Chebyshev Filter Research Articles

Microstrip Lowpass Filter Realization Using Monic Chebyshev Polynomial

This paper presents a novel approach to microwave lowpass filter design that addresses several challenges in modern microwave systems, including size, performance, and cost. With that in mind, we propose using monic Chebyshev polynomials as the characteristic function for the filter to achieve a low passband insertion loss and maximum cutoff slope. The half-power cutoff frequency characterizes these filters, and the ripple factor is not considered a design parameter. To demonstrate the effectiveness of the monic Chebyshev approximation, a comparison is made with chained function (CF) filters designed for microwave applications. It has been shown that the monic Chebyshev filter outperforms CF filters in all applications, including microwaves.

Performance analysis of optimum Chebyshev filters at microwave frequencies

The paper suggests that optimum Chebyshev filters present an excellent choice for microwave filter design, as this approximation offers minimum return loss in the half-power passband, provides a maximum cutoff slope, and maintains low sensitivity in the passband. A comparative analysis is conducted with the chained-function filters to demonstrate the efficacy of this approximation, since chained-function filters also utilize Chebyshev polynomials to shape the filter’s characteristic function. The optimum Chebyshev filter, along with two chained-function filters, each of the sixth-degree, are realized, simulated, and compared as lowpass stepped impedance filters with a half-power passband of 1 GHz. After a detailed comparison, it is concluded that the optimum Chebyshev filter outperforms, or at least matches, the performance of the chained-function filters. This suggests that the optimum Chebyshev filter can effectively replace chained-function filters in all applications, offering a superior solution.

High impedance fault detection method based on improved Mayr Arc model and fitting curve coefficients

To solve the problem of weak transient fault currents and significant nonlinear characteristics caused by arcs in resonant grounding systems, proposing a high-impedance fault (HIF) detection method based on an improved Mayr arc model and fitting curve coefficients. Firstly, to address the issue of low accuracy in simulating fault waveforms in existing HIF models, construct an improved arc model based on Mayr and control the parameter values under different feature dimensions, achieving accurate simulation of arc waveforms. Secondly, based on the impedance characteristics of the feeder, analyze the phase frequency characteristics, determine the first capacitive frequency band, and then determine the cutoff frequency of the Chebyshev filter to improve the ability of waveform feature extraction and fault recognition. Finally, by fitting the voltage and current geometric characteristic curve within the characteristic frequency band, using the least squares method and the quadratic coefficient values of the fitting curve to construct detection criteria, accurate detection of HIF is possible. Research shows that the improved arc model can fully characterize the current arc waveform under various working conditions. Simulations and real-world measurements verify that HIF can be accurately detected using the quadratic coefficient value of the fitting curve.

Improved Least Squares Phase Unwrapping Method Based on Chebyshev Filter

Phase unwrapping of high phase noise and steep phase gradient has always been a challenging problem in interferometric synthetic aperture radar (InSAR), in which case the least squares (LS) phase unwrapping method often suffers from significant unwrapping errors. Therefore, this paper proposes an improved LS phase unwrapping method based on the Chebyshev filter, which solves the problem of incomplete unwrapping and errors under high phase noise and steep phase gradient. Firstly, the steep gradient phase is transformed into multiple flat gradient phases using the Chebyshev filter. Then the flat gradient phases are unwrapped using the LS unwrapping method. Finally, the final unwrapped phase is obtained by iteratively adding the unwrapping results of the flat gradient phases. The simulation results show that the proposed method has the best accuracy and stability compared to LS, PCUA, and RPUA. In the real InSAR phase unwrapping experiment, the RMSE of the proposed method is reduced by 63.91%, 35.38%, and 54.39% compared to LS, PCUA, and RPUA. The phase unwrapping time is reduced by 62.86% and 11.64% compared to PCUA and RPUA.

Improving the estimation of countermovement jump height from force plate recordings by considering the interaction between multiple procedural steps: An optimisation approach

ABSTRACT Force plates are used as standalone measurement systems in research and practice to evaluate metrics such as jump height. Calculating jump height involves multiple procedural steps, but previous investigations aiming to improve calculation procedures have only considered the influence of a single procedural step in isolation. The purpose of this study was to investigate if considering the interacting influence of multiple procedural steps in conjunction would impact the accuracy of jump height calculated from force plate recordings. An optimisation procedure was used to determine the combination of filter type, filter order, filter cut-off, integration start point and instant of take-off, that would minimize the root mean squared difference between force plate calculated jump height and a kinematic criterion. The best filter approach was a fifth order Butterworth filter with a 6 Hz cut-off frequency or a third order Chebyshev filter with a 5 Hz cut-off frequency. The best starting point for integration was approximately 0.25 s prior to the onset of the jump and the instant of take-off was best identified by finding the first instant that the force-time signal decreased by the magnitude of system weight. The presented optimisation technique provides an improved quantitative approach to develop standard procedures.

Designing of CCII-Based Fractional Order Inverse Chebyshev Filters Using Gray Wolf Optimization Approach

The paper introduces a new approach for designing fractional-order inverse Chebyshev low-pass filters (FOICLF), with an emphasis on filters with an order of 1+α. The coefficients for these filters are determined through Gray Wolf Optimization by approximating filter response with the ideal response of same order FOICLF. Stability tests are conducted, and filters are implemented using Multiple Input Single Output topology with commercial ICs. Comparative analysis reveals close proximity between the ideal response of FOICLF and the designed filters, featuring maximum and mean square errors of –22.48 dB and –61.07 dB, respectively, for 1.7 order. Results are benchmarked against existing literature, highlighting superior performance in stopband and passband magnitude errors and stopband attenuation. Process, Voltage, and Temperature analysis assesses the impact of the parameter variations on the –3 dB frequency, assuring the robustness of designed filters with relative standard deviations ranging from 0.003% to 3.013% for the 1.7 order filter.

Scalable computation of anisotropic vibrations for large macromolecular assemblies

The Normal Mode Analysis (NMA) is a standard approach to elucidate the anisotropic vibrations of macromolecules at their folded states, where low-frequency collective motions can reveal rearrangements of domains and changes in the exposed surface of macromolecules. Recent advances in structural biology have enabled the resolution of megascale macromolecules with millions of atoms. However, the calculation of their vibrational modes remains elusive due to the prohibitive cost associated with constructing and diagonalizing the underlying eigenproblem and the current approaches to NMA are not readily adaptable for efficient parallel computing on graphic processing unit (GPU). Here, we present eigenproblem construction and diagonalization approach that implements level-structure bandwidth-reducing algorithms to transform the sparse computation in NMA to a globally-sparse-yet-locally-dense computation, allowing batched tensor products to be most efficiently executed on GPU. We map, optimize, and compare several low-complexity Krylov-subspace eigensolvers, supplemented by techniques such as Chebyshev filtering, sum decomposition, external explicit deflation and shift-and-inverse, to allow fast GPU-resident calculations. The method allows accurate calculation of the first 1000 vibrational modes of some largest structures in PDB ( > 2.4 million atoms) at least 250 times faster than existing methods.

Lower boundary capacity estimations of frequency-selective communication channels with PAM-n-signals achievable using resolution time theory

The issue of ensuring high specific capacity of promising wire telecommunication systems is one of the key problems of the last decade. At the same time, despite the existing spectrally efficient modulation methods that are used in existing communication systems, the majority of leading researchers associate further solution of this issue with the transition to the mode of information transmission at a rate "Faster-than-Nyquist" rate (FTN), in which the information receiving about the channel symbol occurs with pronounced intersymbol interference. In turn, this causes difficulties in the practical implementation of the receiver when using optimal signal processing algorithms with nonpolynomial computational complexity, and in the case of suboptimal demodulation methods implementing various types of channel equalization, due to conceptual limitations cannot provide a wide coverage of speeds in this mode. In this regard, the study of an alternative approach to processing signals with multi-position PAM-n-signals on the output of baseband frequency-selective channels (FSC) is relevant. The object of this paper is the study of the possibilities offered by the theory of resolution time for baseband FSC of the, in which information is transmitted using the PAM-n-signal, in the FTN mode. A modified mathematical model of FSC is presented, thanks to which analytical expressions are obtained for estimating the specific capacity in terms of the low bound capacity estimation introduced by Sh. Shamai, expressions for estimating the BER, including the case under the action of destabilizing factors on the symbol synchronization system. Auxiliary capacity estimations and rules for calculating the conditions for achieving them are introduced, convenient for engineering analysis. By means of numerical simulating for the most typical conditions inherent in wired FSC, which are modeled in this work by Chebyshev filters with ripple level of 3 dB and Butterworth filters, it is shown that in the FSN mode with a S/N ratio of no more than 40 dB and instability of the symbol synchronization system operation of 2.5% of the channel symbol duration with a bit error probability of 10–12, it is possible to expect a specific capacity of 5.7–8 bits/Hz*s. It is shown that these results are achieved by using hybrid forms of partial pulses. Recommendations for choosing a partial pulse shape are presented, their main properties are studied from the point of view of their engineering application.

0.5 V Multiple-Input Fully Differential Operational Transconductance Amplifier and Its Application to a Fifth-Order Chebyshev Low-Pass Filter for Bio-Signal Processing.

This paper presents a multiple-input fully differential operational transconductance amplifier (MI-FD OTA) with very low power consumption. To obtain a differential MOS pair with minimum supply voltage and minimum power consumption, the multiple-input bulk-driven MOS transistor operating in the subthreshold region is used. To show the advantage of the MI-FD OTA, a fifth-order Chebyshev filter was used to realize a low-pass filter capable of operating with a supply voltage of 0.5 V and consuming 60 nW at a nominal setup current of 3 nA. The proposed filter uses five MI-FD OTAs and five capacitors. The total harmonic distortion (THD) was 0.97% for a rail-to-rail sinusoidal input signal. The MI-FD OTA and the filter application were designed and simulated in the Cadence environment using a 0.18 µm CMOS process from TSMC. The robustness of the design was confirmed by Monte Carlo analysis and process, voltage, and temperature corner analysis.

Nature inspired algorithm based design of near ideal fractional order low pass Chebyshev filters and their realization using OTAs and CCII

Fractional order filters offer greater freedom of design and a precise control over stopband attenuation in electronic circuits and systems. This paper presents the design of a fractional order low pass Chebyshev filter (FOLCF) that achieves near-ideal response characteristics. The methodology introduced utilizes metaheuristic optimization methods, including particle swarm optimization, firefly algorithm, and grey wolf optimization. These techniques are employed to precisely adjust the filter coefficients for the orders (1+α), (2+α), and (3+α). The adjustment is carried out by comparing the desired behaviour of the FOLCF with generalized fractional order low pass transfer functions. Throughout these instances, the parameter α is varied within the range of (0, 1). The designed filters are then tested and compared on the basis of various factors. Simulation results demonstrate that the designed filters closely follow the behaviour of an ideal Chebyshev filter with maximum passband and stopband magnitude errors being −31.93 dB and −52.74 dB respectively for (1+α) order filters. These values for (2+α) and (3+α) order FOLCF have been observed to be −30.04 dB and −55.91 dB; −17.72 dB and −49.52 dB respectively. Furthermore, it has been observed that the proposed work outperforms existing state-of-the-art approaches in various aspects, including magnitude error, stopband attenuation, and cut-off frequency. The stability of the designed filters has been verified through stability analysis. Additionally, practical feasibility of the proposed FOLCF is demonstrated through SPICE simulations for α = [0.2,0.5,0.8] using second generation current conveyor (CCII) and operational transconductance amplifier (OTA) based topologies while approximating the constant phase element using fifth order continued fraction expansion. The SPICE implementations closely follow the behaviour of ideal filter with −48.67 dB and −62.8 dB as mean square errors for CCII and OTA circuits respectively, showcasing the proposed filters' superiority and practical applicability in advanced electronic design.

Design of Impedance Matching Network for Low-Power, Ultra-Wideband Applications

This paper addresses the design of ultra-wideband (UWB) impedance matching networks operating in the unlicensed 3.1–10.6 GHz frequency band for low-power applications. It improves the simplified real frequency technique (SRFT) by adding a realizability check and employing an iterative approach with different initial guesses in optimization to achieve realizable solutions under the requirements of UWB, low-power consumption, and a minimum number of circuit components. The comparison of solutions obtained using the SRFT with published solutions based on the Chebyshev filter theory is presented. It is shown that the optimal SRFT solution requires fewer components in the impedance matching network, maximizes the RF power delivery over the UWB spectrum with a reflection coefficient below −10 dB, and allows for circuit optimization to reduce power consumption. Using the improved SRFT, it demonstrates a systematic approach to find the strategies and limitations of designing the input matching networks for low-power UWB applications using GlobalFoundries 90 nm BiCMOS technology.

Reconfigurable integrated photonic filters for optical signal processing using a silicon photonic platform.

We present a systematic photonic filter design approach by deploying pole-zero optimization. The filter transfer function is derived from its specifications by formulating closed-form optimization objective functions and subsequently translating them into optical design parameters. Two distinct filter examples, namely Chebyshev and elliptic filters, are considered for the design and validation. A compact reconfigurable three-pole photonic filter is fabricated on a silicon photonic platform to illustrate the proposed design technique including transmission tunability. Integrated thermal phase shifters coupled with micro-ring resonators are used to reconfigure filter responses. A well-matched experimental demonstration is presented to validate the proposed tuning method. We achieved a sharp out-of-band edge rejection of at least 20 and 40 dB for the elliptic and Chebyshev filter, respectively.

Mitigation of attack detection via multi-stage cyber intelligence technique in smart grid

A smart grid is an electrical system that uses electronic communications to support two distinct data and electricity flows. This makes it possible for the system to recognize, react to, and resolve various problems. Power users of digital technology can take an active role and have the ability to cure themselves. Cybercrimes affecting the security of the smart grid include the compromise of vital client data by attackers, the spread of viruses, cybersecurity mistakes, and vulnerabilities in distributed systems. In order to identify the multi-stage cyberattacks that pose a threat to the smart grid, a novel Multi-Stage Cyber Intelligence (MSCI) technique has been developed in this work. A signal is generated by an intrusion detection system (IDS) sensor and passed through a Chebyshev filter for preprocessing in order to minimize its noise level. The risk will be identified by the security identification block, which also includes risk assessment, risk estimation, and risk identification. The Risk Identification Block finds the risk by gaining access to the Cyber Information Database. If the risk is not found, it is transmitted to the BI-LSTM Network, which verifies if it is an attack. A MATLAB simulator is used to implement the proposed approach. Evaluation criteria like Precision, F1 Score, Specificity, Accuracy, and Detective Rate have been used to assess the effectiveness of the Multi-Stage Cyber Intelligence (MSCI) technique approach that has been provided. The experimental results show that the suggested MSCI strategy has a 99% success rate, which is comparatively high when compared to the current approaches of 9.09%, 22.22%, and 47.47% for the CDS, AD-IOT, and SVM techniques, respectively.

Chebyshev filter and Butterworth filters: Comparison and applications in different cases

This study focuses on the filter selection problem in signal processing and wireless communication applications. Specifically, addressed two different filter selection problems: the Chebyshev filter and the Butterworth filter. Using MATLAB, in order to design and model these two types of filters. The performance, frequency response, transition band width, filter order, design complexity and target application of Chebyshev filter and Butterworth filter under different parameters are analyzed and compared. The selection of the two filters under different conditions and the reasons for choosing them are discussed. The Chebyshev filter is suited for applications that call for a high frequency response, and Chebyshev filters provide a steeper roll-down slope, which can suppress high-frequency noise and interference signals, according to the test results, it is widely used in communication systems. On the other hand, the Butterworth filter is more suitable for applications that require a flat passband and a wide stopband, such as audio systems.

Enhancing power quality in vehicle-to-grid (V2G) operations of FCEVs through the integration of real-time digital IIR filters in power calculations

Fuel cell electric vehicles (FCEVs) are estimated as the future's mobile distributed generators with vehicle-to-grid (V2G) functions. Besides, V2G topologies are required to be designed with an appropriate analog filter by accurately measuring the reference current and voltage values of inverters and converters. Thus, the highest accuracy is required in control structures for charging and grid connection of FCEVs to improve the power quality (PQ). In this study, PQ improvement of V2G operation of FCEVs is proposed by considering the developed real-time digital infinite impulse response (IIR) filters in generating reference signals in the power calculation stage. A band-pass digital IIR filter design is realized with the inverter using LabVIEW infrastructure, and reference signals are smoothed by using IIR filters. The performances of developed different IIR filters' results are examined in the study. Developed filters are designed using the order estimation method. Elliptic, Chebyshev, and Butterworth filters are applied to the voltage and current signals, and the best results are obtained in reference power signals with the Butterworth filter. The Butterworth filter maintains stability in current RMS, induces a 0.09 % decrease in voltage RMS, and shows a slight 0.30 % increase in active power. The proposed approach removes distortions in reference power signals by using a designed filter for a reliable V2G operation of FCEVs.

Research on Teaching and Dance Creation of Chinese Folk Dance in the Information Age

Abstract In this paper, we use motion capture technology to collect typical movements of Chinese folk dances and establish three-dimensional character models with the characteristics of human motion continuity and bone length invariance to discriminate the trajectory of skeletal movements. Video is used to export the data of Chinese folk dance. Design methods for extracting folk music and dance features to form a model for creating dances. Suppressing the noise of the original dance music, improving the accuracy of the fundamental frequency extraction of the music signal, and manually scoring the dance creation generation program are all benefits of using the Chebyshev filter. We propose the teaching method of Chinese folk dance in online broadcasting mode and carry out teaching experiments to compare the cooperative learning effect and dance technique evaluation effect between traditional dance teaching method and online broadcasting video lecture teaching method. The dance creation and generation program proposed in this paper is able to achieve a dance movement similarity of 0.92, which is able to preserve the original dance posture of Chinese folk dances to a greater extent. The results of the technical evaluation show that the teaching effects of the two teaching methods present significant differences in the four methods of basic technique, pair cooperation, dance expression, and total score, i.e., P<0.05, which shows that the online live video explanation method is more suitable for the teaching of ethnic folk dance in the information age.

Design of multi-ensemble hybrid filtering approach for removal of heart sound from lung auscultations

Successful lung sound extraction from lung auscultations requires precise filters. Lung auscultations include heart and lung sounds. Therefore, the filter design should identify heart sound characteristics. These include periodicity, pitch, frequency, amplitude, etc. Auscultation acquisition sensors are inefficient, so these signals have noise. To get a clean auscultation signal, ambient noise, periodic noise, DC offsets, baseline errors, harmonic noise, etc. must be addressed separately. Data cleaning must maintain a high peak-signal-to-noise ratio without removing desirable signal information. Heart sound patterns are extracted from input auscultations using filter banks on these signals. After heart sound extraction, the output sound sample should only contain lung sounds. Still, heart sound harmonics corrupt output lung sound due to similarities between heart and lung sound patterns. This lowers lung-sound extraction quality and automatic lung-based disease identification efficiency levels. This article proposes a 2-level multi-ensemble filtering model with 43 filters that analyze 15 other parameters to denoise and extract lung sound from lung auscultations to eliminate these drawbacks. Combining LMS, NLMS, and RLS is used for denoising process. For heart sound identification, an ensemble of Savitzky-Golay, FIR equiripple, Butterworth, Chebyshev, Elliptic, and wavelet filters is used. This selective combination of filters improves PSNR by 20% compared to sole filter performance, while signal entropy, crest factor, root mean squared error, kurtosis, etc. also improves for different scenarios.

A Detailed Study on IIR-FIR Filters and Design of a Graphical User Interface for Simulation of EEG Signals

Electroencephalography (EEG) plays a pivotal role in accepting brain activity and identifying neurological disorders. The precise analysis and explanation of EEG signals require the solicitation of digital signal processing techniques, such as Infinite Impulse Response (IIR) as well as Finite IJmpulse Response (FIR) filters. This paper investigates into a complete exploration of IIR-FIR filters and their application in EEG signal processing. The first part of this research paper involves a detailed examination of IIR and FIR filter types, their mathematical foundations, pros, and cons. Various filter design methods, such as Chebyshev, Butterworth and Elliptic filters, are discussed as well as compared through literature survey. Speculative aspects, including filter design, transfer functions, and frequency responses, are presented in a clear and much accessible manner. The second phase of the study introduces the design of a Graphical User Interface (GUI) on mathematical modelling tool aimed at enabling EEG signal simulation and analysis. This GUI is designed to enable users, including researchers and clinicians, to generate synthetic EEG signals with controllable parameters, apply IIR-FIR filters in real-time, and thereby visualize the filtered signals. The interface offers user-friendly controls for customizing filter characteristics, such as filter order, cutoff frequencies, and filter type. To validate the efficiency of the designed GUI and the selected IIR-FIR filters, general simulations are conducted using EEG datasets. The results showcase the GUI's efficacy in real-time EEG signal processing, demonstrating its prospective in research, clinical diagnostics, and educational settings and many areas. In summary, this paper presents a full investigation into IIR-FIR filters, proposing insights into their theory and practical application for EEG signal processing. The development of a intelligible GUI for EEG signal simulation and study further enhances the approachability of these mathematical modelling tools to a wider audience, eventually contributing to progressions in the field of neuroscience and brain signal analysis.

A Miniaturized Bandpass Filter with Wideband and High Stopband Rejection Using LTCC Technology

This paper designs an L-band wide stopband bandpass filter by applying low-temperature cofired ceramic (LTCC) technology to the global positioning system (GPS) frequency band. Taking the Chebyshev filter as a prototype, an equivalent collector element (capacitive and inductor) structure is adopted to fully use the three-dimensional package structure of LTCC to reduce the filter size. The filter is integrated into an eight-layer LTCC dielectric, and the series–parallel connection of the collector elements in the resonance unit is utilized to produce out-of-band transmission zeros, while the input and output ports’ capacitance is adjusted to control the bandwidth. Harmonic suppression is achieved by cascading two new compact stopband filters, while the size increase is insignificant due to LTCC technology. The simulation results are as follows: the center frequency is 1.575 GHz, 1 dB relative bandwidth is 6.3%, insertion loss in the passband is as slight as 1.6 dB, return loss is better than 30 dB, rejection bandwidth up to 16 GHz is more than 44 dB, and the volume of the whole filter is 6.2 × 3.7 × 0.78 mm3.

Experimental evaluation of ECG signal denoising methods based on HRV indices and their application in indoor thermal comfort study under different temperatures

The heart rate variability (HRV) features extracted from an electrocardiogram (ECG) signal have been widely used to help improve the performance of thermal comfort models, with the ECG signal denoising method being very important. In this study, 20 volunteers were recruited for experiments in a well-controlled chamber. Their ECG signals (a total of 6,000,000 sets of data) were collected under stable and variable temperature environments. With the use of the setup database, four denoising methods were compared: the fast Fourier transform (FFT), wavelet transform, Chebyshev filter, and Butterworth filter. When the performance of these methods was evaluated from ECG images, the Butterworth filter exhibited a more comprehensive and smoother representation of the original signal. Judging from denoising indices, the Butterworth filter exhibited the best performance, with its denoising indices surpassing those of fast Fourier transform and wavelet transform by differences ranging from 26% to 122%. Judging from HRV index and R-peak positioning, the data processed by Butterworth exhibited the highest reliability (93.5%), outperforming FFT (30.0%), the wavelet filter (72.5%), and the Chebyshev filter (78.5%). Furthermore, the 5th-order Butterworth filter exhibited the largest signal-to-noise ratio (SNR) with 1.1–34.4% larger and the smallest percent root-mean-square difference (PRD) with 15.2–66.1% smaller compared to other orders. Next, the characteristics of denoised HRV features under different temperatures were studied. During a temperature rise stage, the fitting R2 values of rMSSD, SDNN, and HR with temperature were 0.85, 0.64, and 0.78, respectively; meanwhile, during the subsequent temperature drop stage, the fitting R2 values were 0.78, 0.84, and 0.78, respectively. This suggests that changes in temperature can be effectively reflected by HRV indices. When gender was taken into consideration, the HR of females showed a 55.8% higher fitting level compared to males.