Chebyshev Filter Research Articles

An improved design method for even-degree optimum allpole filters with equiripple passband responses

The maximum power transfer between source and load is extremely important in analog signal processing. The main disadvantage of signal processing using the even-degree Chebyshev filter is the impossibility of LC ladder network realization between two equal resistors. Therefore, either the utilization of the ideal transformer or the Chebyshev filter of odd-degree is required to achieve the maximum power transfer. To overcome this limitation, the class of even-degree polynomials with the equiripple behavior, referred to as scaled modified Chebyshev polynomials, can be used as the filter’s characteristic function. Passband ripples of obtained filters can be controlled through an embedded parameter, while normalized half-power frequency is kept equal to unity. Furthermore, these filters can be optimized for the minimum amount of reflected power at the input terminals. In this paper, the optimum modified Chebyshev filters are first compared to the classic Chebyshev filters to show that both filters exhibit similar performances. Second, proposed filters are compared to the Least Square Monotonic (LSM) filters that are optimized by minimizing the area under the characteristic function in the passband. Results of comparison reveal that the proposed even-degree scaled modified Chebyshev filters outperform the LSM filters, as is already proved for the odd-degree filters.

An Efficient Blood Pressure Estimation and Risk Analysis System of PPG Signals Using IDA and MPPIW-DLNN Algorithms

The non-invasive Blood Pressure Estimation (BPE) utilizing the technology of photoplethysmography (PPG) gains significant interest because PPG could be extensively employed to wearable sensors. Here, a method for estimating Systolic Blood pressure (SBP), as well as Diastolic Blood pressure (DBP), grounded only on a PPG signal utilizing the Image Denoising Algorithms (IDA) algorithms is proposed. Also, a classification methodology to execute the risk analysis (RA) of the BP patients utilizing Moore–Penrose Pseudo-Inverse Matrix-Deep Learning Neural Network (MPPIW-DLNN) is proposed. The preprocessing is then done on the input PPG signal utilizing the Modified–Chebyshev Filter (CF) to eradicate the unwanted information existent in the signal. Afterward, the BPE is done utilizing IDA, which categorizes those components into (i) SBP and (ii) DBP. The MPPIW-DLNN provides the results of four sorts of risk classes like (i) stroke, (ii) heart failure (HF), (iii) heart attack (HA), and (iv) aneurysm identified from the inputted PPG signal.

МЕТОДИКА И АЛГОРИТМ СИНТЕЗА УПРАВЛЯЕМЫХ ЦИФРОВЫХ ФИЛЬТРОВ ЧЕБЫШЕВА I РОДА НИЖНИХ ЧАСТОТ НА БАЗЕ МЕТОДА БИЛИНЕЙНОГО ПРЕОБРАЗОВАНИЯ

The article presents a technique for the synthesis of controlled digital recursive Chebyshev lowpassfilters of the first kind with an infinite impulse response. The frequency response of such filters hasripples in the passband and is as flat as possible in the stopband. Controllability is understood as anexplicit dependence of the filter coefficients on the cutoff frequency. The technique is based on the bilineartransformation of the transfer function of the analog low-pass filter prototype and the frequencytransformation of the amplitude-frequency characteristics of the obtained digital filter. The main idea ofthe technique is that for an analog prototype filter with a cutoff frequency of 1 rad/s, the parameters ofthe transfer function of biquadratic or bilinear links, which have the dimension of frequency, will benumerically equal to the correction factors for similar parameters of a controlled filter with an arbitrarycutoff frequency. As an example, the synthesis of a digital Chebyshev filter of the first kind of the fifthorder is considered. In this article, the transfer function of an arbitrary order filter is represented as acascade connection of II order links if the filter is of an even order. In the case of an odd order greaterthan one, one cascaded link of the first order is added. Despite the relative simplicity of the frequencyconversion, in its practical use for digital filters synthesized using computer-aided design of digital filters(or using reference books containing calculated prototype low-pass filters for various approximationsof the frequency response of an ideal low-pass filter), a series arises non-trivial specific momentsthat complicate the engineering use of this method of synthesizing controlled digital filters. Therefore, inaddition to the technique, a step-by-step algorithm has been developed that allows one to synthesize afilter without knowing these moments. The algorithm is implemented in the Mathcad environment; asan example, a digital recursive Chebyshev filter of the 1st kind of the 5th order is calculated.The example shows the calculated coefficients of a digital controlled low-pass filter, which explicitlydepend on the cutoff frequency, the amplitude-frequency characteristics of this filter and its lowfrequencyprototype converted into a filter with the same cutoff frequency, the amplitude-frequencycharacteristics are given in the same coordinates. Due to the good formalization of the algorithm, thelatter is suitable for the implementation of computer-aided design systems for controlled digitalChebyshev low-pass filters of the first kind.

Detecting states of ion channels on the cell membrane using neural networks

The problem of automating the process of analyzing the open states of channels on the membrane of a neuron of a living organism is considered. Taking into account that the registration of the electrical activity of the cell was made by the patch clamp method at various values of the applied potential, a division into intervals with a constant potential is carried out. Further, to eliminate noise, a notch filter, low-frequency and high-frequency Chebyshev filters are applied to the data. A neural network is applied to the normalized data, based on the results of which the data is changed and re-processed by the same neural network. As a result of the algorithm, the dynamics of channel states was obtained, which makes it possible to register up to several open channels simultaneously.

Optimum Chebyshev filter with an equalised group delay response

ABSTRACT The first part of the paper discusses designing of the lowpass filter that gives both a constant group delay over the passband and a sharp cut-off slope, which is one of the most difficult challenges in continuous-time signal processing. Furthermore, equalisation of the group delay distortion of the Chebyshev filter has been performed through a cascade connection of the allpass filters. The Newton–Raphson method is applied for solving the system of nonlinear equations that calculate the allpass filter parameters for equalising the constant group delay in an equiripple sense. This procedure gives nearly symmetric impulse response of the resulting filtering system, as well as a longer duration. In the second part of the paper, two solutions for synthesising polynomial filter transfer functions are discussed: filter with monotonic amplitude characteristic (LSM) and filter using Chebyshev polynomial. For the purpose of comparison, the passband ripple factor of the Chebyshev filter is necessary to be adjusted so that both filters have the same stopband insertion loss, group delay and transient response. It is shown that Chebyshev filter is preferable since the passband magnitude distortions and sensitivity to the element deviation tolerance are significantly superior.

Dynamic Deformation Monitoring of Offshore Oil Platforms with Integrated GNSS and Accelerometer

Dynamic deformation monitoring is a crucial component of the structural health monitoring of an offshore oil platform. Given the insensitivity of the Global Navigation Satellite System (GNSS) to high-frequency vibration information, a combination of GNSS and accelerometer is used for vibration monitoring of platform structures. A hybrid filter based on complementary ensemble empirical mode decomposition (CEEMD) combined with a Chebyshev filter is proposed to process the monitoring data. The extracted GNSS low-frequency displacement is fused with the high-frequency displacement obtained from acceleration integration to obtain the overall dynamic displacement of the platform. The experimental analysis shows that the combination of t-test and correlation coefficient can select the required intrinsic mode function (IMF), the proposed hybrid filter can reduce the noise error to a certain extent, and the quadratic frequency domain integration of the acceleration data can avoid the influence of the integration trend term. The correlation coefficient between the overall reconstructed displacement and the original GNSS monitoring data was 0.8576, and the signal correlation after denoising and refactoring was more than 85%, thereby preserving the essential information components. Integrated GNSS and accelerometer monitoring systems complement each other’s advantages, compensating for their shortcomings in monitoring the dynamic deformation of a structure.

Novel filtering and diplexing linear tapered slot antenna with high-selectivity

In this article, a novel filtering and diplexing antenna using a linear tapered slot antenna (LTSA) are demonstrated. To begin, a highly-selective, second order bandpass filter is designed using generalized Chebyshev filter synthesis technique. Filtering and diplexing antennas are realized by co-designing the filter along with a wideband LTSA. The proposed filtering antenna exhibits 3.21% fractional bandwidth (FBW) over (4.29–4.43) GHz, high band-edge selectivity performance with 6 dBi flat in-band realized gain and stable end-fire radiation patterns with a low cross-polarization level of less than -30 dB. Further, a diplexing antenna with good bandpass filtering characteristics is also implemented. The design shows FBW of 3.32% (3.55–3.67) GHz and 3% (4.91–5.06) GHz and flat-radiation gain of 5.2 dBi and 5 dBi with sharp roll-off in Tx (lower) and Rx (upper) passbands, respectively. It also demonstrates good out-of-band suppression level of more than 20 dB, end-fire radiation patterns with cross-polarization lower than -27 dB and back-lobes lower than -14 dB for both the passbands. In order to validate their functionality, both the designs are fabricated and the experimental results correlate well with the simulated results.

Ultra-wide stopband waveguide bandpass filter based on out-of-band staggered tuning coupling technology

ABSTRACT A design method of greatly widening the stopband of waveguide bandpass filter is proposed in this paper. The parasitic passband of the filter mainly comes from the high-order oscillation mode of the resonant unit. Based on the theory of capacitance loading shortening of the transmission line and the transmission characteristics of each mode in the resonant cavity, a pair of transverse one-dimensional uniform capacitive diaphragms are placed in the center of the resonant cavity to shorten the resonant cavity and suppress the high-order modes. By changing the width of the waveguide and the height of the waveguide on the distribution of out-of-band transmission poles, the out-of-band transmission poles of each resonator can be staggered, which destroys or weakens the high-order oscillation coupling transmission conditions between the resonant units of the filter and further expands the stopband width of the filter. The results show that the length of the X-band waveguide bandpass filter (center frequency 9.5 GHz, bandwidth 400 MHz) is reduced by 54%, and the 40 dB stopband rejection bandwidth is 5.7 times the cutoff frequency of the transmission waveguide, compared with the prototype half-wavelength direct-coupled filter of the conventional Chebyshev filter.

Design of Broadband Aperture-Coupled Stacked Microstrip Antennas Using Second-Order Filter Theory

In this article, the authors propose a lumped circuit methodology for the design of broadband stacked microstrip patch antennas fed through an aperture. First, an equivalent circuit (EC) is introduced for the antenna. The EC consists of an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$LC$ </tex-math></inline-formula> series resonator modeling the feed plus two capacitively coupled <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$LC$ </tex-math></inline-formula> parallel resonators accounting for the radiating patches. Then, a deembedding procedure based on total least squares method is introduced to determine all the parameters of the antenna EC. Second, the circuit stage modeling the patches is designed as a second-order Chebyshev filter based on coupled resonators. Since the standard Chebyshev approach leads to circuit parameters that cannot be physically obtained in practice, a modified second-order quasi-Chebyshev design is presented, which can be physically implemented by stacking one conventional rectangular patch above one rectangular patch with both inner and meandering slots. The proposed methodology is used to design an antenna with over 30% bandwidth at a center frequency of 5.57 GHz. A prototype has been fabricated and measured, and good agreement has been found between simulations and experiments.

Design of an Efficient 24–30 GHz GaN MMIC Power Amplifier Using Filter-Based Matching Networks

A broadband GaN MMIC power amplifier (PA) with compact dimensions of 1.94 × 0.83 mm2 is presented for 5G millimeter-wave communication. To guarantee output capability at the operating band edges where serious performance degradation is likely to occur, the appropriate large-signal matching model and optimal impedance domain need to be carefully determined through load-pull analysis. Broadband matching networks (MNs) in the lowpass form are thereafter developed based on the Chebyshev filter synthesis theory. Using high-pass interstage MN in conjunction with parallel RC lossy circuits to compensate for the transistor’s negative gain roll-off slope ensures a flat frequency response. The input MN is designed as a band-pass filter due to the reactance extracted from the input side of the stabilized device exhibiting series LC resonance characteristics. Measured on-wafer pulsed results for the proposed three-stage PA demonstrate up to 30.9 dBm of output power, more than 28.6 dB of small-signal gain, and a peak power-added efficiency (PAE) of 35.6% at 27 GHz. Both uniform gain and saturated output power (Psat) are achieved across 24–30 GHz with fluctuations of less than 0.8 dB.

Improved Pre-Processing Process of Climate Series Based on Chebyshev Filter

In the process of data mining for time series of environmental factors of dendrobium origin, it is difficult to separate the available features because the feature components are too rich and the de-noising method is not feasible, in this paper, we try to improve the pre-processing process of sequence. In this method, we first de centralize the sequence and check the unit root to evaluate the stationarity of the sequence, and then design a band-pass filter to extract the feature components from the sequence in the range of monthly frequency to annual frequency, then, the features of EEMD and correlation coefficients are extracted by using the EEMD Algorithm, which is commonly used in the field of natural sequence decomposition. Finally, the Savitzky-Golay filter is designed to smooth the reconstructed sequence in order to remove the noise introduced by EEMD, the final usable characteristic component is obtained. Compared with EEMD Algorithm, this method is more reasonable in the pre-processing process, and the power distribution in frequency is more concentrated.

Direct Coupling Matrix Synthesis for Filters With Cascaded Singlets

This article proposes a direct coupling matrix synthesis approach for filters with cascaded singlets. A sequence of elementary matrix transformations is applied in the synthesis procedure to obtain the target coupling topology containing many cross couplings and nonresonant nodes. Two filter synthesis examples are presented to demonstrate the novel synthesis technique. To physically realize synthesized coupling matrices, some singlets need to be transformed into their dual forms, which are also singlets but with different coupling coefficients. A 6–4 generalized Chebyshev filter is designed according to the synthesized coupling matrix, where the singlets are realized as oversized rectangular waveguide cavities employing nonresonant modes. Due to the cascaded singlet coupling configuration, the modular design technique can significantly reduce the simulation time. After the waveguide modules are assembled, the model-based vector fitting technique is applied to aid the fine-tuning of the filter. Both simulation and measurement results are in good agreement with theoretical filter responses, validating the proposed coupling matrix synthesis and design technique for filters with cascaded singlets.

A THz Waveguide Bandpass Filter Design Using an Artificial Neural Network.

This paper presents a 300 GHz waveguide bandpass filter based on asymmetric inductive irises. The coupling matrix synthesis technique is used to design a 6-pole Chebyshev filter. In addition, an artificial neural network is applied to provide the filter geometries using the desired frequency response. The optimized filter is fabricated by the computer numeric controlled milling process. The measurement results show that the insertion loss is less than 3 dB and the return loss is better than 17 dB in the range 276–310 GHz.

A Systematic Design Method for a Wireless Power Transfer System Based on Filter Theory

One of the major considerations for a short- or intermediate-distance wireless power transfer (WPT) system is its robustness against variations of the distance, displacement, misalignment between the transmitting and receiving coils, and variations of the loads. Designing such a robust system has not been easy since most methods require some forms of trial-and-errors or optimization that present different degrees of uncertainty. In this article, we propose a design method to overcome the above issue: we make the power transfer efficiency (PTE) function of the WPT equivalent to that of a modified filter. Then, we apply a well-established filter theory to develop a systematic WPT design method; it can keep the PTE stable within the specified ranges of the distance changes, displacements, misalignments, and load variations. We take the Chebyshev filter as an example to verify the proposed method and build and test the prototype. Experiments show that when distance and misalignments occur, the prototype can maintain the efficiency of around 90% with less than 5% in variations as predicted by the theoretical design. In comparison, the conventional magnetically coupled resonant WPT system can only maintain the efficiency of 82% with more than 20% in variations. Therefore, the proposed design method presents a new efficient and optimized way to develop a robust WPT system for practical applications.

A Comparison Study for Cardiac Arrhythmias Noise Cancellation Techniques

The electrocardiogram (ECG), which represents the electrical activity of the heart, is always chosen as the basic signal for diagnosing cardiac abnormalities and detecting the patient's states. Generally, the various filters are applied (preprocessing) to denoise the artifacts from ECG signal. This step makes the decision making and diagnosis simpler and faster. The most common noise sources are power line interference and baseline wandering. This article discusses different filtering techniques used to denoise the ECG signals. Electrocardiogram signals were downloaded from the MIT-BIH Arrhythmia Database. The MIT-BIH Database was the first set of standard test materials that is generally available to evaluate arrhythmia detection. To remove baseline wander, 4 filters were designed. The filters are a fourth-order high-pass Butterworth filter, a second-order finite impulse response Hamming window, an finite impulse response rectangular window with length L, and an finite impulse response Hanning window. To extract the power line interference (60 Hz), 4 filters were designed: a second-order digital bandpass Butterworth filter, a second-order finite impulse response filter, a Chebyshev filter, and an finite impulse response notch filter with Hanning window. Finally, 5 parameters were used to evaluate filter performance; the parameters are frequency response, phase response, average filter delay (group delay), phase delay, and signal-to-noise ratio. The results show that, for baseline wander filters, a fourth-order high-pass Butterworth filter removes more noise and has no time delay. Power line interference filters have the same signal-to-noise ratio approximately.

Numerical Short-Open-Load (SOL) Calibration Technique for Accurate Extraction of Electrically-Small Planar/Non-Planar Microstrip-Line Circuits

This article presents a numerical short-open-load (SOL) calibration technique for accurate extraction of electrically small planar/nonplanar microstrip-line (MSL) circuits and elements in the interface of 3-D full-wave algorithm or simulator. An additional matched-load condition is established at the reference plane and employed in the whole calibration process. In comparison with the traditional short-open calibration (SOC) method, the proposed SOL technique implemented in the interface of software does not inquire prior simulation of the internal current/voltage at the reference plane of two calibration standards but only needs to know the external port impedances of three calibration standards. After the description of entire extraction process, a few typical electrically small planar circuits, such as MSL open-end and step discontinuities, are first numerically deembedded, and their extracted circuit parameters are evidently confirmed with other published ones. Then, a nonplanar structure of a vertically placed shorting pin in the middle of MSL is studied with different sizes and positions to effectively extract the circuit parameters in the two presented equivalent models. Finally, a third-order Chebyshev filter is designed with pin-loaded MSL structures. Its frequency response is synthesized on the proposed SOL method to validate the correctness of the extracted circuit parameters and further demonstrate the usefulness of this method in synthesis design of electrically large microwave circuits. Good agreement among the filtering frequency responses from equivalent circuit model, full-wave simulation, and measurement has well revealed that the proposed SOL method is indeed accurate in numerical extraction of circuit elements and efficient in synthesis design of an entire circuit with prescribed specifications.

Synthesis of wideband bulk acoustic wave coupled resonator filter combined with lumped components

SummaryA novel wideband bulk acoustic wave (BAW) coupled resonator filter (CRF) combined with external lumped inductors and capacitors is proposed. The filter synthesis method based on the Butterworth–van Dyke (BVD) model of CRF (CRF‐BVD) is also presented. To improve the synthesis accuracy, the CRF‐BVD model is modified and the CRF configuration with a single rather than the traditional multiple coupling layer is adopted in this paper. By establishing equivalence relationships between the modified CRF‐BVD model and the filter prototype synthesis network, exact CRF dimensions are solved through a set of equations without any further parameters tuning. The proposed method exhibits a maximum 37.4% (FBW) for a Chebyshev filter with 9.4‐dB return loss, which overcomes the narrowband limitation of regular BAW filters with FBW below 5%. To demonstrate the synthesis procedure, an n77 band filter with 3.723‐GHz center frequency and 24.2% FBW is designed and simulated. Good agreements are obtained among the simulation results of the prototype synthesis network, the modified CRF‐BVD model, and the co‐simulations of physical model based on the finite element method (FEM) and the CMOS 130‐nm technology.

Realization of Seventh-Order Chebyshev Active Low-Pass Filter

Background: CCCII implementation of the classic seventh-order Chebyshev filter is relatively rare. This work is a supplement to it. Methods: By a floating negative simulating resistance using single the second generation current-controlled conveyor (CCCII), we design a new current buffer to employ one CCCII and one multiple output CCCII (MOCCCII), and a new grounded MOCCCII-employed the frequency-dependent negative resistance (FDNR). Moreover, by employing a classic seventh-order Chebyshev passive filter as a prototype and utilizing adjoint network theory, a seventh-order Chebyshev active low-pass filter is realized through applying the Bruton transform, frequency and impedance scaling technique, FDNR, and component replacement method. The filter employs only grounded capacitors and nine CCCIIs, and its the performance can be controlled through adjusting bias currents of the CCCIIs. Results: The designed circuit is simulated with Multisim, which shows that the filter is correct and effective. Conclusion: A seventh-order Chebyshev active low-pass filter with Amax=0.5 dB and fc=10 kHz, is realized.

Optimization design of fractional‐order Chebyshev lowpass filters based on genetic algorithm

AbstractFractional‐order filters have received extensive attention from international scholars because of their greater design freedom and continuously stepped stopband attenuation rate. Based on genetic algorithm (GA), this paper proposes an optimum design approach for fractional‐order Chebyshev lowpass filters that meet design specifications. The fractional order and ripples attenuation of the normalized Chebyshev lowpass filter are calculated according to specifications, the integer order in the Chebyshev polynomial is replaced with the calculated fractional order, and then the fractional‐order Chebyshev polynomial is substituted into the magnitude response of the normalized Chebyshev lowpass filter along with the ripples attenuation to achieve the ideal response. The transfer function parameters of a fractional‐order filter are optimized using GA to make the magnitude response approximate the ideal response described above. This completes the optimized design of a fractional‐order Chebyshev filter that meets specifications. Given three different sets of design specifications, the fractional‐order Chebyshev filter designed using the proposed method is compared with one designed by another method in the literature. Finally, design examples are presented, stability analysis and Pspice simulations are performed, and an actual circuit is constructed to illustrate the effectiveness of the proposed method.

3-D Printing Quantization Predistortion Applied to Sub-THz Chained-Function Filters

This paper investigates physical dimension limits associated with the low-cost, polymer-based masked stereolithography apparatus (MSLA) 3-D printer, with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$50 ~\mu \text{m}$ </tex-math></inline-formula> pixels defining the minimum print feature size. Based on the discretization properties of our MSLA 3-D printer, multi-step quantization predistortion is introduced to correct for registration errors between the CAD drawing and slicing software. This methodology is applied to G-band <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5^{th}$ </tex-math></inline-formula> order metal-pipe rectangular waveguide filters, where the pixel pitch has an equivalent electrical length of 8.5° at center frequency. When compared to the reference Chebyshev filter, our chained-function filter exhibits superior S-parameter measurements, with a low insertion loss of only 0.6 dB at its center frequency of 182 GHz, having a 0.9% frequency shift, and an acceptable worst-case passband return loss of 13 dB. Moreover, with measured dimensions after the 3-D printed parts have been commercially electroplated with a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$50 ~\mu \text{m}$ </tex-math></inline-formula> thick layer of copper, the re-simulations are in good agreement with the S-parameter measurements. For the first time, systematic (quantization) errors associated with a pixel-based 3-D printer have been characterized and our robust predistortion methodology has been successfully demonstrated with an upper-millimeter-wave circuit. Indeed, we report the first polymer-based 3-D printed filters that operate above W-band. As pixel sizes continue to shrink, more resilient (sub-)THz filters with ever-higher frequencies of operation and more demanding specifications can be 3-D printed. Moreover, our work opens-up new opportunities for any pixel-based technology, which exhibits registration errors, with its application critically dependent on its minimum feature size.