Filter Function Research Articles

A Flux Reconstruction Stochastic Galerkin Scheme for Hyperbolic Conservation Laws

The study of uncertainty propagation poses a great challenge to design high fidelity numerical methods. Based on the stochastic Galerkin formulation, this paper addresses the idea and implementation of the first flux reconstruction scheme for hyperbolic conservation laws with random inputs. High-order numerical approximation is adopted simultaneously in physical and random space, i.e., the modal representation of solutions is based on an orthogonal polynomial basis and the nodal representation is based on solution collocation points. Therefore, the numerical behaviors of the scheme in the (physical-random) phase space can be designed and understood uniformly. A family of filters is developed in multi-dimensional cases to mitigate the Gibbs phenomenon arising from discontinuities in both physical and random space. The filter function is switched on and off by the dynamic detection of discontinuous solutions, and a slope limiter is employed to preserve the positivity of physically realizable solutions. As a result, the proposed method is able to capture the stochastic flow evolution where resolved and unresolved regions coexist. Numerical experiments including a wave propagation, a Burgers’ shock, a one-dimensional Riemann problem, and a two-dimensional shock-vortex interaction problem are presented to validate the current scheme. The order of convergence of the high-order scheme is identified. The capability of the scheme for simulating smooth and discontinuous stochastic flow dynamics is demonstrated. The open-source codes to reproduce the numerical results are available under the MIT license (Xiao et al. in FRSG: stochastic Galerkin method with flux reconstruction. https://github.com/CSMMLab/FRSG, (2021). https://doi.org/10.5281/zenodo.5588317).

A Novel Compact Filtering Antenna for 5.0-GHz WLAN Communication System

The proposed antenna presents a microstrip filter antenna with both filter out-of-band rejection characteristics and antenna radiation characteristics for WLAN communication system. The antenna consists of four U-shaped microstrip resonators, one Γ-shaped antenna, and one parallel coupling line. The Γ-shaped antenna has the filtering function as the last order resonator, and the parallel coupling line integrates the filter and antenna as the conductance converter. After simulation and test, the results show that the center frequency of the filter antenna is 5.25 GHz, the fractional bandwidthis 8.0% (5.0 − 5.42 GHz), the in-band gain changes smoothly, the maximum in-band gain is 3.059 dBi, the gain at 150 MHz outside the passband rapidly decreases to 10.0 dBi, and the overall out-of-band gain drops to below −24 dBi. The filter antenna has a simple structure and thin substrate, which optimizes the overall size of the filter and antenna, reduces the transmission loss between them, and is applicable to the RF front-end of wireless communication systems.

UAV data collection parameters impact on accuracy of Scots pine stand mensuration

A wide range of UAV systems used for forest research requires unified approaches to data collection. The research aims to determine the optimal parameters for UAV data collection to obtain accurate information about stands, considering the cost of resources for its collection. The process of collecting remote sensing data consisted of nine combinations divided into three levels of overlap and three levels of spatial resolution (survey altitude) and changing the degree of filtering of a dense point cloud during image processing. Individual tree detectingin the stand was performed using the R programming language and the ForestTools package. The results of the assessment of the dependence of the radius of tree crowns on their height were used to set the parameters of the variable filter function for finding local maxima for Scots pine stands. Errors in the identification of treetops were estimated using the F-score. The identified heights were compared with the field data of the ground survey. The proportion of classified digital elevation model DEM in the dense point cloud was reduced from the total area of the test site using images of 4.1 cm/pix spatial resolution (150 m survey altitude). The study presents the results of assessing the impact of spatial resolution of optical images collected from UAVs and their overlap on the results of measurements of stands parameters. It is determined that a photogrammetric survey with input images with a longitudinal overlap of less than 90% is not appropriate for the study of forest areas due to the impossibility of aligning all images. The results of the assessment of tree accounting in the stand showed that it is most appropriate to use images with a spatial resolution of up to 3.3 cm/pix (120 m survey altitude), otherwise, the proportion of missed treetops increases. Reducing the spatial resolution of remote sensing data leads to an increase in errors in determining the height of individual trees, and the average heights of the experimental plots had the same trend. Given the combination of the assessed factors, it is not recommended to use images with a spatial resolution of more than 3.3 cm/pix for forestry research due to increased errors in the individual tree detection and tree height determination. The results obtained can be used to select data collection parameters for research on Scots pine stands to assess their growing stock and phytomass

Symmetrical Components Digital Filters for Microprocessor-Based Protection Input Signals

In microprocessor protections, measuring bodies are used that react to individual symmetrical components of signals or a combination of them. This makes the corresponding protection devices more sensitive. Of all the varieties of digital filters of symmetrical components, filters of the negative and zero sequences are mainly used. As for the known algorithms of their software implementation, it is advisable to use filters that form orthogonal components of the required sequence from orthogonal components of phase or phase-to-phase values of signals. Digital Fourier filters, characterized by inertia, are used as formers of the latter. For this reason, their transient modes are accompanied by the appearance of a dynamic error, which can significantly affect the functioning of filters of symmetrical components, worsening their properties. A significant reduction in this effect can be achieved by using shapers with correction of dynamic errors to isolate the orthogonal components of the input signals. They are based on non-recursive digital Fourier filters, the orthogonal components of which are subjected to software correction processing in order to obtain equivalent components characterized by fast-fading dynamic amplitude errors. Correction of the dynamic phase error is realized in the process of obtaining the resulting orthogonal components, which are a combination of Fourier components and calculated ones that have been estimated according to them. Based on the information about the amplitudes and current phases of the signals contained in the equivalent and resultant components, respectively, the resulting orthogonal components are formed, differing in minimal amplitude and phase errors in transient modes. According to these components, the orthogonal components of the signal of the negative and zero sequences in the corresponding filter are calculated. In the dynamic modeling environment of MATLAB-Simulink-SimPowerSystems, a digital model is implemented, which includes a power system, a three-phase group of current transformers, a load, a short-circuit block, as well as models of negative and zero sequence filters. The study of the functioning of these filters was carried out using two types of test actions, viz. a three-phase system of sinusoidal signals and a three-phase system of signals close to real secondary currents in short circuits. The results of the research have demonstrated that the developed digital filters of the negative and zero sequences have 1.1–1.4 times higher performance as compared with similar Fourier filters accepted as reference and that they are distinguished by improved magnitudes of dynamic indicators.

Analysis of PM2.5 Characteristics in Yancheng from 2017 to 2021 Based on Kolmogorov–Zurbenko Filter and PSCF Model

Based on the hourly monitoring data including meteorological elements and PM2.5 mass concentration in Yancheng from 2017 to 2021, PM2.5 mass concentration variations, influencing factors and source apportionment were studied by the Kolmogorov–Zurbenko filter and Potential Source Contribution Function Analysis (PSCF) method. The results showed that the mass concentration of PM2.5 in Yancheng showed a decreasing trend from 2017 to 2021, with a decline rate of about 33.8% (2017, 44.79 ± 31.22 μg/m3; 2021, 29.66 ± 21.69 μg/m3); the visibility increased by 18.4% (2017, 11.69 ± 6.46 km; 2021,13.8 ± 6.24 km), which is mainly related to emission reduction measures in China. The mass concentration of PM2.5 has significant seasonal variation characteristics, with the highest in winter, reaching 60.61 μg/m3, and the lowest in summer, only 23.11 μg/m3. The diurnal variation of PM2.5 showed a unimodal distribution, and concentration difference is obvious under the influence of land–sea breeze (36.60 μg/m3, easterly wind; 43.57 μg/m3, westerly wind). Meteorological factors have an important impact on the mass concentration of PM2.5, which fluctuates with seasons. It is calculated to have a good fitting relationship between the visibility and PM2.5 concentration, and the correlation decreases with the increase in humidity (−0.71 ~ −0.41). The relatively clean atmosphere under high humidity conditions is also prone to the obstruction to vision. The corresponding PM2.5 concentration varies significantly under different wind directions and wind speeds in Yancheng, and high values mainly come from the northwest–southeast–southwest direction. The potential source regions in autumn are mainly distributed in southwestern Jiangsu and northwestern Zhejiang; the potential source regions in winter are mainly located in southwestern Jiangsu, southern Anhui and northern Jiangxi.

Multifunctional terahertz device based on a VO2-assisted metamaterial for broadband absorption, polarization conversion, and filtering

This paper proposes a multifunctional terahertz device based on VO2 with a simple structure that needs only one step lithography. The designed device can realize broadband absorption, reflective broadband cross-polarization conversion, reflective linear-to-circular polarization conversion, transmissive narrowband cross-polarization conversion, and filtering under different working conditions. When VO2 is in a metallic state, the device can perform two different functions depending on the direction of the incident wave. When the electromagnetic wave is a forward incident, the device is a broadband absorber in the frequency range from 3.53 THz to 9.68 THz with a corresponding absorption efficiency above 90% and a relative bandwidth of 93%. When the electromagnetic wave is a backward incident, the device can work as a reflective broadband cross-polarization converter in the frequency range from 0.77 THz to 1.79 THz with a polarization conversion rate greater than 97% and a relative bandwidth of 80% and a reflective linear-to-circular polarization converter at 0.66 THz and 1.86 THz. While for VO2in the insulating state, the device exhibits the transmissive narrowband cross-polarization converter with polarization conversion rate greater than 90% at 1.32 THz and the function of the transmissive narrowband filter with transmittance more than 60% at 1.84 THz for both forward and backward incident waves. This multifunctional device may have great potential in miniaturized terahertz systems.

Optimally Band-Limited Noise Filtering for Single-Qubit Gates

We introduce a quantum control protocol that produces smooth, experimentally implementable control sequences optimized to combat temporally correlated noise for single-qubit systems. The control ansatz is specifically chosen to be a functional expansion of discrete prolate spheroidal sequences, a discrete time basis known to be optimally concentrated in time and frequency, and quite attractive when faced with experimental control hardware constraints. We leverage the filter function formalism to transform the control problem into a filter design problem, and show that the frequency response of a quantum system can be carefully tailored to avoid the most relevant dynamical contributions of noise processes. Using gradient ascent, we obtain optimized filter functions and exploit them to elucidate important details about the relationship between filter function design, control bandwidth, and noise characteristics. In particular, we identify regimes of optimal noise suppression and, in turn, optimal control bandwidth directly proportional to the size of the frequency bands where the noise power is large. In addition to providing guiding principles for filter design, our approach enables the development of controls that simultaneously yield robust noise filtering and high-fidelity single-qubit logic operations in a wide variety of complex noise environments.

Empirical mode decomposition and power spectrum filtering for detection of frequency channels related to multi-scale geochemical anomalies: Metal exploration targeting in Moalleman district, NE Iran

Geochemical anomaly patterns for metal exploration targeting usually reveal non-stationarity due mainly to the non-linear synthesis of ore-forming processes. The spectrum–area (S–A) multifractal filtering and the bidimensional empirical mode decomposition (BEMD) are robust methodologies for detecting geochemical anomalies with different scaling properties. The former portrays the generalized scale invariance characteristics of a geochemical image in the two-dimensional Fourier frequency domain. It relies on estimating scaling exponents of power-law functions in the spectral energy density plane to design filter functions that amplify a geochemical signal in specific frequency channels. The BEMD decomposes a geochemical image into a number of bidimensional intrinsic mode functions (BIMFs). It represents the spatial–frequency–energy distribution of a given image that suits non-stationary geochemical signals arising from non-linear Earth systems. This paper gauges the relevance of BEMD and S–A in signalizing frequency channels that correspond to regional- and local-scale geochemical anomalies through a comparative experiment in the Moalleman district, NE Iran. The BEMD filtered the multi-element anomaly map adaptively into a set of BIMFs (BIMF1, BIMF2, and BIMF3) and a residual signal, in order of decreasing frequency, yielding geochemical patterns with scaling characteristics from local to regional. The S–A model filtered the multi-element anomaly map into very high, high, and low frequency channels that characterize noise signatures and geochemical anomalies associated with local and regional ore-forming processes, respectively. The results indicate that the high frequency channel derived from the BEMD filtering (i.e., BIMF1) can portray more effectively local-scale metal-vectoring anomalies distributed at/around ore-controlling faults/fractures. However, the low frequency channel yielded by S–A filtering has enhanced effectively geochemical anomaly architectures that were developed through regional metallogenesis. Therefore, we considered the local-scale geochemical anomalies (i.e., BIMF1) to delimit metal-vectoring targets, whereby four exploration priorities were defined as new areas for further metal prospecting within the study area.

Nuclear pair electron spin echo envelope modulation

The interaction of electron spins with homonuclear spin pairs in their vicinity is one of the dominating mechanisms of electron spin echo decay at low temperature and low concentration. Here, we study this mechanism using established concepts of electron spin echo envelope modulation (ESEEM). We obtain analytical expressions for the Hahn echo, the refocused echo, the stimulated echo, and Carr–Purcell pulse trains with small numbers of π pulses. Hahn echo decay is well approximated by the product of nuclear pair ESEEM functions. The same approximation can explain dependence of stimulated echo decay on the first interpulse delay and provides reasonable time scale estimates for decay of Carr–Purcell echos after an odd number of π pulses. Carr–Purcell echoes after an even number of π pulses are rather sensitive to correlations within larger nuclear spin clusters. Approximations improve for both odd and even numbers of π pulses by factorising the nuclear spin bath into disjoint clusters, provided that modulation due to pairs of spins belonging to different clusters is considered in addition to cluster modulation. The analytical ESEEM expressions for the Hahn echo and the Carr–Purcell echo after two π pulses have the same mathematical form as the filter functions of these sequences of spin noise spectroscopy. This coincidence provides a computationally very efficient way of predicting Hahn echo decay induced by homonuclear spin pairs. The analytical pair product approximation predicts the previously observed (Bahrenberg et al., 2021) increase of the refocused echo amplitude when one refocusing time is incremented and other one is fixed but longer. In contrast, the spin-noise concept fails to predict this effect.

Digital Ethnic Enclaves: Mate Preferences and Platform Choices Among Chinese Immigrant Online Daters in Vancouver

In light of the growing racialized immigrant population in Canada and advances in dating technologies, this study examines Chinese immigrants' partner preferences and mate selection processes through the lens of online dating. We draw on in-depth interviews with 31 Chinese immigrants who have used online dating services in Metro Vancouver to search for different-sex partners. Chinese immigrant online daters show strong preferences for dating Chinese. They emphasize permanent residency status and similarity in age at arrival when evaluating potential partners. Given their preferences, Chinese immigrants strategically choose the dating platforms they primarily use. Men exhibit higher selectivity in their preferences and choices of platforms. Notably, platforms catering to Chinese users create "digital ethnic enclaves" where Chinese immigrant daters congregate. The findings illuminate the intersection of race, gender, immigrant status, and age at arrival in shaping divergent experiences of mate selection and immigrant assimilation in the digital era.

Capsazepine (CPZ) Inhibits TRPC6 Conductance and Is Protective in Adriamycin-Induced Nephropathy and Diabetic Glomerulopathy.

Reactive oxygen species (ROS), which excessively arise in diabetes and systemic inflammatory diseases, modify cellular lipids and cellular lipid composition leading to altered biophysical properties of cellular membranes. The impact of lipid peroxidation on transmembrane signaling routes is not yet well studied. The canonical transient receptor potential channel 6 (TRPC6) is implicated in the pathogenesis of several forms of glomerular diseases. TRPC6 is sensitive to membrane stretch and relies on a distinct lipid environment. This study investigates the effect of oxidative alterations to plasma membrane lipids on TRPC6 activity and the function of the glomerular filter. Knockout of the anti-oxidative, lipid modifying enzyme paraoxonase 2 (PON2) leads to altered biophysical properties of glomerular epithelial cells, which are called podocytes. Cortical stiffness, quantified by atomic force microscopy, was largely increased in PON2-deficient cultured podocytes. PON2 deficiency markedly enhanced TRPC6 channel currents and channel recovery. Treatment with the amphiphilic substance capsazepine in micromolar doses reduced cortical stiffness and abrogated TRPC6 conductance. In in vivo studies, capsazepine reduced the glomerular phenotype in the model of adriamycin-induced nephropathy in PON2 knockout mice and wildtype littermates. In diabetic AKITA mice, the progression of albuminuria and diabetic kidney disease was delayed. In summary, we provide evidence that the modification of membrane characteristics affects TRPC6 signaling. These results could spur future research to investigate modification of the direct lipid environment of TRPC6 as a future therapeutic strategy in glomerular disease.

Designing Filter Functions of Frequency-Modulated Pulses for High-Fidelity Two-Qubit Gates in Ion Chains

High-fidelity two-qubit gates in quantum computers are often hampered by fluctuating experimental parameters. The effects of time-varying parameter fluctuations lead to coherent noise on the qubits, which can be suppressed by designing control signals with appropriate filter functions. Here, we develop filter functions for M{\o}lmer-S{\o}rensen gates of trapped-ion quantum computers that accurately predict the change in gate error due to small parameter fluctuations at any frequency. We then design the filter functions of frequency-modulated laser pulses, and compare this method with pulses that are robust to static offsets of the motional-mode frequencies. Experimentally, we measure the noise spectrum of the motional modes and use it for designing the filter functions, which improves the gate fidelity from 99.23(7)% to 99.55(7)% in a five-ion chain.

Nestedcv: an R package for fast implementation of nested cross-validation with embedded feature selection designed for transcriptomics and high-dimensional data.

Although machine learning models are commonly used in medical research, many analyses implement a simple partition into training data and hold-out test data, with cross-validation (CV) for tuning of model hyperparameters. Nested CV with embedded feature selection is especially suited to biomedical data where the sample size is frequently limited, but the number of predictors may be significantly larger (P ≫ n). The nestedcv R package implements fully nested k × l-fold CV for lasso and elastic-net regularized linear models via the glmnet package and supports a large array of other machine learning models via the caret framework. Inner CV is used to tune models and outer CV is used to determine model performance without bias. Fast filter functions for feature selection are provided and the package ensures that filters are nested within the outer CV loop to avoid information leakage from performance test sets. Measurement of performance by outer CV is also used to implement Bayesian linear and logistic regression models using the horseshoe prior over parameters to encourage a sparse model and determine unbiased model accuracy. The R package nestedcv is available from CRAN: https://CRAN.R-project.org/package=nestedcv.

Demodulation of optical fiber sensors by MEMS tunable filter

An optical fiber sensor (OFS) demodulation system based on Micro-Electro-Mechanical System (MEMS) tunable filter (MTF) has been proposed and demonstrated in this study. By scanning the MTF, the acquired OFS curves were considered as the convolution of the tunable filter function and the real OFS spectrum. However, the wavelength setting error of the MTF significantly limited the measurement accuracy of the proposed demodulation system. To solve the problem, dual etalons with complementary phase shifts were adopted to calibrate the MTF in real time. For demonstration, a fiber Bragg grating and an open cavity Fabry-Pérot sensor were successfully demodulated by the MTF. Experimental results indicated that the measurement error of the MTF demodulator was improved from ±31 pm to ±3 pm, with the sensing resolution of 0.1 °C and 0.01 MPa, better than traditional grating-based spectrometers..

Optimizing nonadiabatic geometric quantum gates against off-resonance error in a silicon-based spin qubit

Geometric quantum gates are performed by using the geometric phase, making them particularly robust to the pulse amplitude error. However, in many systems, such as the silicon-based spin qubits, the off-resonance error is the dominant noise, which can cause dephasing and is always difficult to deal with for a geometric gate. Thus how to combat with the off-resonance error is very significant for the application of the geometric gates. A recent work [S. Li and Z.-Y. Xue, Phys. Rev. Appl. 16, 044005 (2021).] revealed that by inserting two $\ensuremath{\pi}$ pulses into the evolution paths, the holonomic quantum gate is effective to suppress the pulse amplitude error, however, it is still useless for combating the off-resonance error. Inspired by this work, we combine using the techniques of dynamical correction and path design. Surprisingly, we find that, by picking up a specific evolution path inserted by only a $\ensuremath{\pi}$-pulse, the obtained optimized geometric gate is robust to the off-resonance error, assuming the noise is static. Further, by calculating the filter function considering the realistic $1/f$-type noise in silicon, the related results show that the performance of the optimized geometric gate can also surpass both the conventional geometric gate and the naive dynamical gate constructed without using the geometric phase. Our results indicate dynamical correction is a powerful tool to improve the geometric quantum computation to achieve a high-fidelity quantum gate in silicon.

Advanced detection for faults in front of coal mine roadways using seismic scattered waves

An unsuspected fault in front of a roadway is a key hidden disaster-causing factor that can result in major accidents in coal mines; therefore, the accurate advanced detection of faults is important for the safe coal mining. However, existing seismic advanced detection methods are difficult to execute because of the narrow space limits of roadways. Therefore, on the basis of the generalized theory of scattered waves and the scenes of advanced detections in roadways, we construct a new and superior advanced detection method using scattered waves. In this method, a virtual equivalent survey line perpendicular to the roadway strike is established to reconstruct scattered wave records and a polarization filter function is built to dynamically and accurately extract different types of scattered waves in the target area. An analysis of numerical simulations indicates the following. 1) The true reflection position of a fault in front of a rock roadway is closely related to its dip, and the proposed method can accurately extract and image the scattered multiwaves generated at the true reflection position to identify the inclination of the fault, which can avoid the arc-shaped illusion problem caused by the false reflection signal. 2) Under the condition that the scattered waves at the breakpoint of a broken coal seam are significantly disturbed by the coal seam waveguide effect, the fault inclination of the coal roadway can be determined by the joint imaging and interpretation on the reflected channel wave of the hanging wall breakpoint and the scattered wave of the footwall breakpoint. A field study was performed to verify the effectiveness of the proposed method. The results indicate that this method can effectively identify the position and inclination of faults and provide an effective new means for the accurate detection of faults in front of coal mine roadways.

A filtering monotonization approach for DG discretizations of hyperbolic problems

We introduce a filtering technique for Discontinuous Galerkin approximations of hyperbolic problems. Following an approach already proposed for the Hamilton-Jacobi equations by other authors, we aim at reducing the spurious oscillations that arise in presence of discontinuities when high order spatial discretizations are employed. This goal is achieved using a filter function that keeps the high order scheme when the solution is regular and switches to a monotone low order approximation if it is not. The method has been implemented in the framework of the $deal.II$ numerical library, whose mesh adaptation capabilities are also used to reduce the region in which the low order approximation is used. A number of numerical experiments demonstrate the potential of the proposed filtering technique.

Multifunctional Bandpass Filter/Displacement Sensor Component

This paper presents the design and realization of a multifunctional bandpass-filter/displacement-sensor using an edge-coupled microstrip bandpass filter loaded by a pair of split ring resonators (SRRs). It is shown that while the structure acts as a bandpass filter at its operating frequency, the phase of the reflection coefficient from a movable loading resonator at the resonance frequency of the resonator can be used for displacement sensing. With this aim, and to avoid any interference with the filter functionality, the resonance frequency of the SRRs is chosen within the stopband of the bandpass filter, where all the input signal is reflected back to the input port. Therefore, moving the loading resonators does not have any adverse effect on the filtering performance. To validate the concept, a fifth-order Chebyshev bandpass filter with a feed line loaded with a pair of SRRs is designed and the numerical evaluation of the proposed multifunctional bandpass-filter/displacement-sensor is provided. The proposed multifunctional component is also validated through fabrication and measurement. It is shown that the proposed component has a sensitivity of 8°/mm at the designed frequency of SRRs. However, the sensitivity can be increased by scaling the SRRs to resonate at a higher frequency within the upper stopband of the filter.

A Real-Time Electronically Tunable All-MOS Universal Biquadratic Voltage-Mode Filter

— In this paper, an electronically tunable universal biquadratic voltage-mode filter that is based only on MOS transistors is proposed. Configuration of the proposed filter is simple and there is no need to use component matching. Since the proposed filter contains only MOS transistors, it is very suitable for implementation in system-on-chip (SoC) applications. The cutoff frequency of the lowpass (LP) and highpass (HP) filters as well as the center frequency and the bandwidth of the bandpass (BP) and bandstop (BS) filters can be controlled either in a continuous range or in a discrete manner by means of a digital control word. Besides, the filter type can be changed during the real time by an appropriate code. Operation of all the filtering functions are verified by simulation using the Berkeley predictive-technology models (BPTM) of the 130 nm complementary metal-oxide semiconductor (CMOS) technology with power-supply voltage, VDD, of 1.2 V. The proposed filter is analyzed quantitatively, and the effects of the total-harmonic distortion (THD), noise, process, voltage and temperature (PVT) variations are also investigated. The average power consumption of the LP, HP, BP, BS, and allpass (AP) filters are found to be 30, 118, 74, 118, and 30 (all in µW). The price paid for all these advantages is more sensitivity to process variations for the lowpass filter.

Arbitrary Termination Complex Impedances Tunable Bandpass Filter Using Single and Dual-Mode Resonators

This paper presents a design of microstrip line tunable bandpass filter (BPF) with a transmission zero (TZ) that can accommodate arbitrarily terminated input and output port impedances ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z_s</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Z_L</i> ≠ 50 Ω). We extracted a new coupling matrix to design the proposed tunable BPF and presented intuitive circuit-level implementation using a single dc-bias controlled single and dual-mode resonators. The proposed tunable BPF integrates the function of tunable filter and matching network into a single circuit. To validate the design, three filter prototypes with different input and output port termination impedances (filter A: 50-to-50 Ω, filter B: 20-to-50 Ω, and filter C: (25+j10)-to-50 Ω) are manufactured and their performances were measured. The experimental results are consistent with the simulation showing that the passband frequency of the BPF can be tuned from 1.65 GHz to 2.08 GHz (23.06%) with the insertion loss variation from 3.40 dB to 4.69 dB. The proposed tunable BPFs achieved frequency selectivity characteristics by locating the TZ at a lower stopband. The proposed arbitrary terminated tunable BPF can allow direct connection between power amplifier (PA)/low noise amplifier (LNA) and antenna without extra matching networks, resulting in smaller circuit size and can enhance overall performance of RF front-end.