Smoothing Bandwidth Research Articles

Weighted Frequency Smoothing for Enhanced Speaker Localization

The coherent signal subspace method may be used in order to apply subspace localization methods (e.g. MUSIC) to coherent sources. This method involves a focusing process followed by frequency smoothing, which is intended to decorrelate source signals from coherent sources. In practice, however, only moderate decorrelation is obtained, which may lead to performance degradation. Although decorrelation can be improved by widening the smoothing bandwidth, a wider bandwidth may increase focusing error and the smoothing bandwidth is limited by the bandwidth of the actual signal. In this paper, a weighted frequency smoothing that improves decorrelation for a given bandwidth is proposed. It is shown that better decorrelation is obtained by selecting the weights to be inversely proportional to the source signal power at the given frequency. However, since the power of the source is not known, it is estimated by the trace of the array spatial covariance matrix. An experimental study is presented that investigates the effect of the proposed weighting on DOA estimation of speech sources in a reverberant environment.

A note on density estimation via the hyperbolic secant kernel estimator

Kernel density estimation is a technique for estimating the probability density function, when data are obtained from unknown data generating processes. Because the kernel estimator is a good alternative to the histogram utilized as a relative estimator for the probability density function, it can supply us with the probability of an event of interest. In this note, we contribute to this subject through an extensive study of the hyperbolic secant kernel density estimator. We derived some properties of the obtained estimator, such as bias, variance, optimal bandwidth, and mean squared error. Finally, its performance is investigated using three practical data sets, two of them have both negative and positive values. In addition, a significant smooth bandwidth was proposed during the discussion.

Semi parametric Estimators for Quantile Model via LASSO and SCAD with Missing Data

In this study, we made a comparison between LASSO & SCAD methods, which are two special methods for dealing with models in partial quantile regression. (Nadaraya & Watson Kernel) was used to estimate the non-parametric part ;in addition, the rule of thumb method was used to estimate the smoothing bandwidth (h). Penalty methods proved to be efficient in estimating the regression coefficients, but the SCAD method according to the mean squared error criterion (MSE) was the best after estimating the missing data using the mean imputation method

Standard Errors of Kernel Equating: Accounting for Bandwidth Estimation.

In standardized testing, equating is used to ensure comparability of test scores across multiple test administrations. One equipercentile observed-score equating method is kernel equating, where an essential step is to obtain continuous approximations to the discrete score distributions by applying a kernel with a smoothing bandwidth parameter. When estimating the bandwidth, additional variability is introduced which is currently not accounted for when calculating the standard errors of equating. This poses a threat to the accuracy of the standard errors of equating. In this study, the asymptotic variance of the bandwidth parameter estimator is derived and a modified method for calculating the standard error of equating that accounts for the bandwidth estimation variability is introduced for the equivalent groups design. A simulation study is used to verify the derivations and confirm the accuracy of the modified method across several sample sizes and test lengths as compared to the existing method and the Monte Carlo standard error of equating estimates. The results show that the modified standard errors of equating are accurate under the considered conditions. Furthermore, the modified and the existing methods produce similar results which suggest that the bandwidth variability impact on the standard error of equating is minimal.

Multinomial Naïve Bayes Classifier: Bayesian versus Nonparametric Classifier Approach

This paper proposes a Naïve Bayes Classifier for Bayesian and nonparametric methods of analyzing multinomial regression. The Naïve Bayes classifier adopted Bayes’ rule for solving the posterior of the multinomial regression via its link function known as Logit link. The nonparametric adopted Gaussian, bi-weight kernels, Silverman’s rule of thumb bandwidth selector, and adjusted bandwidth as kernel density estimation. Three categorical responses of information on 78 people using one of three diets (Diet A, B, and C) that consist of scaled variables: age (in years), height (in cm), weight (in kg) before the diet (that is, pre-weight), weight (in kg) gained after 6 weeks of diet were subjected to the classifier multinomial regression of Naïve Bayes and nonparametric. The Gaussian and bi-weight kernel density estimation produced the minimum bandwidths across the three categorical responses for the four influencers. The Naïve Bayes classifier and nonparametric kernel density estimation for the multinomial regression produced the same prior probabilities of 0.3077, 0.3462, and 0.3462; and A prior probabilities of 0.3077, 0.3462, and 0.3462 for Diet A, Diet B, and Diet C at different smoothing bandwidths.

A Sparse Volume Reconstruction Method for Fetal Brain MRI Using Adaptive Kernel Regression.

Slice-to-volume reconstruction (SVR) method can deal well with motion artifacts and provide high-quality 3D image data for fetal brain MRI. However, the problem of sparse sampling is not well addressed in the SVR method. In this paper, we mainly focus on the sparse volume reconstruction of fetal brain MRI from multiple stacks corrupted with motion artifacts. Based on the SVR framework, our approach includes the slice-to-volume 2D/3D registration, the point spread function- (PSF-) based volume update, and the adaptive kernel regression-based volume update. The adaptive kernel regression can deal well with the sparse sampling data and enhance the detailed preservation by capturing the local structure through covariance matrix. Experimental results performed on clinical data show that kernel regression results in statistical improvement of image quality for sparse sampling data with the parameter setting of the structure sensitivity 0.4, the steering kernel size of 7 × 7 × 7 and steering smoothing bandwidth of 0.5. The computational performance of the proposed GPU-based method can be over 90 times faster than that on CPU.

Design of Full-Order State Observer for Motor Drive Systems Based on the Fixed Gain Filter

This paper mainly discusses about the full-order state observation technology for the permanent magnet synchronous motor (PMSM) drive system. First, the concept of the Kalman filter (KF) is synthesized to design a novel fixed gain filter (FGF) with an optimal fixed feedback gain matrix, which ensures a fast and accurate observation for position, speed, acceleration, and load torque. To alleviate the heavy computational load of the KF, second, the feedback gain is configured as a single tunable parameter only, which can be calculated offline. The regulation parameter is refined within a certain small range by fulfilling the system stability criterion. Furthermore, the system dynamic performance indexes, such as noise smoothing capability and bandwidth, are both analyzed to deduce the expected exact value of the regulation parameter. The proposed FGF can provide an accurate observation equivalent to the conventional KF, while the proposed FGF provides a faster tracking performance, an easier parameter tuning mechanism, and a lower program complexity. The performance of the FGF is verified by simulations and experiments in all cases.

A Proposed Adaptive Bitrate Scheme Based on Bandwidth Prediction Algorithm for Smoothly Video Streaming

A robust video-bitrate adaptive scheme at client-aspect plays a significant role in keeping a good quality of video streaming technology experience. Video quality affects the amount of time the video has turned off playing due to the unfilled buffer state. Therefore to maintain a video streaming continuously with smooth bandwidth fluctuation, a video buffer structure based on adapting the video bitrate is considered in this work. Initially, the video buffer structure is formulated as an optimal control-theoretic problem that combines both video bitrate and video buffer feedback signals. While protecting the video buffer occupancy from exceeding the limited operating level can provide continuous video streaming, it may also cause a video bitrate oscillation. So the video buffer structure is adjusted by adding two thresholds as operating points for overflow and underflow states to filter the impact of throughput fluctuation on video buffer occupancy level. Then a bandwidth prediction algorithm is proposed for enhancing the performance of video bitrate adaptation. This algorithm's work depends on the current video buffer level, video bitrate of the previous segment, and iterative throughput measurements to predict the best video bitrate for the next segment. Simulation results show that reserving a bandwidth margin is better in adapting the video bitrate under bandwidth variation and then reducing the risk of video playback freezing. Simulation results proved that the playback freezing happens two times: firstly, when there is no bandwidth margin used and secondly, when the bandwidth margin is high while smooth video bitrate is obtained with moderate value. The proposed scheme is compared with other two schemes such as smoothed throughput rate (STR) and Buffer Based Rate (BBR) in terms of prediction error, QoE preferences, buffer size, and startup delay time, then the proposed scheme outperforms these schemes in attaining smooth video bitrates and continuous video playback.

A Proposed Adaptive Bitrate Scheme Based on Bandwidth Prediction Algorithm for Smoothly Video Streaming

A robust video-bitrate adaptive scheme at client-aspect plays a significant role in keeping a good quality of video streaming technology experience. Video quality affects the amount of time the video has turned off playing due to the unfilled buffer state. Therefore to maintain a video streaming continuously with smooth bandwidth fluctuation, a video buffer structure based on adapting the video bitrate is considered in this work. Initially, the video buffer structure is formulated as an optimal control-theoretic problem that combines both video bitrate and video buffer feedback signals. While protecting the video buffer occupancy from exceeding the limited operating level can provide continuous video streaming, it may also cause a video bitrate oscillation. So the video buffer structure is adjusted by adding two thresholds as operating points for overflow and underflow states to filter the impact of throughput fluctuation on video buffer occupancy level. Then a bandwidth prediction algorithm is proposed for enhancing the performance of video bitrate adaptation. This algorithm's work depends on the current video buffer level, video bitrate of the previous segment, and iterative throughput measurements to predict the best video bitrate for the next segment. Simulation results show that reserving a bandwidth margin is better in adapting the video bitrate under bandwidth variation and then reducing the risk of video playback freezing. Simulation results proved that the playback freezing happens two times: firstly, when there is no bandwidth margin used and secondly, when the bandwidth margin is high while smooth video bitrate is obtained with moderate value. The proposed scheme is compared with other two schemes such as smoothed throughput rate (STR) and Buffer Based Rate (BBR) in terms of prediction error, QoE preferences, buffer size, and startup delay time, then the proposed scheme outperforms these schemes in attaining smooth video bitrates and continuous video playback.

Light amplification via PbS quantum dots-doped tapered fiber coupler: model and theory

In this paper, the gain engineering of a semiconductor quantum dots fiber amplifier (SQDFA) is studied. The optical amplification is realized by exciting the PbS quantum dots coated around the tapered single-mode fiber coupler with an evanescent wave. The gain spectra and saturation properties of the SQDFA are obtained via solving the rate and coupled power equations based on the two-level model. Then, the effect of the signal wavelength, pump power and amplifier length on the saturation characteristics is numerically simulated. The obtained results show that the proposed model is in a good agreement with the previous experimental results. Unique characteristics of the SQDFA such as the broadband optical gain and smooth bandwidth are of great interest for dense wavelength-division multiplexing systems. Therefore, the proposed model show promising applications in the future fiber-optic communications.

Focusing and Frequency Smoothing for Arbitrary Arrays With Application to Speaker Localization

The coherent signal subspace method (CSSM) enables the direction-of-arrival (DoA) estimation of coherent sources with subspace localization methods. The focusing process that aligns the signal subspaces within a frequency band to its central frequency is central to the CSSM. Within current focusing approaches, a direction-independent focusing approach may be more suitable for reverberant environments since no initial estimation of the sources' DoAs is required. However, these methods use integrals over the steering function, and cannot be directly applied to arrays around complex scattering structures, such as robot heads. In this article, current direction-independent focusing methods are extended to arrays for which the steering function is available only for selected directions, typically in a numerical form. Spherical harmonics decomposition of the steering function is then employed to formulate several aspects of the focusing error. A case of two coherent sources is studied and guidelines for the selection of the frequency smoothing bandwidth are suggested. The performance of the proposed methods is then investigated for an array that is mounted on a robot head. The focusing process is integrated within the direct-path dominance (DPD) test method for speaker localization, originally designed for spherical arrays, extending its application to arrays with arbitrary configurations. Finally, experiments with real data verify the feasibility of the proposed method to successfully estimate the DoAs of multiple speakers under real-world conditions.

Smoothing Quantile Regressions

We propose to smooth the objective function, rather than only the indicator on the check function, in a linear quantile regression context. Not only does the resulting smoothed quantile regression estimator yield a lower mean squared error and a more accurate Bahadur–Kiefer representation than the standard estimator, but it is also asymptotically differentiable. We exploit the latter to propose a quantile density estimator that does not suffer from the curse of dimensionality. This means estimating the conditional density function without worrying about the dimension of the covariate vector. It also allows for two-stage efficient quantile regression estimation. Our asymptotic theory holds uniformly with respect to the bandwidth and quantile level. Finally, we propose a rule of thumb for choosing the smoothing bandwidth that should approximate well the optimal bandwidth. Simulations confirm that our smoothed quantile regression estimator indeed performs very well in finite samples. Supplementary materials for this article are available online.

Sufficient dimension reduction with simultaneous estimation of effective dimensions for time-to-event data.

When there is not enough scientific knowledge to assume a particular regression model, sufficient dimension reduction is a flexible yet parsimonious nonparametric framework to study how covariates are associated with an outcome. We propose a novel estimator of low-dimensional composite scores, which can summarize the contribution of covariates on a right-censored survival outcome. The proposed estimator determines the degree of dimension reduction adaptively from data; it estimates the structural dimension, the central subspace and a rate-optimal smoothing bandwidth parameter simultaneously from a single criterion. The methodology is formulated in a counting process framework. Further, the estimation is free of the inverse probability weighting employed in existing methods, which often leads to instability in small samples. We derive the large sample properties for the estimated central subspace with data-adaptive structural dimension and bandwidth. The estimation can be easily implemented by a forward selection algorithm, and this implementation is justified by asymptotic convexity of the criterion in working dimensions. Numerical simulations and two real examples are given to illustrate the proposed method.

Automatic bandwidth selection for recursive kernel density estimators with length-biased data

In this paper we propose an automatic selection of the bandwidth of the recursive kernel estimators of a probability density function defined by the stochastic approximation algorithm in the case of length-biased data. We compared our proposed plug-in method with the cross-validation method and the so-called smooth bootstrap bandwidth selector via simulations as well as a real data set. Results showed that, using the selected plug-in bandwidth and some special stepsizes, the proposed recursive estimators will be very competitive to the non-recursive one in terms of estimation error and much better in terms of computational costs.

Wideband sub-THz half-wave plate using 3D-printed low-index metagratings with superwavelength lattice.

High-index dielectric metasurfaces are rarely reported around 0.1-0.3 THz, as an extremely large etching depth is needed according to the millimeter-scale wavelength. In this work, we propose an easy solution to sub-THz wideband polarization control by utilizing 3D-printed low-index (n~1.5) metagratings. The metagrating with subwavelength lattice is shown as a very efficient half-wave plate (net polarization conversion of 87%) at 0.14 THz but showing noisy spectrum. The design with superwavelength lattice offers a smooth and wide bandwidth for linear polarization rotation. Study of the mechanism shows that the lattice size slightly above wavelength is a better choice for the low-index metadevice as it maintains high efficiency in the zero diffraction order and wide bandwidth due to the small mode dispersion. Such designs offer a feasible solution especially suitable for sub-THz polarization and phase control, complementary to the existing high-index dielectric and metallic metasurfaces.

Nonparametric inference via bootstrapping the debiased estimator

In this paper, we propose to construct confidence bands by bootstrapping the debiased kernel density estimator (for density estimation) and the debiased local polynomial regression estimator (for regression analysis). The idea of using a debiased estimator was recently employed by Calonico et al. (2018b) to construct a confidence interval of the density function (and regression function) at a given point by explicitly estimating stochastic variations. We extend their ideas of using the debiased estimator and further propose a bootstrap approach for constructing simultaneous confidence bands. This modified method has an advantage that we can easily choose the smoothing bandwidth from conventional bandwidth selectors and the confidence band will be asymptotically valid. We prove the validity of the bootstrap confidence band and generalize it to density level sets and inverse regression problems. Simulation studies confirm the validity of the proposed confidence bands/sets. We apply our approach to an Astronomy dataset to show its applicability.

Yb:CALYO-based femtosecond chirped pulse regenerative amplifier for temporally resolved pump-probe spectroscopy

Diode-pumped femtosecond chirped pulse regenerative amplifiers based on Yb3+-materials are of practical importance for wide range of scientific, industrial and biomedical applications. The aim of this work was to study the amplification of broadband chirped femtosecond pulses in regenerative amplifier based on Yb3+:CaYAlO4crystal.Such systems use femtosecond mode-locked lasers as seed pulse sources and amplify nJ-seed pulses to sub-mJ energy range. Most chirped pulse regenerative amplifier systems described in the literature use seed lasers with typical pulse spectral width at the level of 10–15 nm full width at half maximum (FWHM) that limit the seed pulse duration of about 90 fs and amplified pulse duration at the level of 200 fs due to strong influence of gain narrowing effect on the amplified pulse parameters. Yb3+-doped crystals with wide and smooth gain bandwidth as an active medium of chirped femtosecond pulse regenerative amplification systems allow to reduce negative contribution of gain narrowing effect and lead to shortening of amplified pulses. In this research we study the chirped pulse regenerative amplification of broad-band femtosecond pulses (60 nm spectral width FWHM) in the Yb3+:CaYAlO -based chirped pulse regenerative amplifier. Substantial reduction of the amplified pulse duration down to 120 fs (19.4 nm spectral width FWHM) with average power of 3 W at 200 kHz pulse repetition frequency was demonstrated without any gain narrowing compensation technique.The results of experimental investigation of broad-band seeded Yb3+:CaYAlO -based chirped pulse regenerative amplifier are reported for the first time to our knowledge. 120 fs-pulses (19.4 nm FWHM) with average output power of 3 W were demonstrated without any gain narrowing compensation technique. Despite the significant reduction of amplified pulse duration the task of improvement group velocity dispersion balance (including high orders of group velocity dispersion) remains relevant.

The study and comparison of one-dimensional kernel estimators – a new approach. Part 2. A hydrology case study

The main purpose of this article is to present the numerical consequences of selected methods of kernel estimation, using the example of empirical data from a hydrological experiment [1, 2]. In the construction of kernel estimators we used two types of kernels – Gaussian and Epanechnikov – and several methods of selecting the optimal smoothing bandwidth (see Part 1), based on various statistical and analytical conditions [3–6]. Further analysis of the properties of kernel estimators is limited to eight characteristic estimators. To assess the effectiveness of the considered estimates and their similarity, we applied the distance measure of Marczewski and Steinhaus [7]. Theoretical and numerical considerations enable the development of an algorithm for the selection of locally most effective kernel estimators.

Nonparametric independence screening via favored smoothing bandwidth

We propose a flexible nonparametric regression method for ultrahigh-dimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression. Then, an iterative procedure is developed to recover both the important covariates and the regression function. Theoretically, we prove that the favored smoothing bandwidth based screening possesses the model selection consistency property. Simulation studies as well as real data analysis show the competitive performance of the new procedure.

Compact lotus shape dual band patch antenna for Bluetooth and ultra wideband applications

AbstractA compact lotus shape dual band microstrip patch antenna is presented in this article. Dual‐band operation for both Bluetooth and ultra wideband (UWB) is covered with low profile, enriched gain, and small size. The lotus shape patch and Sawtooth ground provide smooth impedance bandwidth, and dual band characteristics are achieved. In lower frequency, the antenna cover about 300 MHz from 2.3 to 2.6 GHz (Bluetooth), while in upper frequency, bandwidth is about 7.7 GHz from 3.3 to 12 GHz which covers UWB band. With a dimension of 44 × 42 mm2, the proposed antenna is fed by a microstrip fed line and printed on less expensive FR‐4 substrate. The simulated and measured result of impedance, radiation pattern, gain, and efficiency are fair enough. This antenna shows an omnidirectional radiation pattern across the integrated Bluetooth and UWB bands both theoretically and experimentally. With an excellent impulse response, high fidelity, and quality factor, the proposed antenna is suitable for using dual band frequency of both Bluetooth and UWB without interference between each other.