied in the work. A high-performance method for determining the autocorrelation function of the signal has been developed. In this paper, it is proposed to use the fast digital correlation theorem in order to accelerate the definition of the autocorrelation function. A recurrent relation is obtained to determine the discrete Fourier transform (DFT) of a subsequence in which a number of samples are updated. The proposed method requires two DFT and one reverse DFT. The synthesis of the correlation window function, which provides the maximum asymptotic rate of decline of the side lobes of the signal power spectrum for a given level of side lobes relative to the level of the main lobe of the spectrum. An expression for estimating the SDP of a random signal is obtained, according to which the statistical stability of the estimation is provided by averaging by processing segments, and correlation weighing allows to control the level of lateral parasitic petals of the spectrum of the studied signal. The research of productivity of the developed method of correlogram estimation of SDP of signals is executed. An expression is obtained to determine the coefficient of productivity, which takes into account the number of multiplication operations in the implementation of correlogram estimation of SDP. The results of the analysis proved that the proposed method makes it possible to significantly reduce the time for determining the SDP of random signals and to ensure the mode of operation of digital spectrum analyzers in a real time scale.

Windows such as Dolph-Chebyshev window and Kaiser window are adjustable, whereas windows such as Hamming window and Blackman window are traditionally not adjustable. In [1], a technique for trading off main lobe width against sidelobe magnitude for any arbitrary window, including the traditionally non-adjustable windows, was presented. However, the method in [1] requires a large number of iterations if the specification is very tight. Developed based on a new perspective on the window adjustment principle, a new method to achieve the same adjustment capability as in [1], but at a very much fewer iterations is presented in this letter. Our new method is particular useful if the specification is very tight.

In order to select the window function and window size adaptively before getting the results, we proposed adaptive moving window principle component analysis (AMWPCA) based OMA method to identify modal shapes and modal natural frequencies of slow LTV structures with weekly damped only from non-stationary vibration response signal online. The adaptive is achieved in two ways: change the window function or window size. We develop an adaptive indicator as the basis for window function and window size changes. Our adaptive approach is to make the difference between adjacent eigenvalues not too small. The operational modal parameter identification results in non-stationarity response signal dataset of a three-degree-of-freedom structure with slow time-varying mass show that comparing with fixed size moving window principle component analysis, our AMWPCA method can identify the modal shapes and modal frequencies better.

Universal-filtered multi-carrier (UFMC) waveformis considered as a potential candidate for next generation wirelesssystems due to its robustness against inter-carrier interference(ICI) and the low latency required in 5G systems. In this paper, apulse shaping approaches in UFMC technique is studied to reducethe spectral leakage into nearby sub-bands. The performance ofvarious types of window functions such as Chebychev, Hamming,Hanning and Blackman with UFMC are compared. This leadsto different coefficients and attenuation shapes, that enabledto choose the proper window function. Finally, a new selectivemapping (SLM) peak to average power ratio (PAPR) reductiontechnique is proposed to enhance the UFMC system performance.Results show that the BER performance of UFMC with allwindows functions are the same. However, Blackman windowfunction has a higher attenuation for sidebands compared withothers.

Resampling technology is becoming increasingly critical, as different frequency components are required to be measured in one device. In this paper, a resampling method based on filter designed by window function is proposed to satisfy the requirements of different sampling rates. The frequency responses of the filter in the resampling model based on the Farrow structure are investigated, and the design criterion of the filter in the resampling model is proposed. A fractional delay filter design model based on window function method is established. A fractional delay filter coefficient matrix, which is expressed by a polynomial form, is constructed. Then, the expression related to the subfilter coefficients is obtained and subfilter coefficients are solved by the least-square method. The simulation results show that the filter designed by the proposed method has better performance when used for resampling as compared those designed by existing methods, and can efficiently prevent the occurrence of frequency aliasing and mirroring components in the process of sampling rate conversion. Therefore, the proposed method meets the conditions for application to existing measurement devices.

Frequency diverse array (FDA) is capable of generating a range-angle-dependent beampattern via adjusting the frequency offset across array elements. The classical linear FDA generates an S-shaped beampattern due to the range-angle-dependent coupling. In order to remove the coupling, and obtain a well-focused dot-shaped beampattern, several FDA frameworks are proposed via adjusting frequency offsets. It seems that the window based tapering frequency offsets are able to form a single maximum with a satisfactory mainbeam sharpness. However, most window-based FDA schemes are focused on classical fixed windows. In this letter, an FDA framework with Taylor windowed frequency offsets is first proposed. Considering that adjustable tapering windows allow adjustments by parameter manipulation, the optimized parameters of the window function are determined. The FDA beamforming results with all kinds of frequency offsets are measured, and compared. Numerical results validate the superiority of proposed FDA in terms of mainlobe width, and sidelobe level.

Delay diversity (DD) is a low-complexity and flexible transmit diversity technology for coded offset quadrature amplitude modulation based filter bank multicarrier (OQAM/FBMC) transmission systems. However, the introduction of delay parameters in DD-OQAM/FBMC systems leads to increased channel frequency selectivity, which makes the channel estimation problem more complicated. In this paper, we analyze and develop preamble-based channel estimation methods in DD-OQAM/FBMC systems from the perspective of frequency-domain, transform-domain, and time-domain aspects. Besides, channel estimators that can obtain the minimum channel estimation mean square error under least squares (LS) and linear minimum mean square error (LMMSE) criteria are derived according to different levels of channel knowledge. Specifically, the proposed frequency-domain method estimates each channel frequency response individually based on a simplified frequency-domain channel model. The transform-domain method first estimates the equivalent single-input-single-output channel observed at the receiver assuming subchannel flatness, and then uses a window function in the time domain to separate the channels of different transmit antennas. The time-domain method is constructed based on an accurate time-domain channel model to directly estimate the channel impulse response without making any assumption about the subchannel flatness. A series of simulation experiments is conducted to verify the effectivity of these channel estimation methods for DD-OQAM/FBMC systems.

Enhanced time-domain spreading is proposed for block-interleaved frequency division multiple access (B-IFDMA) with discrete Fourier transform spread orthogonal frequency division multiplexing (DFT-s-OFDM). By repeating each consecutive modulation symbol prior to the spreading, we show that the DFT of the spreading sequence becomes a window function, which compared to the existing method of repeating the whole block of modulation symbols, offers a signal with both lower cubic metric (CM) and block error rate (BLER). Modulation symbol-specific spreading sequences are further shown to improve the BLER. The new transmission scheme is supported by both time- and frequency domain despreaders, as well as by two channel estimation methods for B-IFDMA.

The memristor is a nano-size electrical device that is widely investigated in memory, logic circuits, and neuromorphic systems. This paper puts forward a general window function for Hewlett-Packard (HP) TiO2 memristor model, which covers almost all typical window functions and resolves the boundary lock problem, the inflexible parameter problem, and the distorted pinched hysteresis loop problem. Several adjustable parameters are introduced in the proposed window function in order to make it more flexible and scalable. A comparison with some classic window functions is given. Meanwhile, the range of these parameters is deduced with the aim of finding suitable parameters to simulate memristor devices. This TiO2 memristor model based on the novel window function is further applied to the spiking neural network and tested with the MNIST database of handwritten digits. The result demonstrates that the memristor-based neural network has higher recognition accuracy and better classification effect, indicating the availability of the entire scheme.

Intensive computerization of radio systems stimulates the use of various technologies in radar and communication systems, which makes it difficult to solve the problem of signal detection and requires the use of modern processing algorithms in radio monitoring systems with the possibility of modifying their parts according to a specific type of signal and interference. To solve this problem, an iterative method for detecting radio signals based on decisive statistics was developed. The key idea of the proposed method is using of statistical differences between the signal and noise not according to the values of the samples of the received signal, but according to some decisive statistics from them. The essence of the method is to transform the sample of the received radio signal using some operator, followed by the calculation of the decisive statistics and its comparison with some threshold. When the threshold is exceeded, the maximum value of the sample from the converted sample is discarded and the procedure is repeated until the value of the decision statistics becomes less than the threshold. The discarded samples refer to the signal, and the rest to noise. The type of operator is selected based on a priori information about the signal and increases its contrast against random noise. Decisive statistics should have small scattering characteristics, and the distance between its values for noise and the signal mixture should be as large as possible for a given signal-to-noise ratio. A study of the developed method for detecting narrowband signals in the frequency domain showed that the Fourier transform is the optimal form of the operator, and the coefficient of variation is optimal decisive statistic. The developed iterative method for the frequency domain allows detecting narrowband signals at unknown values of noise power in the dynamic range, which is limited only by the level of the side lobes of the window function, when the analysis frequency band is loaded no less than 60%., Информатизация радиотехнических систем стимулирует использование разнообразных технологий в радиолокационных системах и системах передачи информации, что затрудняет решение задачи обнаружения сигналов и требует использования в системах радиомониторинга современных алгоритмов обработки с возможностью модификации их отдельных частей для настройки на конкретный вид сигнала и помехи. Для решения данной задачи был разработан итеративный метод обнаружения радиосигналов на основе решающих статистик. Ключевой идеей предложенного метода является использование статистических различий между сигналом и шумом не за величинами отсчетов принятого сигнала, а по некоторым решающим статистикам от них. Сущность метода заключается в преобразовании выборки принятого радиосигнала с применением некоторого оператора с последующим вычислением решающей статистики и ее сравнении с пороговым значением. При превышении порога отбрасывается максимальное значение отсчета с преобразованной выборки и процедура повторяется пока значение решающей статистики не станет меньше порогового. Отброшенные отсчеты относятся к сигнальным, а остальные - к шумовым. Вид оператора выбирается на основании априорных сведений о сигнале и повышает его контраст на фоне случайного шума. Решающая статистика должна иметь малые характеристики рассеивания, а расстояние между ее значениями для шума и сигнальной смеси должна быть как можно больше для заданного значения отношения сигнал-шум. Исследование разработанного метода для обнаружения узкополосных сигналов в частотной области показали, что оптимальным видом оператора является преобразование Фурье, а решающей статистики - коэффициент вариации. Разработанный итеративный метод для частотной области позволяет обнаруживать узкополосные сигналы при неизвестных значениях мощности шума в динамическом диапазоне, который ограничивается только уровнем боковых лепестков оконной функции, при загруженности полосы частот анализа не менее 60%., Інформатизація радіотехнічних систем стимулює використання найрізноманітніших технологій в радіолокаційних системах та системах передавання інформації, що ускладнює вирішення завдання виявлення сигналів та потребує використання в системах радіомоніторингу сучасних алгоритмів оброблення з можливістю модифікації їх окремих частин для налаштування на конкретний вид сигналу і завадову обстановку. Для вирішення даного завдання було розроблено ітеративний метод виявлення радіосигналів на основі вирішуючих статистик. Ключовою ідеєю запропонованого методу є використання статистичних відмінностей між сигналом і шумом не за самими величинами відліків прийнятого сигналу, а за деякими вирішуючими статистиками від них. Сутність методу полягає у перетворенні вибірки прийнятого радіосигналу із застосуванням деякого оператора з подальшим обчисленням вирішуючої статистики та її порівнянні з пороговим значенням. При перевищенні порогу відкидається максимальне значення відліку із перетвореної вибірки і процедура повторюється доки значення вирішуючої статистики не стане менше порогового. Відкинуті відліки відносяться до сигнальних, а решта − до шумових. Вид оператора обирається із апріорних відомостей про сигнал і повинен підвищити його контраст на фоні випадкового шуму. Вирішуюча статистика повинна мати малі характеристики розсіювання, а відстань між її значеннями для шуму і сигнальної суміші повинна бути якомога більшою для заданого значення відношення сигнал-шум. Дослідження розробленого методу для виявлення вузькосмугових сигналів у частотній області показали, що оптимальним видом оператора є перетворення Фур'є, вирішуючої статистики − коефіцієнт варіації. Розроблений ітеративний метод для частотної області дозволяє виявляти вузькосмугові сигнали при невідомих значеннях потужності шуму у динамічному діапазоні, який обмежується лише рівнем бічних пелюсток віконної функції, при завантаженості смуги частот аналізу не менше 60%.

Metameric problems are variable-length optimization problems whose representations take on an at least partially segmented structure. This is referred to as a metameric representation. Frequently, each of these segments defines one of a number of analogous components in the solution. Examples include the nodes in a coverage network or turbines in a wind farm. Locating optimal solutions requires, in part, determining the optimal number of components. Evolutionary algorithms can be applied but require modifications to the traditional fixed-length operators. This study proposes a new selection operator for metameric problems: length niching selection. First, the population is partitioned into several niches based on solution length. A window function determines at which lengths a niche is formed. Local selection is then applied within each niche independently, resulting in a new parent population formed by a diverse set of solution lengths. A coverage and a wind farm problem are used to demonstrate the effectiveness of the new operator.

It is well known that the nonlinear frequency modulation (NLFM) chirp waveform can shape advantageously the power spectrum density (PSD) such that the autocorrelation function exhibits reduced sidelobes as the window function. However, differences between the PSD and window function due to the Gibbs effects caused by the Fresnel integral would lead to deteriorative performance of the NLFM chirp waveform. In particular, the correlation function of NLFM waveform with Chebyshev PSD is seriously inconsistent with the lowest sidelobe level of the Chebyshev window function possesses. To overcome the inconsistency, therefore, in this letter, a novel NLFM waveform with modified Chebyshev window PSD is proposed, which combines the Chebyshev with edge distortion compensation, allowing, in theory, low sidelobe level as Chebyshev window. Using theoretical analysis also confirmed by simulation, this letter shows that the novel NLFM waveform possesses low sidelobes without high computational complexity in design.

Spectral analysis is a significant technique applied in many fields to infer the signal spectral contents. However, the frequency resolution of a signal spectrum estimation result is limited by its finite data length, especially when using a Fourier-based method. Extra processing gain [i.e., signal-to-noise ratio (SNR) improvement] is always required for weak target detection. In this paper, a high-resolution spectrum estimation method using a deconvolution algorithm is proposed. According to classical spectral analysis, a power spectrum derived from a finite data length is related to the convolution of the true power spectrum from an infinite length data set with the power spectrum from a window function. Therefore, using a deconvolution algorithm on the power spectrum estimated by classical spectral analysis can remove the influence from the window function, such as spectral leakage. The deconvolved power spectrum can robustly obtain a sufficiently high-frequency resolution and low sidelobes with relatively few calculations. The proposed method can also provide a deconvolution gain, which plays an important role in weak signal detection as it is capable of enhancing the signal and reducing background noise. Its performance is analyzed in simulations as well as with measured experimental data.

Beamforming plays an important role in the array radar anti-interference. However, the interference targets with fast speed may move out of the narrow null area of the beampattern. A null broadening method with robust adaptive beamforming for frequency diverse array (FDA)-multiple-input and multiple-output (MIMO) systems is proposed in this paper. The projection preprocessing and windowing functions are applied to obtain stable beampatterns. Then, a novel null broadening method based on the covariance matrix reconstruction is realized by setting artificial fluctuations around each actual jammer. Finally, a new convex optimization model is established and solved to estimate the desired steering vector. Numerical simulations results verify the effectiveness of the proposed method.

We present a novel method to design and optimize window functions based on combinations of linearly independent functions. These combinations can be performed using different strategies, such a sums of sines/cosines, series, or conveniently using a polynomial expansion. To demonstrate the flexibility of this implementation, we propose the Generalized Adaptive Polynomial (GAP) window function, a non-linear polynomial form in which all the current window functions could be considered as special cases. Its functional flexibility allows fitting the expansion coefficients to optimize a certain desirable property in time or frequency domains, such as the main lobe width, sidelobe attenuation, and sidelobe falloff rate. The window optimization can be performed by iterative techniques, starting with a set of expansion coefficients that mimics a currently known window function and considering a certain figure of merit target to optimize those coefficients. The proposed GAP window has been implemented and several sets of optimized coefficients have been obtained. The results using the GAP exemplify the potentiality of this method to obtain window functions with superior properties according to the requirements of a certain application. Other optimization algorithms can be applied within this strategy to further improve the window functions.

A novel laser self-mixing interferometry vibration measurement algorithm based on the local maximum detection technique is proposed, that can reconstruct micro vibrations rapidly and easily. In this article, the principles of the local maximum detection algorithm are analyzed in detail, and the process of solving the window function is emphasized. The major advantage of the method is that it does not involve any complicated calculations and removes the need for optical/electromechanical components. The validity of the presented method is confirmed by means of simulated signals and demonstrated via several experiments for harmonic and aleatory motion.

The quality factor (or Q value) is an important parameter for characterizing the inelastic properties of rock. Achieving a Q value estimation with high accuracy and stability is still challenging. In this study, a new method for estimating ultrasonic attenuation using a spectral ratio based on an S transform (SR-ST) is presented to improve the stability and accuracy of Q estimation. The variable window of ST is used to solve the time window problem. We add two window factors to the Gaussian window function in the ST. The window factors can adjust the scale of the Gaussian window function to the ultrasonic signal, which reduces the calculation error attributed to the conventional Gaussian window function. Meanwhile, the frequency bandwidth selection rules for the linear regression of the amplitude ratio are given to further improve stability and accuracy. First, the feasibility and influencing factors of the SR-ST method are studied through numerical testing and standard sample experiments. Second, artificial samples with different Q values are used to study the adaptability and stability of the SR-ST method. Finally, a further comparison between the new method and the conventional spectral ratio method (SR) is conducted using rock field samples, again addressing stability and accuracy. The experimental results show that this method will yield an error of approximately 36% using the conventional Gaussian window function. This problem can be solved by adding the time window factors to the Gaussian window function. The frequency bandwidth selection rules and mean slope value of the amplitude ratio used in the SR-ST method can ensure that the maximum error of different Q values estimation (Q > 15) is less than 10%.

The article is devoted to the research of the method of digital filtering of a mixture of signals at ultra-low frequencies. A mathematical model of the system has been developed that includes an adequate signal model that really brings the result. The type of filter and the window function that is included in it were selected, and an algorithm for digital filtering of the signal mixture was developed that allows the most accurate selection of the received signal parameters. The obtained research results confirmed the efficiency of the mathematical model and the filtering algorithm of the signal mixture, and also proved their practicality in use.

The Hanning window and interpolation algorithm is used to the frequency estimation for voltage and current signals acquired in transformer terminal unit (TTU), and the algorithm is validated by the frequency estimation for actual voltage signals. On this basis, the influence of signal frequency, harmonic, signal-to-noise ratio (SNR), sampling duration, sampling frequency and quantization of analog digital converter (ADC) on the accuracy of frequency estimation is investigated based on the numerically generated voltage signal. The results reveal that the error is proportional to the difference between the actual signal frequency and the rated value (50 Hz). When the total harmonic distortion (THD) varies in the range of 0~10%, the error is almost independent of THD. The error decreases with SNR, and the rate of decrease reduces with SNR. The sampling frequency has little effect on the error when the sampling duration is kept constant. When the quantization bit varies from 4 to 16, it has little effect on the error. Suggestions on the selection of sampling parameters for TTU frequency analysis using the Hanning window and interpolation algorithm are also given.

A fixed window function which is similar in shape to a semi-ellipse is proposed. The semi–ellipse which has its major axis to be equal to the window length and the minor axis at unity produced about 4.2 dB lower ripple ratio than the rectangular window. The proposed window function is derived from the equation of an ellipse in the explicit and parametric forms. First of all, the spectral characteristic of the proposed window is studied in terms of spectral parameters and compared with other fixed windows like Rectangular, Bartlett, Hann, Hamming and Blackman windows. The window simulation results reveal that the proposed window produced comparable spectral characteristic with existing standard fixed windows. Secondly, the paper presents the application of the proposed window in a digital filter design. The filter analysis comparison results with other fixed windows namely Bartlett, Von Hann, Hamming, and Kaiser window, an adjustable window, confirm that filter design with the proposed window exhibits good spectral characteristic, and can be used to design better filter than the Bartlett window using less than half the Bartlett’s filter length for a fixed transition width. The similicity of its coefficients formulation and design algorithm makes it a good choice for digital filter design applications.

The staggered-grid finite-difference method (SGFDM) has been extensively employed in numerical modeling, seismic imaging, and waveform inversion because of its high efficiency, accuracy, and practicality. Numerical modeling accuracy is crucial for imaging and inversion. Truncating the spatial convolution sequence of the pseudospectral method by window functions can derive the finite-difference method. However, truncation error is inevitable; it can create illusions in numerical modeling, leading to misjudgments. To reduce the truncation error and improve numerical modeling accuracy, enhancing the performance of the truncated window function is imperative. In this study, a new optimal window function was investigated based on the least-squares combination of square windows. Then, the new optimized window function was used to truncate the spatial convolution sequence of the pseudospectral method and obtain an optimized SGFDM. Dispersion analysis showed that the optimized SGFDM has wider spectrum coverage than the conventional SGFDM at the same order. In addition, at low orders, the error range of the new optimized SGFDM could be strictly controlled within 1‱, whereas, at high orders, while ensuring accuracy, the spectrum coverage significantly improved. Finally, numerical modeling for elastic waves demonstrated that the optimized SGFDM could superiorly suppress numerical dispersion and improve calculation efficiency.

When the fast Fourier transform (FFT) algorithm is used to analyze demodulate interference signal, nonsynchronous sampling of the interference optical spectrum would cause spectral leakage and fence effect, decreasing demodulation accuracy. Window functions and interpolation algorithms can effectively improve the demodulation accuracy of the FFT algorithm. Therefore, in this work, we propose an algorithm of cavity length demodulation for optical fiber F-P sensors based on Nuttall window four-spectrum-line interpolation FFT. The simulation results of numerical calculation show that the demodulation accuracy and speed of this algorithm are better than cubic spline interpolation and FFT algorithm.

The trend in the conception of future satellite system and modern communication systems are undoubtedly in the direction of the use of digital beamformer. These systems will include many digital links. These beamformer needs to control their weights adaptively for build intelligent systems. For controlling these weights, various blind and nonblind algorithm apply as per applications. Blind learning process is based on constant modulus algorithm (CMA) and least square CMA (LS-CMA) analyses. Also, to improve converge area and side lob level reduction, modified Hamming window-based algorithm to constant modulus algorithm and least square simulate using MATLAB. These algorithms are validated for linear, circular and planar antenna array geometry.

Two methods for the directive shaping of propagating plane-wave fast multipole method (FMM) translation operators (TLOPs) are discussed and compared. In the first approach, a real windowing function as often found in signal processing is considered within the truncated Legendre-polynomial series representation of the standard FMM TLOPs. The second approach utilizes Gaussian-beam (GB) TLOPs, which are obtained from complex-source theory. Both methods achieve considerable directive shaping and side-lobe suppression of the TLOPs and allow, thus, to drop a certain amount of plane-wave samples in the numerical integration of the corresponding planewave spectra in the FMM-based evaluation of time-harmonic electromagnetic integral operators. It is found that the GB TLOPs exhibit considerably better performance than TLOPs with standard real windowing functions. This is explained based on the observation that GB TLOPs can be interpreted as windowed TLOPs with a more appropriate complex windowing function, whose magnitude can even be larger than one. In order to achieve an accurate and efficient evaluation of the relevant integral operators, both approaches for directive shaping should work with an oversampled spectral representation as compared to the standard case together with a very careful choice of all relevant parameters.

Aiming at the use of traditional Fourier transform (FFT) for harmonic detection, due to non-synchronous sampling and non-integral period truncation, which will affect the calculation accuracy of each harmonic, this paper proposes a dual Hanning self-multiplication window (HSMW) and FFT/apFFT integrated phase difference power harmonic detection method. The algorithm combines the traditional FFT and apFFT phase difference method, which has the advantage that the amplitude and phase can be obtained by accessing only one spectral line. At the same time, a dual HSMW window is designed to suppress spectral leakage. The simulation comparison experiment with traditional FFT spectrum analysis and dual Hanning window FFT/apFFT integrated phase difference method verifies the effectiveness and stability of the algorithm proposed in this paper.

In this article an enhanced and simplified alteration of a memristor model based on tantalum oxide is proposed. Its application in hybrid memory crossbars is presented. The suggested model is founded on the classical Hewlett Packard Ta 2 O 5 memristor model including several main refinements – incorporation of a simple window function, enhancement of its efficiency applying rationalized expression for the current-voltage relation and by substitution of the Heaviside function with continuous and smooth logistic function. The memristor model’s parameters are obtained by collation to tentative current-voltage characteristics and applying procedure for parameters estimation. A LTSpice library model is generated in agreement to the considered memristor model. The modified model of tantalum oxide memristor is tested in a hybrid memory crossbar. After comparison to several basic models the major advantages of the suggested memristor model are demonstrated – better performance, higher speed of operation, improved adjustment process and a sound switching representation.

Recently, we proposed a Spectral Domain Sparse Representation (SDSR) approach for the direction-of-arrival estimation of signals incident to an antenna array. In the approach, sparse representation is applied to the conventional Bartlett spectra obtained from snapshots of the signals received by the antenna array to increase the direction-of-arrival (DOA) estimation resolution and accuracy. The conventional Bartlett spectra has limited dynamic range, meaning that one may not be able to identify the presence of weak signals in the presence of strong signals. This is because, in the conventional Bartlett spectra, uniform weighting (window) is applied to signals received by various antenna elements. Apodization can be used in the generation of Bartlett spectra to increase the dynamic range of the spectra. In Apodization, more than one window function is used to generate different portions of the spectra. In this paper, we extend the SDSR approach to include Bartlett spectra obtained with Apodization and to evaluate the performance of the extended SDSR approach. We compare its performance with a two-step SDSR approach and with an approach where Bartlett spectra is obtained using a low sidelobe window function. We show that an Apodization Bartlett-based SDSR approach leads to better performance with just single-step processing.

We make use of recent developments in the analysis of galaxy redshift surveys to present an easy to use matrix-based analysis framework for the galaxy power spectrum multipoles, including wide-angle effects and the survey window function. We employ this framework to derive the deconvolved power spectrum multipoles of 6dFGS DR3, BOSS DR12 and the eBOSS DR16 quasar sample. As an alternative to the standard analysis, the deconvolved power spectrum multipoles can be used to perform a data analysis agnostic of survey specific aspects, like the window function. We show that in the case of the BOSS dataset, the Baryon Acoustic Oscillation (BAO) analysis using the deconvolved power spectra results in the same likelihood as the standard analysis. To facilitate the analysis based on both the convolved and deconvolved power spectrum measurements, we provide the window function matrices, wide-angle matrices, covariance matrices and the power spectrum multipole measurements for the datasets mentioned above. Together with this paper we publish a \code{Python}-based toolbox to calculate the different analysis components. The appendix contains a detailed user guide with examples for how a cosmological analysis of these datasets could be implemented. We hope that our work makes the analysis of galaxy survey datasets more accessible to the wider cosmology community., 39 pages, 16 figures, one table

This paper proposes a concise window function to build a memristor model, simulating the widely-observed nonlinear dopant drift phenomenon of the memristor. Exploiting the non-linearity, the memristor model is applied to the in-situ neuromorphic solution for a cortex-inspired spiking neural network (SNN), spike-based Bayesian Confidence Propagation Neural Network (BCPNN). The improved memristor model utilizing the proposed window function is able to retain the boundary effect and resolve the boundary lock and inflexibility problem, while it is simple in form that can facilitate large-scale neuromorphic model simulation. Compared with the state-of-the-art general memristor model, the proposed memristor model can achieve a $5.8 \times$ reduction of simulation time at a competitive fitting level in cortex-comparable large-scale software simulation. The evaluation results show an explicit similarity between the non-linear dopant drift phenomenon of the memristor and the BCPNN learning rule, and the memristor model is able to emulate the key traces of BCPNN with a correlation coefficient over 0.99.

The purpose of this research is to analyze convolutional windows and compare their performance to that of traditional windows. The window is convoluted on its own to create convolutional windows. These new windows are used to create a pseudo-LFM signal utilising two stage piece wise linear frequency functions. The proposed LFM signal was simulated using both traditional and convolutional window functions, and it was discovered that convolutional windows produce better peak to side lobe level ratio (PSLR) values than traditional windows.

Conventional algorithms for galaxy power-spectrum estimation measure the true spectrum convolved with a survey window function, which, for parameter inference, must be compared with a similarly convolved theory model. In this work, we directly estimate the unwindowed power spectrum multipoles using quadratic estimators akin to those introduced in the late 1990s. Under Gaussian assumptions, these are optimal and free from the leading-order effects of pixelization and non-Poissonian shot noise. They may be straightforwardly computed given the survey dataset and a suite of simulations of known cosmology. We implement the pixel-based maximum-likelihood estimator and a simplification based on the Feldman-Kaiser-Peacock weighting scheme, both of which can be computed via FFTs and conjugate-gradient descent methods. Furthermore, the estimators allow direct computation of spectrum coefficients in an arbitrary linear compression scheme, without needing to first bin the statistic. Applying the technique to a subset of the BOSS DR12 galaxies, we find that the pixel-based quadratic estimators give statistically consistent power spectra, compressed coefficients, and cosmological parameters to those obtained with the usual windowed approaches. Because of the sample's low number density and compact window function, the optimal weighting scheme gives little improvement over the simplified form; this may change for dense surveys or those focusing on primordial non-Gaussianity. The technique is shown to be efficient and robust, and shows significant potential for measuring the windowless power spectrum and bispectrum in the presence of weak non-Gaussianity.

For past many years, Time delay estimation (TDE) has been a booming area of interest for research due to its widespread applications in many fields such as ultrasonic, radar, seismology, identifying, detecting and finding the location of radiating sources, sonar systems and other communication fields. Finding time difference of arrival (TDOA) between the signals received at an array of antennas is done basically in time delay estimation. Usually, the peak of cross-correlation gives the value of time delay. A generalized cross-correlation (GCC) is a well-known technique for time delay estimation. In this paper, generalized cross-correlation is used for time delay estimation between the signals. This technique utilizes various windowing functions to improve the delay estimation by narrowing the main lobe and reducing the side lobes in cross-correlation function. These window functions use a specific characteristic of signals itself and embedded noise. Typically, GCC is applied to narrow band systems such as radar, sonar etc. This paper proposes an analysis of GCC techniques for direction finding in wideband signals and compute root mean square error (RMSE) for the delay estimates obtained over the range of SNRs. Analysis, simulation and results are obtained by using MATLAB.

This article introduces an improved Gerchberg–Papoulis algorithm (IGPA) to resolve truncation errors in planar near-field (NF) antenna measurement and seeks to define the most accurate means of recovering patterns. The truncation errors in planar NF measurements can be reduced by considering the evanescent modes and introducing a new convergence criterion and a window function in the IGPA. A detailed design procedure is presented, and its effect on the field distribution of key parameters is discussed, which can be found in the Appendix at https://web.xidian.edu.cn/xli/files/Appendix.pdf . The results of a simulation and physical measurement are used to assess the validity and applicability of the proposed approach.

Transmissibility based operational modal analysis (TOMA) method is an effective solution to modal parameter estimation problem for a linear system under non-white stochastic excitations. However, the TOMA method has two main limitations. Firstly, the transmissibility function defined in frequency domain necessitates Fourier transform to acquire frequency-domain data, thus leading to leakage errors and window function selection problem. Secondly, it needs multiple sufficiently different load cases to estimate the modal parameters, and how to quantify the difference between different load cases remains a problem. To remove these two limitations, this paper proposes the time-domain representation of transmissibility based operational modal analysis technique. This technique contains two methods, namely time-domain transmissibility based method and correlation function transmissibility (CFT) based method. Both methods employ the time-domain data directly and thus avoid the Fourier transform. The CFT based method combines CFT functions with different transfer outputs instead of different load cases to estimate modal parameters. Numerical and laboratory examples show that the proposed two methods eliminate the leakage errors thoroughly and window function selection problem, showing higher accuracy and lower sensitivity to short response data than the existing frequency-domain methods. Furthermore, two methods can be expressed in a unified mathematical form through which the modal parameters can be obtained by solving an eigenvalue problem in low computational cost.