Search

This study introduces a new adjustable window derived from the recently proposed fractional modified Bessel function of the first kind with zero order. The proposed window, referred to as the fractional Kaiser window in this study, is obtained using the Kaiser approach, which was originally used to develop the well-known Kaiser window, and encompasses the Kaiser window as a special case. First, spectral analysis of the proposed window is conducted across various window lengths to evaluate its spectral performance. The comparative results reveal that the proposed window offers superior ripple ratio values, ranging from 1.67 dB to 5.20 dB, compared to the Kaiser window for the same half-mainlobe width at N = 51. Next, the effectiveness of the proposed window in the design of finite impulse response (FIR) digital filters is assessed. After analyzing the filter’s spectral performance for different values of the independent parameters, a general comparison is made with filters designed using the Kaiser window, demonstrating that superior filters can be achieved with the proposed window. Finally, three design examples of digital filters are provided, with different filter lengths ( $N =51$ , 71, and 101) and filter transition widths, to compare with other windows in the literature. The simulation results indicate that the proposed window consistently produces better filter designs in all three examples by offering the largest minimum stopband attenuation values.

This paper presents, for the first time, analytical solutions for the charge and flux as a function of the state variable in the case of the HP memristor, modeled as an ideal generic memristor with Joglekar and Prodromakis window functions for a general value of the control parameter. The solutions are in the closed form of finite sums for an arbitrary positive integer values of the control parameter. Our approach is based on the decomposition of original problems using appropriate pairs of smooth hinge functions. The generalization of this approach allows us to define a novel window function based on smooth hinge functions, which brings simpler analytical expressions for charge and flux as a function of the state variable, and faster simulations when the model is used.

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

There are nonlinear drift memristor models utilizing window functions in the literature. The resistive memories can also be modeled using memristors. If the memristor’s resistance switches from its minimum value to its maximum value or from its maximum value to its minimum value, the transition phenomenon is called resistive or memristive switching. The value of the time required for this transition is especially important for resistive computer memory applications. The switching time is measured by experiments and should be calculatable from the parameters of the memristor model used. In the literature, to the best of our knowledge, the resistive switching times have not been calculated except for the HP memristor model and a piecewise linear memristor model. In this study, the memristive switching times of some of the well-known memristor models using a window function are calculated and found to be infinite. This is not feasible according to the experiments in which a finite memristive switching time is reported. Inspired by these results, a new memristor window function that results in a finite switching time is proposed. The results of this study and the criteria given here can be used to make more realistic memristor models in the future.

In order to further reduce the errors arising in synchronous sampling, this paper designs a multi-channel hybrid sampling electrical parametric feature modeling method based on an AIOT sensing module in the process of design. The AIOT sensing module is used to process the received RF signals using a transconductance amplifier to improve the digitization and reconfigurability of the RF front-end circuit. The signal is transformed and calculated using the Fast Fourier Transform to obtain electrical parameters such as the amplitude of each harmonic and the power factor. The results show that the variation amplitude of the window function of the design method in this paper is generally maintained between -1.5 and 1.5, the amplitude accuracy of the active power rate is within 3.17555%, and the relative error accuracy is within 0.000951%. It can be seen that the AIOT-based sensing module can significantly improve the calculation accuracy of electrical parameters and can be applied to the process of sampling digital measurements of other power signal characteristics.

The problem of changes in the audio signal when changing the sampling frequency arose a long time ago, but interest in it has recently become more acute with an increase in the quality of signal formation and transmission. To some extent, this was also determined by the methods of assessing the quality of changes in the harmonic signal without taking into account changes in the actual broadcast signal. Algorithms for the formation of a new digital sequence after changing the sampling rate provided perfect quality in the conversion of the sinusoidal signal and large errors in the conversion of the real signal. Algorithms for changing the sampling rate Fd have been improved. The aim of this work is to study the features of changes in the sampling frequency in the paths of the broadcast channel and to develop algorithms for converting the sampling frequency in the frequency domain with an increase in conversion accuracy. It is shown that the algorithms for converting the sampling rate in the time domain have reached perfection and cannot be improved, so the transition to processing in the frequency domain is important. An algorithm for converting the sampling frequency in the frequency domain has been developed. The spectrum of the error signal for various types of converters is determined and the need for its compensation is determined. A method for introducing predistortions for converters with known and unknown sequence of sample rates used has been developed. The use of the results of this work makes it possible to improve the quality of broadcasting signals and information programs.

Window functions are required to achieve excellent frequency resolution, peak sidelobe ratio, and sidelobe decay. The cosine-sum window function satisfies these requirements. However, conventional cosine-sum windows limit the number of terms and coefficient values. Therefore, this study proposes a new class of cosine-sum windows that has more terms than those in the conventional cosine-sum window and considers positive and negative coefficients. For such windows, we present three design examples. The first is a window function with low sidelobe decay, which reduce the sidelobes by adding correction terms to the conventional windows without damaging the sidelobe decay. The second is a window function that improves the frequency resolution by emphasizing the discontinuities of the extracted signal. The third is a window function that reduces sidelobes further without deteriorating the frequency resolution by adding correction terms to the window functions, which are designed in advance. We confirmed the effectiveness of these examples of the proposed window function.

A multithreaded convolution implementation based on block algorithms is considered. Convolution is essentially the basis of many methods that solve the problem of determining the degree of similarity or independence of two processes, in other words, when it is necessary to determine the degree of correlation. The algorithm itself is executed with a significant delay, because for its execution it is necessary to accumulate the entire signal and then process it. The analysis showed that one of the possible ways to reduce time costs is a multithreaded implementation of convolution based on block algorithms. The article shows the main features of the convolution implementation by the overlap method with addition and the overlap method with addition, as well as numerical examples. The results obtained show that the application of these methods without the use of a window function leads to significant distortions in the signal spectrum. Based on the results of the analysis, a universal scheme for performing convolution based on multithreaded processing of an input data block is proposed. This allows to achieve a good compromise between computational complexity, system architecture, and time costs.

Crosshole seismic testing is commonly used to determine detailed and reliable wave velocity profiles. Material damping measurements can also be performed in crosshole seismic testing, but these measurements require a window function to maintain similar amplitude shapes over the frequency range of interest for the calculation. In-situ seismic testing, including downhole and seismic cone penetration testing (SCPT), also requires a window function for the material damping calculations. However, the length of the window function has the largest influence on the material damping calculation. Therefore, the half-power bandwidth method is introduced to determine the material damping ratio without the window function in crosshole testing by replicating the unconfined, free-free, resonant column (Fr-Fr) test. To demonstrate the influence in the length of the window function, the first cycle of the signal is used in the material damping calculation. The half- power bandwidth method is verified using synthetic signals and field data. Two sets of crosshole and downhole tests were performed, one at a backfill test pad and the second at a Hornsby Bend research site operated by the University of Texas at Austin. The in-situ material damping ratio calculated from these two sets of crosshole tests using the half-power bandwidth method are compare with the Spectral Ratio Slope (SRS) method applied to the downhole testing at these sites. The material damping calculated from the half-power bandwidth method using the full signal results in a reliable and precise damping value compared to the SRS method applied to the downhole data.

In the paper, the systematic (bias) error of digital processing of the biharmonic signal of two multiplexed fiber-optic interferometers under spectral interrogation, when the registered spectral transfer function being processed through a discrete Fourier transform has been analyzed. The synthesis of a special weighted window function was put forward; this made it possible to reduce the systematic errors in determining the frequencies of a polyharmonic signal without a significant increase in the random (noise) error. The effectiveness of this approach was proven through numerical simulation and experimentally by comparison with the error when using standard Dolph – Chebyshev window. The proposed approach can be applied in any problems related to the estimation of frequencies and phases of polyharmonic signals.

As complementary to Synthetic Aperture Radar (SAR) Differential Interferometry (DInSAR), SAR Offset Tracking (OT) is an efficient tool for large ground deformation monitoring in situations when DInSAR cannot work. However, SAR images are affected by speckle noise and some strong point-like scatters which can cause what is known as Patch Like (PL), a kind of errors that can be seen as homogeneous patches of almost constant deformation in the results. These errors are clearly visible in the results as non-consistent deformations along time, but they are difficult to detect with the traditional metrics that evaluate the cross-correlation results, like the Signal to Noise Ratio (SNR). This paper addresses this problem and proposes a simple amplitude filter to reduce PL named as Patch Like Reduction (PLR). The main idea is to find a sensor and scene independent threshold to remove the high amplitude pixels prone to cause PL. Five different SAR data sets and in-field GPS measurements are used to determine the optimal threshold and evaluate the performance of the proposed method. The results show that PL effects can be reduced with the proposed amplitude filter. The processing parameters of the improved OT processing chain are optimized as well to preserve the results resolution as much as possible.

In recent years, there have been increased demands for aggregating sensor information from several sensors owing to the spread of the Internet of Things (IoT). However, packet communication, which is a conventional multiple-access technology, is hindered by packet collisions owing to simultaneous access by sensors and waiting time to avoid packet collisions; this increases the aggregation time. The physical wireless parameter conversion sensor network (PhyC-SN) method, which transmits sensor information corresponding to the carrier wave frequency, facilitates the bulk collection of sensor information, thereby reducing the communication time and achieving a high aggregation success rate. However, when more than one sensor transmits the same frequency simultaneously, the estimation accuracy of the number of accessed sensors deteriorates significantly because of multipath fading. Thus, this study focuses on the phase fluctuation of the received signal caused by the frequency offset inherent to the sensor terminals. Consequently, a new feature for detecting collisions is proposed, which is a case in which two or more sensors transmit simultaneously. Furthermore, a method to identify the existence of 0, 1, 2, or more sensors is established. In addition, we demonstrate the effectiveness of PhyC-SNs in estimating the location of radio transmission sources by utilizing three patterns of 0, 1, and 2 or more transmitting sensors.

The paper introduces a set of models of memristive devices for a reliable, accurate and fast analysis of large networks in the SPICE (Simulation Program with Integrated Circuit Emphasis) environment. The modeling starts from the recently introduced TEAM (ThrEshold Adaptive Memristor Model) and VTEAM (Voltage ThrEshold Adaptive Memristor Model). A number of improvements are made towards the stick effect elimination and other numerical refinements to make the analysis of large networks fast and accurate. A set of models are proposed that utilize the synergy of several techniques such as window asymmetrization, integration with saturation, state equation preprocessing, scaling, and smoothing. The performance of models is tested in Cadence PSPICE 17.2 and particularly in HSPICE v2017, the latter on a large-scale CNN (Cellular Nonlinear Network) for detecting edges of binary images. The simulations manifest the usability of developed models for fast and reliable operation in networks containing more than one million nodes.

Abstract In this article, we give a definition and discuss several properties of the δ-β-Gabor integral operator in a class of locally integrable Boehmians. We derive delta sequences, convolution products and establish a convolution theorem for the given δ-β-integral. By treating the delta sequences, we derive the necessary axioms to elevate the δ-β-Gabor integrable spaces of Boehmians. The said generalized δ-β-Gabor integral is, therefore, considered as a one-to-one and onto mapping continuous with respect to the usual convergence of the demonstrated spaces. In addition to certain obtained inversion formula, some consistency results are also given.

The design of memristor-based electronic circuits and devices gives researchers opportunities for the engineering of CMOS-memristor-based electronic integrated chips with ultra-high density and various applications. Metal-oxide memristors have good compatibility with the present CMOS integrated circuits technologies. The analysis of new electronic circuits requires suitable software and fast-functioning models. The main purpose of this paper is to propose the application of several modified, simplified, and improved metal-oxide memristor models in electronic devices and provide a comparison of their behavior, basic characteristics, and properties. According to this, LTSPICE is utilized in this paper because it is a free software product with good convergence. Several memristor-based electronic circuits, such as non-volatile passive and hybrid memory crossbars, a neural network, and different reconfigurable devices–filters, an amplifier, and a generator are analyzed in the LTSPICE environment, applying several standards and modified metal-oxide memristor models. After a comparison of the operation of the considered schemes, the main advantages of the modified metal-oxide memristor models, according to their standard analogs, are expressed, including fast operation, good accuracy, respectable convergence, switching properties, and successful applicability in complex electronic circuits.

Purpose: Analyzing the output signal structure of the optimum filter of chirp-pulse compression in order to look into causes of discrepancy between the sidelobe level, which is obtained using standard tapered windows, with the literature data. Design/methodology/approach: To calculate the response structure of the optimum filter with a tapered window of an arbitrary form, the standard methods of mathematical physics and statistical theory of signal processing are used. Findings: Expressions have been derived for estimating the maximum number of zeros and maxima of the response of the optimum filter of chirp-pulse compression and separation between adjacent and “like” (with the same numbers) zeros and maxima in dependence on the signal base. Formulas have been obtained for loss in the signal-to-noise ratio due to application of smoothing functions. The case of applying window functions in the form of cosine harmonics of the Fourier series, which describes a rather great number of the standard windows, is analyzed in detail. An analytical expression has been derived for the output signal of the chirp-pulse compression filter on the basis of such windows, and a formula for estimating the amount of loss in the signal-to-noise ratio is presented. A comparative performance analysis of the Hamming and Blackman windows has been made in dependence on the signal base B It has been found that application of the Hamming window is more efficient for B ≤ 80. For greater values of B, the Blackman window shows a higher efficiency. As B increases, the efficiency of both windows steadily increases asymptotically approaching the figure declared in the literature. Coefficients of window functions containing three cosine harmonics of the Fourier series have empirically been selected that made it possible to reduce the sidelobe level by approximately 0.34 dB for B = 21 and more than by 1 dB for B = 7 as compared with the Hamming window. Conclusions: The obtained results allow concluding that the optimization problem for the window function parameters in the case of small signal bases should be solved individually for each specific value of B. Most likely it would be impossible to obtain the extremely low sidelobe level, however a certain improvement of the characteristics of the chirp-pulse compression filter seems to be quite possible.

In this paper, a Hewlett-Packard (HP) memristor model with a new window function and its versatile characteristics are presented. SPICE behaviors of the linear and nonlinear memristor model are studied through PSpice simulation. High flexibility is demonstrated for emulating the behaviors of the practical HP memristors. Furthermore, the characteristics of the composite SPICE behaviors are both investigated when two memristors are connected in series and in parallel. The polarity of each memristor is also taken into consideration. The relationships among flux, charge, voltage, current, and memristance of the double memristor circuits are simulated and analyzed.

In this paper, an improved and simplified modification of a tantalum oxide memristor model is presented. The proposed model is applied and analyzed in hybrid and passive memory crossbars in LTSPICE environment and is based on the standard Ta2O5 memristor model proposed by Hewlett–Packard. The discussed modified model has several main enhancements—inclusion of a simplified window function, improvement of its effectiveness by the use of a simple expression for the i–v relationship, and replacement of the classical Heaviside step function with a differentiable and flat step-like function. The optimal values of coefficients of the tantalum oxide memristor model are derived by comparison of experimental current–voltage relationships and by using a procedure for parameter estimation. A simplified LTSPICE library model, correspondent to the analyzed tantalum oxide memristor, is created in accordance with the considered mathematical model. The improved and altered Ta2O5 memristor model is tested and simulated in hybrid and passive memory crossbars for a state near to a hard-switching operation. After a comparison of several of the best existing memristor models, the main pros of the proposed memristor model are highlighted—its improved implementation, better operating rate, and good switching properties.

The paper proposes an algorithm for frequency estimation of a pulse signal with constant beat under significant distortion conditions with the use of spectral analysis methods. The sequential processing of the signal based on the recurrent usage of discrete Fourier transform is shown. The initial pulse signal is represented as a fragment of the Dirac comb. Its Fourier spectrum also contains a fragment of the Dirac comb. To reduce the effect of leakage due to the application of Fourier transform to the finite sequence, a convolution of the signal with a weight window is used. To increase the signal-to-noise ratio and reduce the side lobe level, the spectrum of the initial signal is taken as the original for Fourier transform with an increased number of spectral lines. The necessity of recurrent transformation usage is brought about by the noise of the initial signal and the resulting spectrum after the first application of Fourier transform. In comparison with a single application of the transformation, this approach provides an opportunity to recognize a useful signal both against the background of Gaussian and aperiodic impulse noise, and against the background of signals containing such noise in the Fourier spectrum. We give a method for checking the local maxima of the amplitudes of the obtained discrete Fourier transform for periodicity. The frequency of a pulse signal with constant beat is determined by the element index with the largest number of fulfillment of the periodicity condition.

Abstract Window functions have been a part of the SQL standard since 2003 and have been studied extensively during the past decade. They are widely used in data analysis; almost all the current mainstream commercial databases support window functions. However, in recent years the size of datasets is growing steeply; the existing window function implementations are not efficient enough. Recently, some sampling-based algorithms (e.g., online aggregation) are proposed to deal with large and complex data in relational databases, which offer us a flexible trade-off between accuracy and efficiency. However, few sampling techniques has been considered for window functions in databases. In this paper, we extend our previous work (Song et al. in Asia-Pacific web and web-age information management joint conference on web and big data, Springer, pp 229–244, 2017) and proposed two new algorithms: range-based global sampling algorithm and row-labeled sampling algorithm. The proposed algorithms use global sampling rather than local sampling and are more efficient than other existing algorithms. And we find our proposed algorithms out performed the baseline method over the TPC-H benchmark dataset.

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.

This work studies the application of short-time Fourier transform (STFT) to extract current harmonics of various fault types to design a protection method for meshed multi-terminal voltage source converter-high-voltage direct current (VSC-HVDC-MTDC) grids. The frequency spectrum of fault current harmonics is used to detect internal and external faults, the faulty pole and fault type. The method does not need the implementation of series inductance on the sides of the DC lines and it is also effective for lines combining overhead lines and cables. The window function and hop size play the primary role in STFT, which are investigated in a sensitivity analysis. A modified version of CIGRE meshed DC grid system is simulated in PSCAD in order to show the robustness of the method, and further signal processing analysis is done in MATLAB. The results show the accurate detection and discrimination between faulty sections using the proposed harmonic-based method and how important the STFT parameters are in order to have a robust protection algorithm.

The geological and structural conditions define the radon situation inside a building. While the geological realities can be specified by the content of radium-226 and the ratio of radon-222 emitted from the ground the structural conditions are defined by the tightness of the building envelope. The radon concentration inside has an unsteady character, which is caused by meteorological conditions outside and the air change rate (ACH or ACR), which in turn is influenced by the residents’ behaviour such as venting and heating. For the assessment of the radon exposition, it is necessary to perform measurements for a long time. An approach to reduce this time by eliminating the inhabitants influence on the radon concentration is the radon emission rate, also known as radon entry rate. This variable is based on the measurement of the radon concentration and the parallel determination of the air change rate via a tracer gas method, the result expresses a released activity per time. Due to their noisy character, it is necessary to apply a smoothing algorithm to the input parameters. In addition to mean values, the use of window functions, known from digital signal processing, was analysed. For the verification of the whole calculation procedure, simulations and measurements under defined conditions were used. Furthermore, measurements in an uninhabited house showed proof of the capability of the assessment of the radon potential. First examinations of influencing parameters of the radon emission rate showed a possible dependence on the temperature difference inside and outside the building.

The purpose of this paper was to propose a complete analysis and parameter estimations of a new simplified and highly nonlinear hafnium dioxide memristor model that is appropriate for high-frequency signals. For the simulations; a nonlinear window function previously offered by the author together with a highly nonlinear memristor model was used. This model was tuned according to an experimentally recorded current−voltage relationship of a HfO2 memristor. This study offered an estimation of the optimal model parameters using a least squares algorithm in SIMULINK and a methodology for adjusting the model by varying its parameters overbroad ranges. The optimal values of the memristor model parameters were obtained after minimizing the error between the experimental and simulated current−voltage characteristics. A comparison of the obtained errors between the simulated and experimental current−voltage relationships was made. The error derived by the optimization algorithm was a little bit lower than that obtained by the used methodology. To avoid convergence problems; the step function in the considered model was replaced by a differentiable tangent hyperbolic function. A PSpice library model of the HfO2 memristor based on its mathematical model was created. The considered model was successfully applied and tested in a multilayer memristor neural network with bridge memristor−resistor synapses

Weighting window functions are commonly used in Synthetic Aperture Radar (SAR) imaging to suppress the high Peak SideLobe Ratio (PSLR) at the price of probable Signal-to-Noise Ratio (SNR) loss and mainlobe widening. In this paper, based on the method of designing a mismatched filter, we have proposed a Quadratically Constrained Quadratic Program (QCQP) approach, which is a convex that can be solved efficiently, to optimize the weighting window function with both amplitude and phase, expecting to offer better imaging performance, especially on PSLR, SNR loss, and mainlobe width. According to this approach and its modified form, we are able to design window functions to optimize the PSLR or the SNR loss under different kinds of flexible and practical constraints. Compared to the ordinary real-valued and symmetric window functions, like the Taylor window, the designed window functions are complex-valued and can be asymmetric. By using Synthetic Aperture Radar (SAR) point target imaging simulation, we show that the optimized weighting window function can clearly show the weak target hidden in the sidelobes of the strong target.

Seismometer self-noise levels were determined using Sleeman's three-sensor method in combination with the Welch method for different parameter combinations. The self-noise levels decreased with the increasing segment window length, which is equivalent to the subwindow length, and with the increasing segment overlap rate for different frequency points at a fixed band. After the statistical examination of 9800 different parameter combinations, a zone of reasonable self-noise calculation parameter combinations was identified. Reasons for the unsuitability of certain parameter combinations were explored with respect to their distortion of the seismometer's self-noise levels.

In this paper, we present a memristor model with piecewise window function, which is continuously differentiable and consists of three nonlinear pieces. By introducing two parameters, the shape of this window function can be flexibly adjusted to model different types of memristors. Using this model, one can easily obtain an expression of memristance depending on charge, from which the numerical value of memristance can be readily calculated for any given charge, and eliminate the error occurring in the simulation of some existing window function models.

Terahertz (THz), as an advanced spectral technology, has unique absorption characteristics for most biological macromolecules. In this work, the theoretical fundamentals for the application of THz time-domain spectroscopy (THz-TDS) to molecular characterization and fingerprint peak detection of three plant growth regulators (PGRs), including 2,4-Dichlorophenoxyacetic acid (2,4-D), forchlorfenuron (CPPU) and indole-3-acetic acid (IAA) were researched. Meanwhile, the effects of eight types of window functions on THz spectra were studied when converting time-domain spectra into frequency-domain spectra by Fourier transform. Based on the optimal window function, the THz absorption coefficient and refractive index of PGRs in frequencies of 0.2–3 THz were extracted. The molecule structure and vibration mode of three PGR samples were simulated by using density functional theory (DFT). The results showed that the three PGRs had different fingerprint peaks. Characteristic absorption and anomalous dispersion of 2,4-D were found at 1.35, 1.57 and 2.67 THz, those of CPPU were found at 1.77 and 2.44 THz, and the absorption peak of IAA was located at 2.5 THz. The absorption peaks obtained from THz spectra were identified according to the theoretical calculation results of DFT. These fingerprint peaks in THz spectra were generated by the interior stretching vibration and external deformation vibration of molecular groups. The experimental results revealed the feasibility of identifying PGRs species and detecting residues using THz-TDS.

The behaviour of harmonic and chirp functions was studied on the time-frequency plane with the help of fractional Fourier transform (FRFT). Studies were also carried out through simulation with different numbers of samples of the functions. Variations were observed in the maximum side-lobe level (MSLL), half main-lobe width (HMLW) and side-lobe fall-off rate (SLFOR) of the functions. The parameters of these functions were compared with a similar set of parameters of some of the popular window functions. It can thus be concluded that in the time-frequency plane, the chirp function provides better spectral parameters than those of Boxcar window function with some particular values of rotational angle. A similar type of inference can also be drawn for the harmonic function in the time-frequency plane. Of course the rotational angle might vary in this case and a comparative analysis was carried out with Fejer window and the cosine-tip window functions. This study may prove to be helpful in replacing these existing window functions in a variety of applications where a particular parameter or group of parameters of the harmonic and chirp functions are found superior.

A mathematical model of the prototype of memristor, manufactured in 2008 in Hewlett-Packard Labs, is described in the paper. It is shown that the hitherto published approaches to the modeling of boundary conditions need not conform with the requirements for the behavior of a practical circuit element. The described SPICE model of the memristor is thus constructed as an open model, enabling additional modifications of non-linear boundary conditions. Its functionality is illustrated on computer simulations.