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The industry-standard phased-array pattern coordinate system, sine space, leads to a representation of polarized fields which can be misleading. This is especially true at the array’s boresight, where the polarization vector degenerates and becomes multivalued. This article presents a mixed-coordinate polarization representation for phased-array fields, with position components in sine space and vector components in a selectable, rotated-coordinate-system basis. The transforms required to move to this representation, ${E}_{El'}{(}{u'}{,}\,{v'}{)}$ and ${E}_{Az'}{(}{u'}{,}\,{v'}{)}$ , from the fields described in a local spherical basis, ${E}_{\mathit{\theta}}{(}\mathit{\theta}{,}\mathit{\phi}{)}$ and ${E}_{\mathit{\phi}}{(}\mathit{\theta}{,}\mathit{\phi}{)}$ , are given. Although the formulation focuses on phased arrays, the transforms are general to the fields generated from any source (e.g., single-antenna and phased, conformal, and distributed arrays). Several applications of the developed basis transformations are provided to demonstrate their use and validity. Circular-polarization purity degradation based on a cross-Hertzian dipole pair is considered and quantified for a dual-polarized communication link. Additionally, the impact of different measurement approaches on the observed polarization is also examined. Finally, platform rotation with respect to a static polarization frame is investigated to quantify increases in the cross-polarization coupling of an antenna array over the observation angle, which may negatively impact a linearly polarized communication link due to an incurred polarization mismatch loss. [ABSTRACT FROM AUTHOR]

The fuzzy transform (F-transform) is ubiquitous in different research fields and applications, such as image and data compression, data mining, knowledge discovery, and the analysis of linguistic expressions. As a generalization of the F-transform, in this article, we introduce the continuous F-transform and its inverse, as an integral operator induced by a kernel function. Through the relation between membership functions and integral kernels, we show that the main properties (e.g., continuity and symmetry) of the membership functions are inherited by the continuous F-transform. Then, the relation between the continuous F-transform and integral operators is used to introduce a data-driven F-transform, which encodes intrinsic information (e.g., structure, geometry, and sampling density) about the input data. In this way, we avoid coarse fuzzy partitions, which group data into large clusters that do not adapt to their local behavior, or a too dense fuzzy partition, which generally has cells that are not covered by the data, thus being redundant and resulting in a higher computational cost. To this end, the data-driven membership functions are defined by properly filtering the spectrum of the Laplace–Beltrami operator associated with the input data. Finally, we introduce the space of continuous F-transforms, which is useful for the comparison of different continuous F-transforms and for their efficient computation. [ABSTRACT FROM AUTHOR]

A volume equivalent shooting and bouncing ray (VESBR) method is proposed to analyze the electromagnetic scattering of dielectric and composite objects with thick dielectric medium. Different from traditional high-frequency methods which utilize surface sources, this VESBR considers the propagation of electromagnetic waves inside the dielectric media and introduces volume equivalent sources to calculate the scattering fields. Compared with traditional methods, two different problems need to be solved in this method, i.e., the ray tracing on dielectric boundary and the volume integral in ray tube. For ray tracing process, a refined formula is proposed to acquire the information of reflection waves and transmission waves on dielectric boundary. For volume integral in ray tube, the integral is transformed to five surface integrals based on Gauss’s law. The simulations of four cases show that the results of VESBR agree well with those of surface integral equation (SIE), while the computation time and the required memory of VESBR are much less than those of SIE. [ABSTRACT FROM AUTHOR]

An accurate method is proposed to calculate volume integrals arising from integral equation (IE) analysis using the Schaubert–Wilton–Glisson (SWG) basis function (BF). The volume integral is transformed into a summation of some of line integrals. The dimension reduction is achieved using the divergence theorem twice. Finally, each line integral is evaluated using an accuracy-controllable quadrature rule. We compare our results with those generated by Mathematica. Good agreement is found, which verifies the effectiveness and correctness of our method. [ABSTRACT FROM AUTHOR]

This paper is devoted to make a framework for studying a class of uncertain differential equations called Z-differential equations. In order to achieve the purpose, we first introduce four basic operations on $Z^{+}$ -numbers based on semigranular function. Then, the limit and continuity concepts of a Z-number-valued function are given, under a definition of a metric on the space of $Z^{+}$ -numbers. Moreover, the concepts of Z-differentiability, Z-integral, and Z-Laplace transform of a Z-number-valued function are introduced. In addition, by giving some theories proved in this paper, a basis for calculus—Z-calculus—is established. We further give theories based on which existence and uniqueness of Z-differential equations are investigated. A conceptual unity between Z-differential equations and $Z^{+}$ -numbers is also shown. The conceptual unity demonstrates that a Z-differential equation may be expressed as a bimodal differential equation combining a fuzzy differential equation (FDE) and a random differential equation. Moreover, the concept of a bimodal cut called $ (s, \mu)$ -cut is introduced and its relation to other new concepts such as acceptable time and acceptable information area is explained. Using an example, the application of Z-differential equations in medicine is clarified. It is demonstrated that Z-differential equations outperform FDEs in making a decision under uncertainty. [ABSTRACT FROM AUTHOR]

Interpretability has always been a major concern for fuzzy rule-based classifiers. The usage of human-readable models allows them to explain the reasoning behind their predictions and decisions. However, when it comes to Big Data classification problems, fuzzy rule based classifiers have not been able to maintain the good tradeoff between accuracy and interpretability that has characterized these techniques in non-Big-Data environments. The most accurate methods build models composed of a large number of rules and fuzzy sets that are too complex, while those approaches focusing on interpretability do not provide state-of-the-art discrimination capabilities. In this paper, we propose a new distributed learning algorithm named CFM-BD to construct accurate and compact fuzzy rule-based classification systems for Big Data. This method has been specifically designed from scratch for Big Data problems and does not adapt or extend any existing algorithm. The proposed learning process consists of three stages: Preprocessing based on the probability integral transform theorem; rule induction inspired by CHI-BD and Apriori algorithms; and rule selection by means of a global evolutionary optimization. We conducted a complete empirical study to test the performance of our approach in terms of accuracy, complexity, and runtime. The results obtained were compared and contrasted with four state-of-the-art fuzzy classifiers for Big Data (FBDT, FMDT, Chi-Spark-RS, and CHI-BD). According to this study, CFM-BD is able to provide competitive discrimination capabilities using significantly simpler models composed of a few rules of less than three antecedents, employing five linguistic labels for all variables. [ABSTRACT FROM AUTHOR]

We investigate the performance of mixed free-space optical (FSO)/millimeter-wave (mmWave) relay networks with interference at the destination. The FSO/mmWave channels are assumed to follow Málaga- $\mathcal {M}$ /generalized- $\cal K$ fading models with pointing errors in the FSO link. The H-transform theory, wherein integral transforms involve Fox’s H-functions as kernels, is embodied to unifying the performance analysis framework that encompasses closed-form expressions for the outage probability, the average bit error rate (BER), and the average capacity. By virtue of some H-transform asymptotic expansions, the high signal-to-interference-plus-noise ratio (SINR) analysis reduces to easy-to-compute expressions for the outage probability and BER, which reveals inside information for the system design. We finally investigate the optimal power allocation strategy that minimizes the outage probability. [ABSTRACT FROM AUTHOR]

Bound water saturation ($S_{\mathrm {wb}}$) and permeability are the important petrophysical parameters. However, the traditional methods for the calculation of $S_{\mathrm {wb}}$ and permeability based on the nuclear magnetic resonance (NMR) transverse relaxation time ($T_{2}$) distributions are not applicable for tight sandstone because the NMR data have a low signal-to-noise ratio and the calculation models have certain disadvantages. In this paper, we present a new method for the calculation of $S_{\mathrm {wb}}$ and permeability using integral transforms (ITs) of the NMR echo data in tight sandstone. First, the tapered cutoff function was established using the Laplace transform function of the exponential hyperbolic sine function based on the film model; $S_{\mathrm {wb}}$ was directly calculated from the echo data using the exponential hyperbolic sine transform without an inversion of the $T_{2}$ distribution. The position and slope of the median point, both of which control the shape of the tapered cutoff function, were determined by core experiments. Subsequently, the tapered cutoff function representing the proportion coefficients of the free fluids in the pore space was added to the arithmetic mean of the $T_{2}$ ($T_{\mathrm {2am}}$) as a weight to construct the weighted $T_{\mathrm {2am}}$ ($T_{\mathrm {2wam}}$). $T_{\mathrm {2wam}}$ was highly suitable for reflecting the seepage ability of the pores and was directly calculated from the NMR echo data using an IT without an inversion. A new permeability calculation model was developed based on $T_{\mathrm {2wam}}$. The numerical simulation and core experimental results verified the effectiveness of the new method. [ABSTRACT FROM AUTHOR]

We introduce a framework for the reconstruction of the amplitude, phase, and polarization of an optical vector-field using measurements acquired by an imaging device characterized by an integral transform with an unknown spatially variant kernel. By incorporating effective regularization terms, this new approach is able to recover an optical vector-field with respect to an arbitrary representation system, which may be different from the one used for device calibration. In particular, it enables the recovery of an optical vector-field with respect to a Fourier basis, which is shown to yield indicative features of increased scattering associated with tissue abnormalities. We demonstrate the effectiveness of our approach using synthetic holographic images and biological tissue samples in an experimental setting, where the measurements of an optical vector-field are acquired by a multicore fiber endoscope, and observe that indeed the recovered Fourier coefficients are useful in distinguishing healthy tissues from tumors in early stages of oesophageal cancer. [ABSTRACT FROM AUTHOR]

With the emergence of the mission-critical Internet of Things applications, ultra-reliable low-latency communications are attracting a lot of attentions. Non-orthogonal multiple access (NOMA) with multiple-input multiple-output (MIMO) is one of the promising candidates to enhance connectivity, reliability, and latency performance of the emerging applications. In this paper, we derive a closed-form upper bound for the delay target violation probability in the downlink MIMO-NOMA, by applying stochastic network calculus to the Mellin transforms of service processes. A key contribution is that we prove that the infinite-length Mellin transforms resulting from the non-negligible interferences of NOMA are Cauchy convergent and can be asymptotically approached by a finite truncated binomial series in the closed form. By exploiting the asymptotically accurate truncated binomial series, another important contribution is that we identify the critical condition for the optimal power allocation of MIMO-NOMA to achieve consistent latency and reliability between the receivers. The condition is employed to minimize the total transmit power, given a latency and reliability requirement of the receivers. It is also used to prove that the minimal total transmit power needs to change linearly with the path losses, to maintain latency and reliability at the receivers. This enables the power allocation for mobile MIMO-NOMA receivers to be effectively tracked. The extensive simulations corroborate the accuracy and effectiveness of the proposed model and the identified critical condition. [ABSTRACT FROM AUTHOR]

The mutual reactance between two elements of a lineal array is formulated using Fourier transform, autocorrelation, convolution, and Hilbert transform concepts, with the invocation of the Hilbert transform being the novel contribution of this paper. It is shown herein that the mutual reactance of an array can be determined from the radiation pattern, if one considers the entire time-averaged power delivered to both the visible and the nonvisible far-field regions. Power to the nonvisible region corresponds to stored energy in the Poynting volume; stored energy corresponds to reactive power, which is in quadrature with the nonvisible, time-averaged power; and quadrature suggests the invocation of the Hilbert transform. The end result of the Hilbert transform process is a straightforward, closed-form analytical expression for the mutual reactance. Since the closed-form mutual resistance has been determined previously, both closed-form expressions can be combined to provide an elegant, but easy-to-use formulation for the mutual impedance. For a given current distribution, the results are exact and validated against data obtained numerically. Cases associated with the half-wave dipole, generalized dipole distribution, and the uniform distribution are provided herein as examples of the robustness of the presented theory. [ABSTRACT FROM AUTHOR]

Approximate computing has emerged as a circuit design technique that can reduce system power without significantly sacrificing the output quality in error-resilient applications. However, there exists only a few approaches for systematically and efficiently determining the error introduced by approximate hardware units. This paper focuses on the development of error analysis techniques for approximate circuits consisting of adders and multipliers, which are the key hardware components used in error-resilient applications. A novel algorithm has been presented, using the Fourier and the Mellin transforms, that efficiently determines the probability distribution of the error introduced by approximation in a circuit, abstracted as a directed acyclic graph. The algorithm is generalized for signed operations through two’s complement representation, and its accuracy is demonstrated to be within 1% of Monte Carlo simulations, while being over an order of magnitude faster. [ABSTRACT FROM AUTHOR]

This paper is a contribution to the old problem of representing a signal in the coordinates of time and frequency. We review the fundamental Hilbert transform relationship in systems analysis and argue that the dual relationship assumed in signal analysis, i.e. spectral single-sidedness is not necessarily justifiable. Therefore, we abandon the analytic signal and utilize a carefully parameterized signal model composed of a superposition of complex, AM–FM components that enables rigorous definition of instantaneous amplitude and instantaneous frequency. We then propose the instantaneous spectrum (IS) and prove that it exactly localizes signal components in an instantaneous bandwidth sense. The relation of the IS to traditional time-frequency distributions is discussed and comparative examples are provided. It is shown that under certain conditions the IS specializes to the Fourier spectrum and properties of the IS, similar to standard Fourier transform properties, are given. [ABSTRACT FROM AUTHOR]

In order to increase fundamental voltage transfer ratio for ultrasparse matrix converter, a novel multimode space vector overmodulation strategy is proposed. First, the relationship among voltage transfer ratio (VTR), the output voltage harmonic distortion rate under three inverter modulation methods and the input current harmonic distortion rate under two rectifier modulation methods is analyzed. After that, according to minimum principle of output voltage and input current harmonics, the three overmodulation modes are divided: the output voltage minimum-phase-error, input current minimum-magnitude-error (MME), and output voltage MME overmodulation strategies are realized in overmodulation mode I, II, and III, respectively. The proposed multimode overmodulation strategy not only extends the maximum VTR to 1.05, but also reduces the output low-frequency harmonic voltage components of the overmodulation mode I and mode II. In addition, the harmonic components of output voltage and input current in overmodulation mode are analyzed by double Fourier integral transform method. Finally, the effectiveness of the proposed multimode overmodulation strategy and the correctness of harmonic analysis method are verified by experiments. [ABSTRACT FROM AUTHOR]

In this paper, we consider the performance of sampling associated with the linear canonical transform (LCT), which generalizes a large number of classical integral transforms and fundamental operations linked to signal processing and optics. First, we revisit sampling approximation in the LCT domain to introduce a generalized approximation operator. Then, we derive an exact closed-form expression for the integrated squared error that occurs when a signal is approximated by a basis of shifted, scaled, and chirp-modulated versions of a generating function in the LCT domain. Several basic properties of the approximation error are presented. The derived results can be applied to a wide variety of sampling approximation schemes in the LCT domain. Finally, experimental examples are given to illustrate the theoretical derivations. [ABSTRACT FROM AUTHOR]

Most electricity spot price series exhibit price spikes. These extreme observations may significantly impact the obtained model estimates and hence reduce efficiency of the employed predictive algorithms. For markets with only positive prices, the logarithmic transform is the single most commonly used technique to reduce spike severity and consequently stabilize the variance. However, for datasets with very close to zero (like the Spanish) or negative (like the German) prices the log-transform is not feasible. What reasonable choices do we have then? To address this issue, we evaluate 16 variance stabilizing transformations within a comprehensive forecasting study involving two model classes (regression models, neural networks) and 12 datasets from diverse power markets. We show that the probability integral transform combined with the standard Gaussian distribution yields the best approach, significantly better than many of the considered alternatives. [ABSTRACT FROM AUTHOR]

Empirical mode decomposition is a nonparametric adaptive tool that decomposes signals into a set of zero-mean modes called intrinsic mode functions (IMFs) that can be used to denoise a signal by selecting the relevant (noise-free) modes. In this paper, the statistical properties of IMFs, produced by a range of signal distributions, are examined. Insight from the statistical analysis is used in a null hypothesis test that validates a best fit model distribution of the IMFs. This test is then used in a de-noising scheme, which is evaluated using different test signals corrupted with white and colored noise. Simulations under different scenarios demonstrate the efficacy of the proposed method as compared to other EMD-based de-noising techniques. [ABSTRACT FROM PUBLISHER]

In this paper, we investigate a frequency domain approach for eigenvalue-based detection of a primary user, based on equal gain combining (EGC) and spectrum estimation with Bartlett’s method. This paper considers two techniques for eigenvalue detection which are Maximum Eigenvalue Detection (MED) and the Maximum-Minimum Eigenvalue (MME) detector. We exploit the eigenvalues that are associated with the Hermitian form representation of Bartlett’s estimate to assess the performance of the aforementioned eigenvalue techniques in the frequency domain. For each case, we quantify the performance based on the probabilities of false alarm and missed detection over Rayleigh and Rician fading. A bivariate Mellin transform approach is employed to obtain the probability distribution function for the ratio of the extreme eigenvalues under each hypothesis. All obtained formulas are validated via Monte-Carlo simulations, and the results give a clear insight into the performance of the investigated methods. In frequency domain, MED outperforms both the MME detector and Periodogram-based energy detection even in a worst case scenario of noise uncertainty, while the MME detector exhibits heavy-tailed statistical characteristics and thus its receiver operating characteristics tend to stay on the line of no-discrimination. The performance of MED is further enhanced by careful choice of combinations of the total length of the sensing frame and number of sub-slots. [ABSTRACT FROM PUBLISHER]

Sport, fitness, as well as rehabilitation activities, often require the accomplishment of repetitive movements. The correctness of the exercises is often related to the capability of maintaining the required cadence and muscular force. Failure to maintain the required force, also known as muscle fatigue, is accompanied by a shift in the spectral content of the surface electromyography (EMG) signal toward lower frequencies. This paper presents a novel approach for simultaneously obtaining exercise repetition frequency and evaluating muscular fatigue, as functions of time, by only using the EMG signal. The mean frequency of the amplitude spectrum (MFA) of the EMG signal, considered as a function of time, is directly related to the dynamics of the movement performed and to the fatigue of the involved muscles. If the movement is cyclic, MFA will display the same pattern and its average will tend to decrease. These two effects have been simultaneously modeled by a two-component AM–FM model based on the Hilbert transform. The method was tested on signals recorded using a wireless system applied to healthy subjects performing dumbbell biceps curls, dumbbell lateral rises, and bodyweight squats. Experimental results show the excellent performance of the proposed technique. [ABSTRACT FROM PUBLISHER]

The diagnosis of portions in a cable that are severely degraded before breakdown occurs is of prime importance. This paper presents a novel method based on the broadband impedance spectroscopy (BIS) to precisely locate local degradations in a cable and determine their insulation conditions. Firstly, an integral transform (IT) algorithm is developed to transform the frequency-dependent BIS to a spatial domain function, which characterizes the changes of propagation constant along the cable and then degradations can be located. Next, a procedure based on the particle swarm optimization (PSO) is worked out to minimize the error between the measured impedance of the cable and that calculated by a model, and then the complex dielectric permittivity for each of the degradations is figured out to assess the insulation condition. Simulation results show that portions with loss tangent (tan δ) higher than the adjacent regions can be clearly located with a spatial resolution as short as 0.01 m even if the cable length is 500 m. After the PSO procedure, tan δ of the degraded portions can be obtained to indicate the severity of the degradation. The validity of the method is also verified by experiments performed on a 50 m long cable. [ABSTRACT FROM PUBLISHER]

This paper presents an approach to measure the duration and the energy of instantaneous frequencies (EIFs) of the aortic (A2) and pulmonic (P2) valve closure sounds for the second heart sound (S2) based on analytic signal representation. In past studies, concepts were usually surrounded around the measurement of splits (i.e., delays between the A2 and the P2) in medical terms based only on visual inspections of the time-frequency representation of the S2s. The values were empirically estimated, and the two vital issues—A2 and P2 overlaps and low energies of P2s—were ignored. In this paper, such issues are addressed, and the relevant parameters are measured by identifying the starting and the ending positions of A2s and P2s. The diagnosis related to the duration and the EIFs of the A2 and the P2 is also examined. Furthermore, the proposed method explicitly guides to distinguish the normal/abnormal S2s and the types of S2 splits. The proposed method is characterized by the Hilbert transform-based IF estimation as well as the localization technique based on the reassignment of smoothed pseudo-Wigner–Ville distribution. To validate the idea, total 31 S2s collected from six healthy normal subjects were tested. The result computed by the proposed method shows that the mean ± standard deviation (SD) of the duration of A2s and P2s is 46.7 ± 2.5 and 41.8 ± 2.4 ms, respectively. The mean ± SD of the EIFs of A2s and P2s is 13.8 ± 2.4 and 10.5 ± 1.7, respectively. These estimated results accord with the evidence in the literature. Moreover, when the proposed method was applied to the abnormal S2s, collected from the database of the Texas Heart Institute, it could correctly distinguish the types of abnormal splits. The experimental result reveals that the accuracy rate of the proposed method is as high as up to 97%, thereby demonstrating the effectiveness of the proposed idea. [ABSTRACT FROM PUBLISHER]

The Wigner distribution (WD) and ambiguity function (AF) associated with the linear canonical transform (LCT) play a major role in non-stationary signal processing. Many novel time-frequency analysis tools for it exist, such as the linear canonical WD (LCWD), the linear canonical AF (LCAF), the WD in the LCT domain (WDL) and the AF in the LCT domain (AFL). The purpose of this letter is to introduce new integral transforms that can be regarded as the generalization of LCWD, LCAF, WDL, and AFL. Moreover, the newly defined integral transforms are shown to be useful and effective in filter design in the LCT domain for the separation of multi-component signals and detection of linear frequency-modulated (LFM) signals. The results show that the new integral transforms achieve better detection performance than LCWD, LCAF, WDL, and AFL. Simulations are also performed to verify the rationality and effectiveness of the derived methods. [ABSTRACT FROM AUTHOR]

In a nonsinusoidal alternating current (ac) circuit, the instantaneous impedances of the linear inductance and the linear capacitance have not been defined because no applicable law as the Ohm's law exists; hence, the analysis of the nonsinusoidal ac circuit is incomplete, and the design of the nonsinusoidal ac circuit lacks systematic consideration. This paper presents an expansion of the Ohm's law in the nonsinusoidal ac circuit by defining instantaneous impedance, instantaneous admittance, and analytic signals of the instantaneous voltage and current. It has been demonstrated that the presented definitions are reasonable generalizations of the Ohm's law in the nonsinusoidal ac circuit including ac/dc link circuit in theory analyses and experimental results in this paper. The presented expansion of the Ohm's law provides a distinct instruction for analyzing and designing nonsinusoidal circuit including ac/dc link circuit particularly for the power electronic circuit. [ABSTRACT FROM PUBLISHER]

Electromagnetic radiation from a circular cavity with multiple circular apertures in a conducting plane is investigated. An electromagnetic boundary-value problem of the circular cavity with circular apertures is solved based on the Green's function, integral transform, superposition, and mode matching method. The radiated fields from the circular cavity are calculated in terms of the aperture geometry to understand the radiation behaviors and measured to check the validity of our theoretical formulations. [ABSTRACT FROM PUBLISHER]

The far field pattern from a nonuniformly spaced antenna array is computed using a least squares method. The method originally developed for spectral estimation for a nonuniformly spaced finite data set is applied for the analysis of the far field pattern from unevenly spaced antennas, as the far field pattern is due to the spectrum of the location of the antenna elements. The advantage of using a nonuniformly sampled data is that it is not necessary to satisfy the Nyquist sampling criterion as long as the average value of the sampling rate is less than the Nyquist rate. For a Fourier-based technique which also computes a least squares solution for the spectrum using a periodic data set, the finite data set then has to be periodically repeated resulting in bias in the solution. The methodology presented in the paper does not assume a periodic extension of the data set and can discern between the positive and negative frequencies of the spectrum unlike in the well-known Lomb periodogram. Finally, by exploiting a Hilbert transform relationship between the coefficients of the parameters in the least squares formulation an approximate fast way to compute the spectrum from unevenly spaced finite-sized non-periodic samples of the data can be realized. The example presented in this paper deals with a one-dimensional array even though this methodology is general in nature and can easily be extended to the two-dimensional case. [ABSTRACT FROM PUBLISHER]

An improved version of the near-field-to-far-field transformation (NFFFT) for determining the radar cross section (RCS) of electrically large targets from the scattered field measured with a monostatic radar over a circle in the near field of the targets is presented. The characteristic feature of the proposed NFFFT is an improved imaging operator which is derived by requiring that the integral transformations involved in the NFFFT scheme be self-consistent for every electrically small scatterer. The presented NFFFT version is expected to lead to more accurate RCS values for strongly asymmetric targets measured at smaller facilities. [ABSTRACT FROM PUBLISHER]

Real-time stereo vision has proven to be a useful technology with many applications. However, the computationally intensive nature of stereo vision algorithms makes real-time implementation difficult in resource-limited systems. The field-programmable gate array (FPGA) has proven to be very useful in the implementation of local stereo methods, yet the resource requirements can still be a significant challenge. This paper proposes a variety of sparse census transforms that dramatically reduce the resource requirements of census-based stereo systems while maintaining stereo correlation accuracy. This paper also proposes and analyzes a new class of census-like transforms, called the generalized census transforms. This new transform allows a variety of very sparse census-like stereo correlation algorithms to be implemented while demonstrating increased robustness and flexibility. The resource savings and performance of these transforms is demonstrated by the design and implementation of a parameterizable stereo system that can implement stereo correlation using any census transform. Several optimizations for typical FPGA-based correlation systems are also proposed. The resulting system is capable of running at over 500 MHz on a modern FPGA, resulting in a throughput of over 500 million input pixel pairs per second. [ABSTRACT FROM PUBLISHER]

A new concept for the low-frequency dispersion aspect of large-signal modeling of microwave III–V field-effect transistors is presented. The approach circumvents the integrability problem between the small-signal transconductance GmRF and the output conductance GdsRF by means of an integral formulation and simultaneously yields a proper description of the drain channel current in the small- and large-signal regime. In the theoretical description of the approach and in an extraction example of an AlGaN/GaN HEMT, it is shown that three independent 2-D nonlinear quantities determine the intrinsic drain channel current ( GmRF, GdsRF, and dc current). The concept is transferred to the modeling of the nonlinear charge control, where the integrability problem between the large-signal charge functions and the small-signal intrinsic capacitance matrix ( Cgs, Cgd, and Cds) is addressed consistently under consideration of the charge control delays. For the large-signal modeling under pulsed-dc/RF excitation, the dc continuous wave (dc-CW) modeling approach is combined with the state-modeling concept using a superposition formula for drain current and charges, respectively. The new model is implemented in ADS using a 12- and 14-port symbolically defined device for both the dc-CW and pulsed-RF case, respectively. The model has been verified by comparison to measured CW and pulsed-RF load–pull and waveform data at 10-GHz fundamental frequency. [ABSTRACT FROM AUTHOR]

A cylindrical structure composed of a circular, PEC cylinder, having a longitudinal slot and enclosing an arbitrary number of eccentric, dielectric cylinders, embedded in a dielectric sheath, is considered in this paper. Excitation is provided by a plane wave, normally incident upon the structure. Both TE and TM polarizations are considered for the incident wave. The scattered wave, as well as the electromagnetic (EM) field within the scatterer, are determined by using a dual-series approach combined with the translational addition theorem for cylindrical wave functions. The Abel integral-transform method is applied in order to regularize the dual-series equations to a matrix Fredholm equation of the second kind. The resulting infinite set of linear algebraic equations (i.s.l.a.e.) is truncated and solved numerically. The solution inherently contains the behavior of the field near the aperture rim, as required by Meixner's edge condition. The numerical application manifests how the internal structure of the scatterer and the polarization of the incident wave affect backscattering by the cylindrical cavity. [ABSTRACT FROM PUBLISHER]

An algebraic integer (AI)-based time-multiplexed row-parallel architecture and two final reconstruction step (FRS) algorithms are proposed for the implementation of bivariate AI-encoded 2-D discrete cosine transform (DCT). The architecture directly realizes an error-free 2-D DCT without using FRSs between row–column transforms, leading to an 8\,\times\,8 2-D DCT that is entirely free of quantization errors in AI basis. As a result, the user-selectable accuracy for each of the coefficients in the FRS facilitates each of the 64 coefficients to have its precision set independently of others, avoiding the leakage of quantization noise between channels as is the case for published DCT designs. The proposed FRS uses two approaches based on: 1) optimized Dempster–Macleod multipliers, and 2) expansion factor scaling. This architecture enables low-noise high-dynamic range applications in digital video processing that requires full control of the finite-precision computation of the 2-D DCT. The proposed architectures and FRS techniques are experimentally verified and validated using hardware implementations that are physically realized and verified on field-programmable gate array (FPGA) chip. Six designs, for 4-bit and 8-bit input word sizes, using the two proposed FRS schemes, have been designed, simulated, physically implemented, and measured. The maximum clock rate and block rate achieved among 8-bit input designs are 307.787 MHz and 38.47 MHz, respectively, implying a pixel rate of 8\times 307.787\approx 2.462∼GHz if eventually embedded in a real-time video-processing system. The equivalent frame rate is about 1187.35 Hz for the image size of 1920\,\times\,1080. All implementations are functional on a Xilinx Virtex-6 XC6VLX240T FPGA device. [ABSTRACT FROM AUTHOR]

Existing video coding standards use only 4\,\times\,4 and 8\,\times\,8 transforms for energy compaction. Recent research has found that the use of larger transforms, such as 16\,\times\,16, together with the existing transforms can improve coding performance especially in high-definition (HD) videos which are becoming more and more common. This raises the interest of seeking high-performance higher-order transforms with low computation requirement. In this paper, a method to derive orthogonal integer cosine transforms is proposed. The order-2N transform is defined using the order-N transform. A family of these integer transforms, Loeffler, Ligtenberg, and Moschytz (LLM) integer cosine transform, is derived using this method. Its fast algorithm structure is the same as LLM fast discrete cosine transform (DCT) algorithm but requires integer operations only. This new family of transforms is not only very close to the DCT but also has excellent coding performance. [ABSTRACT FROM AUTHOR]

With the popularity of mobile devices with embedded video cameras, real-time video encoding on hand-held devices becomes increasingly popular. Reducing the power consumption during real-time video encoding to suspend the battery life with the same encoding performance is very important to improve the quality of service. Although some workload estimation techniques have been developed for video decoding to reduce power consumption for video playback applications, they present inefficiency in being transferred to video encoding directly because the compressed information cannot be retrieved before encoding and the future input video content is often nondeterministic. In this paper, a workload estimation scheme targeting video encoding applications is proposed. Based on the definition of video encoding workload and the analysis of the features, a Hilbert transform-based workload estimation model is proposed to predict the overall variation trend in the encoding workload to overcome the workload fluctuations and the nondeterministic content variations, e.g., burst motion. The effectiveness of the proposed algorithm is demonstrated on two H.264/AVC encoders on PC and an embedded platform by encoding different video contents at different bit-rates. The proposed algorithm provides a negligible deadline missing ratio around 4.8%, which is much lower than the previous solutions, together with platform and content robustness. Compared with the previous solutions, the proposed algorithm provides up to 61.69% power reduction under the same performance constraint. [ABSTRACT FROM PUBLISHER]

Implicit Runge-Kutta based schemes are proposed for solving the time domain integral equations of electromagnetic theory. The proposed technique maps a Laplace-domain equation to a \cal Z-domain equation using the Butcher tableau of the implicit Runge-Kutta scheme. A discrete time domain system is recovered by computing the inverse \cal Z-transform numerically. The resulting technique is capable of third- or fifth-order accuracy in time, and is stable independent of time step. Numerical results illustrate the accuracy and stability of the technique. [ABSTRACT FROM AUTHOR]

The H.264/AVC standard achieves a high coding efficiency compared to previous standards. However, this gain is accomplished at great computational cost, with mode decision being one of the most demanding subsystems. In this paper, a two-level classification-based approach to the inter mode decision problem is proposed. A first classifier detects SKIP/Direct modes, while a second one is able to decide whether to use a large (16\,\times\,16, 16\,\times\,8, and 8\,\times\,16) or a small mode (8\,\times\,8, 8\,\times\,4, 4\,\times\,8, and 4\,\times\,4). The suggested classifiers are binary and linear, and the input features in the classifiers have been carefully selected. A novel cost function that pays more attention to the most critical samples during the classifier training process has been designed. The experimental results show an average computational savings of 60% of the total encoding time with respect to JM10.2 over a comprehensive variety of sequences and formats. This is achieved with negligible degradation in rate-distortion performance and compares favorably with state-of-the-art fast mode decision methods. Furthermore, the proposed method has been successfully assessed at different levels of complexity reduction. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new discrete cosine transform (DCT)-like kernel IK(5, 7, 3) and revitalize another DCT-like kernel IK(13, 17, 7) for the transform coding process of hybrid video coding. Making use one of these kernels together with the H.264/AVC kernel IK(1, 2, 1), we are able to design new multiple-kernel schemes which give better coding performance over that of the conventional approaches. All these schemes make use of the adaptive kernel mechanism at macroblock-level (MB-AKM), which requires heavy computation during the encoding process. We subsequently discovered that a rate-distortion feature extracted from a pair of kernels gives an intrinsic property that can be used to select a better kernel for a two-kernel MB-AKM system. This is a powerful tool with theoretical interest and practical uses. In order to reduce computation substantially, we make use of this tool to make an analysis and design of a frame-level adaptive kernel mechanism and come up with a simple solution that the kernel IK(1, 2, 1) be used for I-frames and P-frames and the kernel IK(5, 7, 3) be used for B-frames coding. This proposed frame-based AKM gives similar, or even better, performance as the proposed macroblock-based AKM. Furthermore, it substantially reduces computation and certainly gives a good improvement in terms of the PSNR and bitrate compared to those obtained from the H.264/AVC default scheme and other MB-AKM schemes available in the literature. [ABSTRACT FROM AUTHOR]

When the fast Hankel transform (FHT) filter technique is used to calculate the spatial-domain Green's functions for planar multilayered media, it can be difficult to obtain accurate numerical results because of branch-cut singularities and the surface-wave pole singularities. Although the singularities can be efficiently avoided through deforming the integration path of the Hankel transform from the real axis to the first quadrant in the complex plane, the argument of the integral kernel becomes a complex number so that the FHT filter algorithm cannot be directly applied. The modified FHT filter algorithm is proposed to overcome this problem by expressing the Bessel function with a complex argument as a sum of terms of product of Bessel function with the real part of the argument and Bessel function with the imaginary part of the argument. The FHT filter technique can then be applied to each expansion term. Numerical results confirm that the proposed approach has high accuracy and good efficiency in the near and intermediate fields. More importantly, it successfully extends the applicability of the conventional FHT method for general multilayered geometries. [ABSTRACT FROM AUTHOR]

Temperature imaging with a non-invasive modality to monitor the heating of tumors during hyperthermia treatment is an attractive alternative to sparse invasive measurement. Previously, we predicted monotonic changes in backscattered energy (CBE) of ultrasound with temperature for certain sub-wavelength scatterers. We also measured CBE values similar to our predictions in bovine liver, turkey breast muscle, and pork rib muscle in 2-D in vitro studies and in nude mice during 2-D in vivo studies. To extend these studies to three dimensions, we compensated for motion and measured CBE in turkey breast muscle. 3-D data sets were assembled from images formed by a phased-array imager with a 7.5-MHz linear probe moved in 0.6-mm steps in elevation during uniform heating from 37 to 45°C in 0.5°C increments. We used cross-correlation as a similarity measure in RF signals to automatically track feature displacement as a function of temperature. Feature displacement was non-rigid. Envelopes of image regions, compensated for non-rigid motion, were found with the Hilbert transform then smoothed with a 3 x 3 running average filter before forming the backscattered energy at each pixel. CBE in 3-D motion-compensated images was nearly linear with an average sensitivity of 0.30 dB/°C. 3-D estimation of temperature in separate tissue regions had errors with a maximum standard deviation of about 0.5°C over 1-cm³ volumes. Success of CBE temperature estimation based on 3-D non-rigid tracking and compensation for real and apparent motion of image features could serve as the foundation for the eventual generation of 3-D temperature maps in soft tissue in a non-invasive, convenient, and low-cost way in clinical hyperthermia. [ABSTRACT FROM AUTHOR]

The convergence behavior of a convolution representation of stable linear time-invariant (LTI) systems operating on the Zakai class of bandlimited signals is analyzed. It is shown that there are signals in the Zakai class for which the convolution integral diverges if the system is the Hilbert transform or the ideal low-pass filter with bandwidth less than or equal to the signal bandwidth. Moreover, using a previously obtained result of Habib, it is proved that the class of stable LTI systems that map the Zakai class into itself does not include the Hilbert transform and the ideal low-pass filter with bandwidth less than or equal to the signal bandwidth. Finally, it is shown that the concept of the analytical signal, which is used in communications, is problematic for the signal space Zπ, because the operator for its computation is unbounded and discontinuous. [ABSTRACT FROM AUTHOR]

This paper proposes a general-purpose method for estimating the skew angles of document images. Rather than to derive a skew angle merely from text lines, the proposed method exploits various types of visual cues of image skew available in local image regions. The visual cues are extracted by Radon transform and then outliers of them are iteratively rejected through a floating cascade. A bagging (bootstrap aggregating) estimator is finally employed to combine the estimations on the local image blocks. Our experimental results show significant improvements against the state-of-the-art methods, in terms of execution speed and estimation accuracy, as well as the robustness to short and sparse text lines, multiple different skews and the presence of nontextual objects of various types and quantities. [ABSTRACT FROM AUTHOR]

A method is introduced to track the object's motion and estimate its pose directly from 2-D image sequences. Scale-invariant feature transform (SIFT) is used to extract corresponding feature points from image sequences. We demonstrate that pose estimation from the corresponding feature points can be formed as a solution to Sylvester's equation. We show that the proposed approach to the solution of Sylvester's equation is equivalent to the classical SVD method for 3D-3D pose estimation. However, whereas classical SVD cannot be used for pose estimation directly from 2-D image sequences, our method based on Sylvester's equation provides a new approach to pose estimation. Smooth video tracking and pose estimation is finally obtained by using the solution to Sylvester's equation within the importance sampling density of the particle filtering framework. Finally, computer simulation experiments conducted over synthetic data and real-world videos demonstrate the effectiveness of our method in both robustness and speed compared with other similar object tracking and pose estimation methods. [ABSTRACT FROM AUTHOR]

In this letter, an efficient integer transform based reversible watermarking is proposed. We first show that Tian's difference expansion (DE) technique can be reformulated as an integer transform. Then, a generalized integer transform and a payload-dependent location map are constructed to extend the DE technique to the pixel blocks of arbitrary length. Meanwhile, the distortion can be controlled by preferentially selecting embeddable blocks that introduce less distortion. Finally, the superiority of the proposed method is experimental verified by comparing with other existing schemes. [ABSTRACT FROM AUTHOR]

Chromatic series expansions of bandlimited functions provide an alternative representation to the Whittaker-Shannon-Kotel'nikov sampling series. Chromatic series share similar properties with Taylor series insofar as the coefficients of the expansions, which are called chromatic derivatives, are based on the ordinary derivatives of the function. Chromatic derivatives are linear combinations of ordinary derivatives in which the coefficients of the combinations are related to a system of orthonormal polynomials. But unlike Taylor series, chromatic series have more useful applications in signal processing because they represent bandlimited functions more efficiently than Taylor series. The goal of this article is to generalize the notion of chromatic derivatives and then extend chromatic series expansions to a larger class of signals than the class of bandlimited signals. In particular, we extend chromatic series to signals given by integral transforms other than the Fourier transform, such as the Laplace and Hankel transforms. [ABSTRACT FROM AUTHOR]

Ultrasound nonlinear imaging using microbubble-based contrast agents has been widely investigated. Nonetheless, its contrast is often reduced by the nonlinearity of acoustic wave propagation in tissue. In this paper, we explore the use of empirical mode decomposition (EMD) and ensemble empirical mode decomposition (EEMD) in the Hilbert-Huang transform (HHT) for possible contrast improvement. The HHT is designed for analyzing nonlinear and nonstationary data, whereas EMD is a method associated with the HHT that allows decomposition of data into a finite number of intrinsic modes. The hypothesis is that the nonlinear signal from microbubbles and the tissue nonlinear signal can be better differentiated with EMD and EEMD, thus making contrast improvement possible. Specifically, we tested this method on pulse-inversion nonlinear imaging, which is generally regarded as one of the most effective nonlinear imaging methods. The results show that the contrast-to-tissue ratios at the fundamental and second-harmonic frequencies were improved by 10.2 and 4.3 dB, respectively, after EEMD. Nonetheless, image artifacts also appeared, and hence further investigation is needed before EMD and EEMD can be applied in practical applications of ultrasound nonlinear imaging. [ABSTRACT FROM AUTHOR]

This paper presents a general method for detecting curvilinear structures, like filaments or edges, in noisy images. This method relies on a novel technique, the feature-adapted beamlet transform (FABT) which is the main contribution of this paper. It combines the well-known Beamlet transform (BT), introduced by Donoho et al., with local filtering techniques in order to improve both detection performance and accuracy of the BT. Moreover, as the desired feature detector is chosen to belong to the class of steerable filters, our transform requires only O(N log(N)) operations, where N : n² is the number of pixels. Besides providing a fast implementation of the FABT on discrete grids, we present a statistically controlled method for curvilinear objects detection. To extract significant objects, we propose an algorithm in four steps: 1) compute the FABT, 2) normalize beamlet coefficients, 3) select meaningful beamlets thanks to a fast energy-based minimization, and 4) link beamlets together in order to get a list of objects. We present an evaluation on both synthetic and real data, and demonstrate substantial improvements of our method over classical feature detectors. [ABSTRACT FROM AUTHOR]

The S transform is a useful linear time-frequency distribution with a progressive resolution. Since it is linear, it filters efficiently in a time-frequency domain by multiplying a mask function. Several different inverse algorithms exist, which may result in different filtering effects. The conventional inverse S transform (IST) proposed by Stockwell et a!. is efficient but suffers from time leakage during filtering. The recent algorithm proposed by Schimmel and Gallart has better time localization during filtering but suffers from a reconstruction error and the frequency leakage during filtering. In this paper, two new IST algorithms are proposed that have better time.frequency localization in filtering than the previous two methods. [ABSTRACT FROM AUTHOR]

In this letter, a new decomposition algorithm of type-IV discrete cosine transform/type-IV discrete sine transform (DCT-IV/DST-IV) and architecture of a hardware accelerator for realizing fast inverse modified discrete cosine transform (IMDCT) computation are presented. The comparisons of computational complexity with some well-known algorithms show that the proposed algorithm possesses the advantages of higher computational efficiency and simpler hardware implementation. A real-time audio decoding experiment was performed to verify the efficiency of the proposed algorithm. Experimental results show more than one third of computational cycles are saved compared with one of reported fast algorithms for IMDCT computation. [ABSTRACT FROM AUTHOR]

The Standard Hough Transform is a popular method in image processing and is traditionally estimated using histograms. Densities modeled with histograms in high dimensional space and/or with few observations, can be very sparse and highly demanding in memory. In this paper, we propose first to extend the formulation to continuous kernel estimates. Second, when dependencies in between variables are well taken into account, the estimated density is also robust to noise and insensitive to the choice of the origin of the spatial coordinates. Finally, our new statistical framework is unsupervised (all needed parameters are automatically estimated) and flexible (priors can easily be attached to the observations). We show experimentally that our new modeling encodes better the alignment content of images. [ABSTRACT FROM AUTHOR]

Linear canonical transforms (LCTs) are a family of integral transforms with wide application in optical, acoustical electromagnetic, and other wave propagation problems. The Fourier and fractional Fourier transforms are special cases of LCTs. We present the exact relation between continuous and discrete LCTs (which generalizes the corresponding relation for Fourier transforms), and also express it in terms of a new definition of the discrete LCT (DLCT), which is independent of the sampling interval. This provides the foundation for approximately computing the samples of the LCT of a continuous signal with the DLCT. The DLCT in this letter is analogous to the DFT and approximates the continuous LCT in the same sense that the DFT approximates the continuous Fourier transform. We also define the bicanonical width product which is a generalization of the time-bandwidth product. [ABSTRACT FROM AUTHOR]