Filter Transfer Function Research Articles

Frequency-dependent synaptic plasticity model for neurocomputing applications

In neuroscience, there is substantial evidence that suggests temporal filtering of stimulus by synaptic connections. In this paper, a novel frequency-dependent plasticity mechanism (FDSP) for neurocomputing applications is presented. It is proposed that synaptic junctions could be used to perform bandpass filtering on the input stimulus. The unique transfer function of a bandpass filter replaces the conventional weight value associated with synaptic connections. The proposed model has been simulated and rigorously tested with standard machine learning benchmarks such as XOR and multivariate IRIS dataset while utilising minimum resources. The proposed model offers a unique advantage and has the potential to overcome the burden of hidden layer neurons from the network. Exclusion of hidden layer from the network significantly reduces the size of the network and hence the computational effort required for classification tasks. The proposed FDSP mechanism allows for complete analogue system design with a frequency multiplexed communication scheme. The main goal of this study is to establish frequency-dependent plasticity as an alternative to existing time-domain-based techniques. The proposed method has a number of applications in neurocomputing, low power IoT devices and compute-efficient deep convolutional neural networks (DCNNs).

Frequency-dependent synaptic plasticity model for neurocomputing applications

In neuroscience, there is substantial evidence that suggests temporal filtering of stimulus by synaptic connections. In this paper, a novel frequency-dependent plasticity mechanism (FDSP) for neurocomputing applications is presented. It is proposed that synaptic junctions could be used to perform bandpass filtering on the input stimulus. The unique transfer function of a bandpass filter replaces the conventional weight value associated with synaptic connections. The proposed model has been simulated and rigorously tested with standard machine learning benchmarks such as XOR and multivariate IRIS dataset while utilising minimum resources. The proposed model offers a unique advantage and has the potential to overcome the burden of hidden layer neurons from the network. Exclusion of hidden layer from the network significantly reduces the size of the network and hence the computational effort required for classification tasks. The proposed FDSP mechanism allows for complete analogue system design with a frequency multiplexed communication scheme. The main goal of this study is to establish frequency-dependent plasticity as an alternative to existing time-domain-based techniques. The proposed method has a number of applications in neurocomputing, low power IoT devices and compute-efficient deep convolutional neural networks (DCNNs).

A 6-nW 0.0013-mm² ILO Bandpass Filter for Time-Based Feature Extraction

Event-driven wake-up sensing methods are emerging functions necessary to increase the autonomy of power-hungry multisensors Internet-of-Things applications. To decrease the power consumption of feature extraction function essential for event-based wake-up, this letter introduces a novel injection-locked oscillator (ILO) filter architecture, to be used in a time-based filter bank for feature extraction. After reviewing the phase shifter property and dynamic behavior of a switched-capacitor injected relaxation ILO, ILO high-pass and bandpass filter designs and transfer functions are presented, resulting in the implementation of a four-channel ILO filter bank in a 65-nm CMOS technological node. Experimental measurements demonstrate the ILO bandpass filtering function works at a power consumption of 6 nW, an active area of 0.0013 mm2 and an output dynamic range of 46 dB. The filter bank average power consumption reaches 3 nW/channel for a total bandwidth from 130 Hz to 5.5 kHz.

Spectral Graph Based Vertex-Frequency Wiener Filtering for Image and Graph Signal Denoising

In this article, we propose and develop a spectral graph based vertex varying Wiener filtering framework in the joint vertex-frequency domain for denoising of graph signals defined on weighted, undirected and connected graphs. To this end, we first extend the Zadeh time-frequency filter concept to graph signals and obtain vertex-frequency transfer function of the proposed Wiener filter by transforming its vertex varying impulse response that minimizes the mean square error between original and recovered signals. To facilitate the derived Wiener filter, we present a detailed derivation of a recently proposed graph Rihaczek vertex-frequency signal distribution (GRD) so as to match the structure of the proposed graph Zadeh filter, based on a graph translation operator defined by generalized convolution with a delta signal. We express the filter transfer function in terms of this graph transform of the original, noiseless signal. The form of the obtained Wiener filter is, interestingly, different than those of time-frequency Wiener filters prevalent in the classical signal processing. We also investigate the invertibility of the employed GRD. Assuming that the original graph signal of interest can be viewed as deterministic, we propose two algorithms to implement the proposed vertex-frequency Wiener filter from a single realization of a noisy, input signal. We derive mean and variance of the GRD of the noisy signal, since they are required in one of these algorithms. We apply proposed Wiener filter algorithms to denoise a standard set of images and three irregularly structured graph signals, and demonstrate their competitiveness with compared high performance denoising methods.

Відмовостійкий алгоритм ідентифікації бортової математичної моделі авіаційного двигуна ТВ3- 117 в складі його системи автоматичного управління

The subject matter of the article is TV3-117 aircraft engine and methods for monitoring and diagnosing its technical condition. The goal of the work is development of fault-tolerant algorithms for identification of the onboard mathematical model of the TV3-117 aircraft engine as part of its automatic control system in flight modes. The following tasks were solved in the article: recovering of lost information by an auto-associative neural network in case of a single sensor failure, recovering of lost information by an «optimal» auto-associative neural network in case of single sensor failures of the on-board control and diagnostic system, recovering of lost information by an auto-associative neural network and an on-board control and diagnostic system from the gas temperature registration sensor in front of the turbine compressor in case of failure. The following methods used are – substantiation of expediency of Kalman-filtration use in TV3-117 aircraft engine automatic control system, determination of Kalman filter transfer function, determination of algorithm of detection and localization of channel failure of two-channel sensor, determination of frequency characteristics of TV3-117 aircraft engine automatic control system, proof of equality of unit coefficient fault-tolerant filter unit . Conclusions: The frequency properties of the automatic control system of the aircraft engine TV3-117 are investigated, the equality of the unit of the gain of the developed fault-tolerant filtering unit and the absence of additional phase shifts introduced by the possible net delay due to the peculiarities of the implemented algorithms mathematical model. The absence of their influence on the stability of aircraft engine TV3-117 automatic control system is proved. Approbation of the developed algorithms showed that the average relative error in dynamics does not exceed 0.15 %, and in statics at the maximum expense – decreases to 0.01 % that corresponds to modern requirements of accuracy of algorithms of identification on a contour of dosing needle . Keywords: aircraft engine, neural network, Kalman filtering, failure detection and localization

Silicon Photonics High-Order Distributed Feedback Resonators Filters

High-order distributed feedback resonators realized in silicon-on-insulator technology for the implementation of high-performance integrated optical filters are reported. This approach combines design simplicity and flexibility in a compact footprint with filter transfer functions featuring a flat-top response, large out-of-band rejection of more than 40 dB, ultra-steep roll-off up to 1000 dB/nm, and unprecedented stopband-to-passband ratios up to 600 for high-index-contrast technology. Active control of the coupled cavities through local micro heaters is employed for optimizing the filter response and passband tuning. Exemplary implementations of a box-like transfer function filter with a bandwidth of 25 GHz and of a narrow linewidth 2 GHz filter realized with 6 th - and 3 rd -order filter designs, respectively, are presented.

Impedance Characteristics and Chip-Parasitics Extraction of High-Performance VCSELs

In order to analyze the physical limitations and develop highly performing vertical-cavity surface-emitting lasers (VCSELs), it is essential to have an in-depth understanding of their intrinsic laser dynamics. However, the high-speed performance of such devices is impaired by its extrinsic dynamic response associated with the VCSEL chip parasitics. A first-order low-pass filter transfer function is traditionally used to de-embed this parasitic part from the total VCSEL modulation response. However, this oversimplification results in large discrepancies between the modeled and the measured parasitic-network response, leading to a high level of uncertainty in the extracted circuit component values. Further, intrinsic parameters can only be gained to a frequency range, where the parasitic response is flat and de-embedding not critical. In this work, a novel advanced parasitic-network model that well describes the extrinsic behavior of high-performance VCSELs is reported. In this model, besides the standard parasitic elements, the contact-pads with their capacitance with frequency-dependent dielectric losses and their inductance are considered. Moreover, for this advanced parasitic-network model to reveal its full potential, a rigorous fitting methodology is also described in this work. This proposed novel model, along with the strict fitting procedure, accurately replicate the delicate $S_{{11}}$ data even at high-frequencies and enable the extraction of highly reliable circuit component values. This model can not only describe and model the parastitic chip response accurately but can be implemented to optimize the chip design, hence improving the parasitic bandwidth limitations in high-speed VCSELs.

A Compact Fully Passive Loop Filter-Based Continuous Time $\Delta\Sigma$ Modulator for Multi-Channel Biomedical Applications

For the first time, we present a generic, formal design and optimization method for a fully-passive loop filter based CTDSM. The presented method aims at the automatic design of compact, low energy and simple, fully passive CTDSM for multi-channel biomedical applications. The challenges involving high RC variations, low energy consumption and compactness for multi-channel applications necessitates automated design and optimization of the CTDSM. The proposed method uses a simple linear model to arrive at the loop filter transfer function and minimize the SNR degradation across RC corners while minimizing the area and power per channel. The method was implemented in Matlab and verified using Spectre simulations. For target ENOB of 9 bits and consumed energy of less than 60 fJ/conv a CTDSM was automatically designed using the proposed method and fabricated in standard 180 nm CMOS mixed mode technology. The CTDSM uses a fully passive second order modulator with the CIFF architecture eliminating active summer circuits. The measurement results show that the modulator achieves peak SNDR of 55.42 dB at 1V supply while consuming 61.2 fJ/conv and occupies an extremely small area of 0.068 mm2 making it the most compact reported CTDSM modulator among the low energy moderate resolution CTDSM.

Group delay equalisation of discrete Butterworth tan filters in the continuous domain

ABSTRACTA new optimisation method for equalising the group delay frequency response of the discrete transfer function of recursive digital filters, so-called tan filters, is presented in this paper. The method is based on an algorithm that is used for a stable all-pass filter approximation. Allpass filter acts as a group delay equaliser, with the purpose of equalising group delay of the discrete tan filter in a maximal flat sense. The algorithm relies on a set of simultaneous nonlinear equations. These set equations are derived directly from the flatness conditions of the equalised group delay response at the origin in the analogue -domain, in order to obtain the unknown coefficient values of the discrete allpass filter. The iterative method most widely used for solving set nonlinear equations and Symbolic Math Toolbox for Matlab features for finding numerical solutions are presented in detail.In the given examples, firstly a discrete Butterworth tan filter was designed by using transfer function poles in closed form. Secondly, the Butterworth tan filter was augmented with cascade connection of non-minimum phase all-pass discrete filter, in order for the group delay response of the whole filter to be equalised in a maximally flat sense.

Control System Design for 3x3 Processes Based on Effective Transfer Function and Fractional Order Filter

Designing of PI/PID controller with fractional order set point filter is proposed to achieve the improved performance of 3x3 processes. But the design of controller for such higher dimensional multivariable processes is too difficult task because of interaction involved between the process variables. So interaction must be taken into design consideration. In this method of design determines the interaction between the variables using RGA and RNGA methods and uses it in converting the multivariable processes into multiple single loops. The interaction problems between the loops are overcome by incorporating the decouplers in the control loops. Then, the Effective Transfer Function (ETF) has obtained to design PI/PID controller for each individual element as in single input processes. The fractional order filter is also added to improve the servo response of the processes. Hence, the proposed system improves the overall performance by minimizing the interaction effects due to set point variations. This method is also validate by using a case study.

Метод генерації гіперкомплексних числових систем для моделювання цифрових реверсивних фільтрів 4-го порядку

A digital filter is a digital system used to filter a discrete signal. It can be implemented either by software or by specialized equipment. The use of hypercomplex numbers for building digital filter structures can provide significant benefits. Digital filters with hypercomplex parameters have higher speed and better performance in terms of total parametric sensitivity. Although in previous works software filter of 3 th order structure synthesis algorithms were proposed, in this paper only software filter of 4 th order structure synthesis algorithms are considered. Studies have shown that the expression analysis method for the transfer function denominator norms of the hypercomplex filter allows you to effectively select the hypercomplex number system, which has all the necessary properties. It is shown that only quadriplex number system K and hypercomplex number system obtained by auto doubling of a double-number system W are suitable for the structures synthesis of fourth-order hypercomplex digital filters. These hypercomplex number systems allow to get a complete set of filter transfer function shift operator steps. On the other hand, they have isomorphic weakly filled hypercomplex number systems. Transition to such systems can significantly reduce the number of real operations during the filter operation time. In the work, all transformations and calculations in the hypercomplex domain were performed using the software module for hypercomplex calculations in the Maple computer algebra framework. This fact confirms the efficiency of this software module. Tabl.: 2. Refs: 17 titles.

Control System Design for 3x3 Processes Based on Effective Transfer Function and Fractional Order Filter

Designing of PI/PID controller with fractional order set point filter is proposed to achieve the improved performance of 3x3 processes. But the design of controller for such higher dimensional multivariable processes is too difficult task because of interaction involved between the process variables. So interaction must be taken into design consideration. In this method of design determines the interaction between the variables using RGA and RNGA methods and uses it in converting the multivariable processes into multiple single loops. The interaction problems between the loops are overcome by incorporating the decouplers in the control loops. Then, the Effective Transfer Function (ETF) has obtained to design PI/PID controller for each individual element as in single input processes. The fractional order filter is also added to improve the servo response of the processes. Hence, the proposed system improves the overall performance by minimizing the interaction effects due to set point variations. This method is also validate by using a case study.

An Adaptive Power Sharing Control for Management of DC Microgrids Powered by Fuel Cell and Storage System

This paper presents an adaptive power-sharing methodology for management of dc microgrids powered by fuel cell (FC) and storage system (SS). In this context, the use of an adaptive k -sharing function in the control scheme is proposed to compensate the fast transients on the ac side and manage the power sharing at steady-state regime between the FC and SS. The adaptive k -sharing is implemented with a low-pass filter transfer function for the FC and a complementary transfer function associated with the adaptive k -sharing gain for the SS. The proposed adaptive k -sharing function links the FC and the SS dynamics with the management of the dc microgrid, ensuring that the entire FC operation is performed in accordance with its operational limits. One of the main advantages of the proposed adaptive k -sharing is to reach high levels of stability and minimum disruptions on the FC terminals. To evaluate the feasibility of the proposed approach, we analyze the k -sharing behavior to determine the operational limits of the dc microgrid. Finally, to support the theoretical analysis, we carried out a set of experimental results.

Converting Series Biquad Filters Into Delayed Parallel Form: Application to Graphic Equalizers

Digital filter transfer functions can be converted between the direct form and parallel connections of elementary sections, typically second-order (“biquad”) sections. The conversion from direct to parallel form is performed using a partial fraction expansion, which usually requires long division of polynomials when expanding proper and improper transfer functions. This paper focuses on the conversion of a series of biquad sections to the parallel form, and proposes a novel way to implement the partial-fraction expansion without the use of long division. Additionally, the resulting structure is the delayed parallel form in which the section gains remain small. The new design and previous methods are compared in a case study on graphic equalizer design. The delayed parallel filter is shown to use the same number of operations as the series form during filtering. The conversion of a recently proposed series graphic equalizer into the delayed parallel form leads to an improved parallel graphic equalizer design relative to all known prior approaches. The proposed conversion technique is widely applicable to the design of parallel infinite impulse response filters, which are becoming popular as they are well suited to implementation using parallel computers.

Low-Complexity 2-D Digital FIR Filters Using Polyphase Decomposition and Farrow Structure

This paper proposes a novel realization technique for quadrantally symmetric 2-D finite impulse response filters with a guaranteed reduction in the hardware complexity. Here, the concept of Farrow structure-based interpolation filter design using the polyphase decomposition of the 1-D filter transfer function is effectively utilized in the 2-D domain. The proposed 2-D filter makes use of row-wise polyphase decomposition of the 2-D transfer function or frequency response, followed by the polynomial approximation of the individual polyphase coefficients resulting in Farrow structures corresponding to each row filter. The final coefficients are implemented by varying the delay values in all the Farrow structures, followed by the interpolation of the coefficients obtained from each delay value, which in turn forms the rows in the 2-D kernel. The major highlight of the proposed method is the highly reduced implementation complexity in terms of the number of multipliers and adders, with a low normalized root-mean-square error. Design examples of the circularly symmetric and fan-type filters have been considered to show the efficiency of the approach. The results show a drastic reduction in the implementation complexity of the 2-D filters of upto 20%, with significantly low normalized root-mean-square error lesser than 0.5%.

Sonar signal representation mimicking the inner ear of horseshoe bats

Current models of the initial stages of auditory processing in mammals usually agree that the input signals are split into a bank of bandpass filters. However, the available models differ substantially in their level of complexity and the number of parameters needed. In the current work, the varying levels of complexity in filterbank models of the basilar membrane have been evaluated in the context of modeling the cochlear processing of natural biosonar echoes in horseshoe bats. To this end, three different types of filterbank models have been implemented to represent the range of complexity spanned by models that are in use for the human inner ear: The simplest model, a gammatone filterbank, is a linear model with symmetric filter transfer functions. The gammachirp filterbank is also linear, but mimics the asymmetric transfer functions of the basilar membrane. Finally, the dual resonance nonlinear (DRNL) model adds a level-dependent behavior. Here, all three models have been adapted to the specifics of the basilar membrane of horseshoe bats which is characterized by an “auditory fovea” with exceptionally high filter qualities. The outputs of the different models have been encoded into a sequence of neural spike times before being evaluated with various information-theoretic methods.

Partial fraction expansion–based realizations of fractional‐order differentiators and integrators using active filters

SummaryApproximations of the fractional‐order differentiator and integrator operators s±r are proposed in this work. These approximations target the realization of these operators using standard active filter transfer functions. Hence, circuit implementations in integrated circuit form or in discrete component form are significantly facilitated. Complementary metal‐oxide‐semiconductor (CMOS) realizations of the proposed approximations are given and validated via simulations using the AMS 0.35 μm CMOS technology, while experimental results using operational amplifier circuits are tested and confirm the proposed theory.

Plasmonic metamaterial-based filtering structures with dynamic tunability.

In this Letter, we report the design, analysis, and characterization of first- and second-order plasmonic metamaterial-based multi-mode filtering structures. Further, electronic adaptivity in filter transfer functions is introduced and characterized. First, the basic operating principle of the engineered multi-mode resonator-based bandpass filter is presented. Then the concept is extended by introducing electronic (dynamic) tuning of the bandwidth using semiconductor varactor diodes. Afterwards, to enhance the selectivity and out-of-band filtering response, second-order multi-mode designs are realized. For experimental verification, the hardware prototype is fabricated and characterized using the Keysight analyzer N9918A. The design filtering structures will pave an important role in tunable plasmonic circuits and systems.

Event-based mixed ℋ ∞ and passive filtering for discrete singular stochastic systems

ABSTRACT This work devotes to the event-based mixed and passive filter analysis and design problems of discrete-time singular stochastic network systems with Markovian jump parameters. Using the event-triggered communication approach, we first derive a network-induced delay discrete error singular stochastic network model. With the help of event-triggered method and stochastic Lyapunov function scheme, sufficient conditions are then established such that the resulting error stochastic model is regular, causal, stochastically mean-square stable with a mixed and passivity performance index. By applying slack matrix variables and filter transfer function equivalent method, an event-triggered mixed and passive filter is designed such that the resulting error singular stochastic network system satisfies certain mixed and passive filter performance index, and the derived conditions could be solved in terms of linear matrix inequality method. Finally, the effectiveness of the proposed methods is illustrated by a numerical example.

Symbolic Analysis of an Analog Active Filter as Path for Conversion to Digital Filter

Abstract Recently have been reported methods to deliver a digital filter from an analog active filter, described only by its circuits diagram. The proposed approaches have been implemented in MATLAB and Python, and they were based on state-space conversion from analog to digital domain. Based on the Python approach, we show in this paper how to compute the transfer function of a large order analog active filter. The analog filter is described only by its circuits diagram. Finally, the analog filter is converted to the corresponding digital filter, having similar frequency gain and phase characteristics.