Chebyshev Type Research Articles

Low sensitivity complex image rejection filter for GNSS receivers

In this paper, a new approach for the design of a low sensitivity complex-filter is proposed. The approach is based on realising the filter using low sensitivity allpass sections. The complex filter obtained can be used as image-reject filter in low-IF GNSS receivers. The filter configuration is modular, i.e. is composed of the same subcircuits which simplifies the design of the circuit. A Chebyshev type OTA-C image-reject filter obtained by cascading two third-order allpass-based complex filters is presented. Post layout simulation results of the filter using SPECTRE in CADENCE design tool verifying its proper operation are provided.

Choice of the Method of Probabilistic Modeling of Statistical Dynamics of Autonomous Power Supply Systems

The results of comparative analysis of simulation methods of dynamic modes of autonomous power supply systems are considered. The method of statistical tests, the method of equivalent perturbations, and the interpolation method are discussed. The disadvantages and advantages of these approaches are noted. The problem of the labor-intensiveness of modeling using the methods of statistical tests and the interpolation method is studied using concrete examples. A general conclusion as to the advisability of using the interpolation method is drawn. The mathematical apparatus to be used to calculating the output characteristics is presented. Recommendations are given on the choice of Christoffel numbers and nodes of Chebyshev type for the investigation of the statistical dynamics of autonomous power supply systems.

Some weighted inequalities of Chebyshev type via RL-approach

Some weighted inequalities of Chebyshev type via RL-approach

New extensions of Chebyshev type inequalities using generalized Katugampola integrals via Polya-Szegö inequality

A number of Chebyshev type inequalities involving various fractional integral operators have, recently, been presented. In this work, motivated essentially by the earlier works and their applications in diverse research subjects, we establish some new Polya-Szego inequality involving generalized Katugampola fractional integral operator and use them to prove some new fractional Chebyshev type inequalities which are extensions of the results in the paper: [On Polya-Szego and Chebyshev type inequalities involving the Riemann-Liouville fractional integral operators, J. Math. Inequal, 10(2) (2016)].

Gait and tremor investigation using machine learning techniques for the diagnosis of Parkinson disease

Parkinson’s disease (PD) is a chronic and progressive movement disorder affecting patients in large numbers throughout the world. As PD progresses, the affected person is unable to control movement normally. Individuals affected by Parkinson’s disease exhibit notable symptoms like gait impairments and tremor occurrences during different stages of the disease. In this paper a novel approach has been proposed to diagnose PD using the gait analysis, that consists of the gait cycle, which can be broken down into various phases and periods to determine normative and abnormal gait. Initially, the raw force data obtained from physionet database was filtered using a Chebyshev type II high pass filter with a cut-off frequency 0.8 Hz to remove noises arising from the changes in orientation of the subject’s body and other factors during measurement. The filtered data was used for extracting various gait features using the peak detection and pulse duration measuring techniques. The threshold values of the gait detection algorithm were tuned to individual subjects. From the peak detection algorithm, various kinetic features including the heel and toe forces, and their normalized values were obtained. The pulse duration algorithm was developed to extract different temporal features including the stance and swing phases, and stride time. Tremor is a common symptom in PD. Tremor is an involuntary movement of body parts. At first the tremor may appear in a specific body part like an arm, leg or one side of the body and later it may spread to both sides . This rest tremor is a cardinal sign of PD. An average accuracy of 92.7% is achieved for the diagnosis of PD from gait analysis and tremor analysis is used for knowing the severity of PD.

Chebyshev type inequalities by means of copulas

A copula is a function which joins (or ‘couples’) a bivariate distribution function to its marginal (one-dimensional) distribution functions. In this paper, we obtain Chebyshev type inequalities by utilising copulas.

Dual‐band filter with fully independent passbands based on unequal‐length coupled lines and stubs

In this work, a dual-band filter that has completely independent passbands is demonstrated. The complete independence of the two passbands is achieved by simultaneously abandoning the classical restriction on electrical lengths for dual-band operation and allowing all the components to have different lengths. As a result, the proposed filter has different sets of J-inverter values and susceptance slope parameters independently at two centre frequencies. Therefore, the two passbands can be designed to have not only different bandwidths, but also different passband responses simultaneously; i.e. one passband can be designed to be a Chebyshev type while the other is a Butterworth type, or a Chebyshev type with different passband ripple levels. Rigorous design equations are derived and various design curves are provided to discuss the practicality of the proposed method. Finally, two filters with different bandwidths and passband types are demonstrated experimentally. The excellent agreement between the simulated and measured results verifies the practicality of the proposed method.

A Fractional Order Collocation Method for Second Kind Volterra Integral Equations with Weakly Singular Kernels

In this paper, we develop a fractional order spectral collocation method for solving second kind Volterra integral equations with weakly singular kernels. It is well known that the original solution of second kind Volterra integral equations with weakly singular kernels usually can be split into two parts, the first is the singular part and the second is the smooth part with the assumption that the integer m being its smooth order. On the basis of this characteristic of the solution, we first choose the fractional order Lagrange interpolation function of Chebyshev type as the basis of the approximate space in the collocation method, and then construct a simple quadrature rule to obtain a fully discrete linear system. Consequently, with the help of the Lagrange interpolation approximate theory we establish that the fully discrete approximate equation has a unique solution for sufficiently large n, where $$n+1$$ denotes the dimension of the approximate space. Moreover, we prove that the approximate solution arrives at an optimal convergence order $$\mathcal{O}(n^{-m}\log n)$$ in the infinite norm and $$\mathcal{O}(n^{-m})$$ in the weighted square norm. In addition, we prove that for sufficiently large n, the infinity-norm condition number of the coefficient matrix corresponding to the linear system is $$\mathcal{O}(\log ^2 n)$$ and its spectral condition number is $$\mathcal{O}(1)$$ . Numerical examples are presented to demonstrate the effectiveness of the proposed method.

Integrated Open Loop Resonator Filter Designed with Notch Patch Antenna for Microwave Applications

This paper presented the design of integrated open loop resonator bandpass filter with notch type antenna for the use in microwave applications. Chebyshev type filter is selected as the filter characteristics and cascaded design with the antenna to produce a single module, Integrated Filter Antenna (IFA). Special feature of the antenna is the implementation of notch on the patch antenna to improve the efficiency. IFA is then simulated in electromagnetic simulation tool, Agilent Advance Design System (ADS) version 2016 and measured using R&S Vector Network Analyzer. It shows that the proposed IFA produced good measured return loss >-30dB with both vertical and horizontal gain of 9.11dBi and 8.01dBi respectively.

Digital filters for clustered-OFDM-based PLC systems: Design and implementation

This work aims to investigate the design and implementation of digital filters for separating clusters in a clustered-orthogonal frequency-division multiplexing scheme for power line communication systems. In this regard, we formulate the mathematical problem and present a criterion which is capable of searching for digital filters that maximizes data rate. In the following, several finite impulse response and infinite impulse response digital filters are analyzed in order to validate the proposed criterion and to verify the best one which fulfills the given constraints. Furthermore, regarding only the best digital filters obtained, a finite precision and complexity analyses are carried out by using a field-programmable gate array device. Based on numerical results, we show that finite impulse response equiripple minimum phase and infinite impulse response Chebyshev type II digital filters yield the best data rates among the chosen digital filters. Moreover, we point out that equiripple minimum phase digital filters consume more hardware resources than Chebyshev type II digital filters, although the first one deal better with the field-programmable gate array constraints when more bits are used to implement the digital filter. Due to that, finite impulse response digital filters are more indicated to be implemented in a field-programmable gate array device.

A new two-dimensional matched filter based on the modified Chebyshev type I function for retinal vessels detection.

Retinal vessel segmentation takes a significant part in an automated diabetic retinopathy screening task. However, this can be a challenging job because of the low contrast retinal images and the presences of retinal pathologies. Hence, in this paper, we propose a novel matched filter based on the modified Chebyshev type I function for retinal blood vessels candidates detection. The proposed method is combined with the pre-processing and the post-processing phases to have a complete retinal vessel segmentation scheme. The retinal images from the DRIVE and STARE databases, which are equipped with the ground truths are used to evaluate our proposed method in the segmentation scheme. Using our method, the achieved average levels of sensitivity, specificity, and accuracy are 0.756, 0.973, and 0.954, for the DRIVE database, and 0.731, 0.972, and 0.953, for the STARE database, being better than other presented methods. The high results indicate that our method is reliable to be used in an automated detection tool for diabetic retinopathy.

A refined Frequency Domain Decomposition tool for structural modal monitoring in earthquake engineering

Output-only structural identification is developed by a refined Frequency Domain Decomposition (rFDD) approach, towards assessing current modal properties of heavy-damped buildings (in terms of identification challenge), under strong ground motions. Structural responses from earthquake excitations are taken as input signals for the identification algorithm. A new dedicated computational procedure, based on coupled Chebyshev Type II bandpass filters, is outlined for the effective estimation of natural frequencies, mode shapes and modal damping ratios. The identification technique is also coupled with a Gabor Wavelet Transform, resulting in an effective and self-contained time-frequency analysis framework. Simulated response signals generated by shear-type frames (with variable structural features) are used as a necessary validation condition. In this context use is made of a complete set of seismic records taken from the FEMA P695 database, i.e. all 44 “Far-Field” (22 NS, 22 WE) earthquake signals. The modal estimates are statistically compared to their target values, proving the accuracy of the developed algorithm in providing prompt and accurate estimates of all current strong ground motion modal parameters. At this stage, such analysis tool may be employed for convenient application in the realm of Earthquake Engineering, towards potential Structural Health Monitoring and damage detection purposes.

On Chebyshev Type Inequalities Using Generalized k-Fractional Integral Operator

In this paper, using generalized k-fractional integral operator (in terms of the Gauss hypergeometric function), we establish new results on generalized k-fractional integral inequalities by considering the extended Chebyshev functional in case of synchronous function and some other inequalities.

Convergence of Chebyshev type regularization method under Morozov discrepancy principle

In this paper we investigate the convergence of Chebyshev type regularization strategy combined with the Morozov discrepancy principle, which is an a posteriori parameter choice rule and independent of the a priori information of exact solution. Compared with the standard Tikhonov regularization method, the Chebyshev type regularization method has no saturation restriction so that its convergence order holds for any υ ≥ 1 2 , where p = 2 υ + 1 2 υ in the H o ̈ l d e r type estimate.

Automatic segmentation of Phonocardiogram using the occurrence of the cardiac events

This paper presents automatic method of segmentation of heart sound using the occurrence of the cardiac rhythmic events. Noisy heart sound is filtered using the 6th order Chebyshev type I low pass filter to remove the redundant noise. Bark Spectrogram is calculated from the cardiac signal by converting spectrogram to the bark scale. The bark spectrogram is smoothened and the loudness index is calculated by averaging the amplitude across all frequency bands. The loudness index is smoothened and differentiated to obtain the event detection function. The smoothened event detection function gives the occurrence of the cardiac events namely the first and the second heart sounds. This method is highly effective in identifying peaks S1 and S2 with the segmentation accuracy of 96.98% giving an F1 measure of 97.09%. This method does not require the setting up of any type of threshold. So it is a highly effective type of segmentation under noisy conditions.

On Higher-Dimensional Fibonacci Numbers, Chebyshev Polynomials and Sequences of Vector Convergents

We study higher-dimensional interlacing Fibonacci sequen\-ces, generated via both Chebyshev type functions and $m$-dimensional recurrence relations. For each integer $m$, there exist both rational and integer versions of these sequences, where the underlying prime congruence structures of the rational sequence denominators enables the integer sequence to be recovered. From either the rational or the integer sequences we construct sequences of vectors in $\mathbb{Q}^m$, which converge to irrational algebraic points in $\mathbb{R}^m$. The rational sequence terms can be expressed as simple recurrences, trigonometric sums, binomial polynomials, sums of squares, and as sums over ratios of powers of the signed diagonals of the regular unit $n$-gon. These sequences also exhibit a ``rainbow type'' quality, and correspond to the Fleck numbers at negative indices, leading to some combinatorial identities involving binomial coefficients. It is shown that the families of orthogonal generating polynomials defining the recurrence relations employed, are divisible by the minimal polynomials of certain algebraic numbers, and the three-term recurrences and differential equations for these polynomials are derived. Further results relating to the Christoffel-Darboux formula, Rodrigues' formula and raising and lowering operators are also discussed. Moreover, it is shown that the Mellin transforms of these polynomials satisfy a functional equation of the form $p_n(s)=\pm p_n(1-s)$, and have zeros only on the critical line $\Re (s)=1/2$.

Comonotonic stochastic processes and generalized mean-square stochastic integral with applications

The concept of monotonic stochastic processes was introduced by Skowronski [Aequationes mathematicae 44 (1992) 249–258]. In this paper, we introduce the concept of comonotonic stochastic processes. As an application, we propose the well-known Chebyshev type inequality for two comonotonic stochastic processes via the generalized mean-square stochastic integral.

Certain inequalities associated with Hadamard k-fractional integral operators

We aim to present some new Polya-Szego type inequalities associated with Hadamard k-fractional integral operators, which are also used to derive some Chebyshev type integral inequalities. Further we apply some of the results presented here to a function which is bounded by the Heaviside functions.

Comparative studies between KVL and BPFT in magnetically‐coupled resonant wireless power transfer

Kirchhoff's voltage law (KVL) and band-pass filter theory (BPFT) have been utilised for estimating the power transfer efficiency (PTE) and power delivered to the load (PDL) of magnetically-coupled resonant wireless power transfer (WPT). By using the two approaches, three aspects for in-depth understanding of power transfer characteristics and designing a high-efficiency WPT system are illuminated in this research. First, by introducing generalised mistuning factor and using diagram discriminance method in KVL, the effect conditions of source- and load-loaded quality factors on PTE and PDL are analysed. Then, by applying frequency and element transformations in BPFT, the restraints of Butterworth and Chebyshev type filter for WPT application are revealed. Third, it is verified that BPFT is a special case of KVL, and the former simplifies the design and analysis under the derived restraints than the latter. The maximal PDL at original frequency and the transfer characteristics in frequency splitting region can be easily achieved by Butterworth and Chebyshev type, respectively. The PTE and PDL versus frequency and coupling coefficient can be analysed in detail by KVL. Finally, the calculated results of the design examples are verified through experimental measurements.

On the Minkowski-Hölder type inequalities for generalized Sugeno integrals with an application

In this paper, we use a new method to obtain the necessary and sufficient condition guaranteeing the validity of the Minkowski-H\"{o}lder type inequality for the generalized upper Sugeno integral in the case of functions belonging to a wider class than the comonotone functions. As a by-product, we show that the Minkowski type inequality for seminormed fuzzy integral presented by Daraby and Ghadimi in General Minkowski type and related inequalities for seminormed fuzzy integrals, Sahand Communications in Mathematical Analysis 1 (2014) 9--20 is not true. Next, we study the Minkowski-H\"{o}lder inequality for the lower Sugeno integral and the class of $\mu$-subadditive functions introduced in On Chebyshev type inequalities for generalized Sugeno integrals, Fuzzy Sets and Systems 244 (2014) 51--62. The results are applied to derive new metrics on the space of measurable functions in the setting of nonadditive measure theory. We also give a partial answer to the open problem 2.22 posed by Borzov\'a-Moln\'arov\'a and et al in The smallest semicopula-based universal integrals I: Properties and characterizations, Fuzzy Sets and Systems 271 (2015) 1--17.