Infinite Impulse Response Digital Filters Research Articles

A Fresh Revisit of the Issues and Improvements in Impulse Invariance Filter Design for Infinite Impulse Response Filters

The objective of this paper is to first present some issues with impulse invariance filter (IIF) design during the design of digital infinite impulse response (IIR) filters. Engineers are often confused about some inconsistent observations. For instance, if the impulse response of a digital filter is designed using the impulse invariance procedure, then the analog and digital filters’ frequency and step responses are very different. Two simple remedies are presented in this paper. One is a post-processing approach that scales the frequency and step responses of the digital filter by the sampling interval T. Another one is a pre-processing approach that scales the impulse response of the analog filter by T. However, even after these remedies, there is still a steady state bias in the step response of the digital filter for certain cases where there is discontinuity in the analog impulse response. A recommendation is to include a correction term in the digital filter. After that, the steady state bias in the digital filter is then suppressed. Moreover, the MATLAB R2021a command “impinvar” needs to also include a correction term so that the frequency and step responses can be more accurate in the digital filter. Two comparative studies were carried out to compare the improved IIF filter with three competing digital IIR filter design methods. Although the above issues and improvements have been proposed by researchers in the past, many researchers, engineers, and students are still not aware of them. This paper provides a fresh revisit of these issues and improvements by using figures, equations, and examples. Proper credits are also given to those researchers who first pointed out those issues and improvements. It is hoped that through an open access journal, future rediscovery of issues and improvements in IIF can be prevented.

GENERALIZATION OF THE TIME INFINITE IMPULSE RESPONSE DIGITAL FILTERS

This work describes the generalization of a new kind of infinite impulse response (IIR) digital filter to filter the pulse signal periods. This kind of digital filter was designed using the previously designed frequency-locked loops (FLL), which are based on the time measurement and processing of both the input and output periods. FLL is a linear discrete system. Starting from the general form of difference equation of the IIR FLL digital filter of the third and fourth orders, the transfer functions and Z transform of the outputs are developed for the IIR FLL digital filter of any order. To demonstrate the capabilities and utility of the general equations, they were applied to design a suitable IIR digital filter using a fourth-order FLL. The filtering abilities and the analyses in the frequency domain of the designed low pass IIR digital filter are demonstrated using the theory of IIR digital filter and the corresponding MATLAB tools. Analyses of the fourth-order IIR FLL digital filter were also performed in the time domain using computer simulation in MATLAB.

Numerical Solution of Linear Second-Kind Convolution Volterra Integral Equations Using the First-Order Recursive Filters Method

A new numerical method for solving Volterra linear convolution integral equations (CVIEs) of the second kind is presented in this work. This new approach uses first-order infinite impulse response digital filters method (IIRFM). Three convolutive kernels were analyzed, the unit kernel and two singular kernels: the logarithmic and generalized Abel kernels. The IIRFM is based on the combined use of the Laplace transformation, a first-order decomposition, and a bilinear transformation. This approach often leads to simple analytical expressions of the approximate solutions, enabling efficient numerical calculation, even using single-precision floating-point numbers. When compared with the method of homotopic perturbations with Laplace transformation (HPM-L), the IIRFM approach does not present, in linear cases, the convergence difficulties inherent to iterative approaches. Unlike most solution methods based on the Laplace transform, the IIRFM has the dual advantage of not requiring the calculation of the Laplace transform of the source function, and of not requiring the systematic calculation of inverse Laplace transforms.

Dynamics of Interacting Colloidal Particles Using the IIR Recursive Digital Filter Method

This paper focuses on the numerical study of spherical particle sedimentation, taking into account hydrodynamic interactions. Infinite impulse response (IIR) digital filters, specially tailored to solve the sedimentation dynamics, were used in the present study to numerically solve the coupled ordinary differential equations with the time-dependent coefficients of the problem. Hydrodynamic interactions are modeled using the Rotne–Prager–Yamakawa (RPY) approximation, to which a correction is made to better account for short-range interactions. In order to validate both the proposed numerical resolution method and the RPY correction, this paper begins with the study of two interacting spherical particle sedimentation methods. Comparisons with previously published analytical or numerical results confirm the relevance of the present approach.

Digital IIR filters: Effective in edge preservation?

Infinite Impulse Response (IIR) filtering stands as a fundamental technique in various signal processing applications. Despite its widespread use, the scientific community widely acknowledges the suboptimal nature of IIR filters in preserving edges or abrupt transitions in piecewise signals. In situations where meticulous preservation of abrupt signal transitions is crucial, signal processing practitioners often explore alternative methodologies tailored to specific application demands. Consequently, the effectiveness of digital IIR filters in preserving signal edges while filtering out undesirable noise components continues to be a topic of active debate.In response to this limitation (or answering the question posed by the above title), the paper demonstrates that the suboptimal nature of IIR filters in preserving edges arises from the conventional methodology used to compute the output of zero-phase IIR filters. The standard method of output computation equates to solving an unconstrained optimization problem with an ℓ2-norm penalty term. Following this analysis, the paper introduces a refined approach to compute the output of digital IIR filters, aiming to overcome the challenge of preserving abrupt signal transitions. This innovative proposal replaces the ℓ2-norm with an ℓ1-norm, resulting in the development of an IIR filter that dynamically adjusts its coefficients based on the input signal. As a result, this novel approach to output computation effectively preserves essential signal features while simultaneously reducing noise, highlighting the efficacy of digital IIR filters in edge preservation. Therefore, the answer to the aforementioned question greatly depends on the chosen method for computing the output. By employing the suggested approach, the answer is unequivocally yes.

NEW KIND OF IIR DIGITAL FILTERS INTENDED FOR PULSE PERIOD FILTERING

This paper describes a new kind of infinite impulse response (IIR) digital filter designed for pulse period filtering. The IIR digital filter is designed using a third-order IIR frequency locked loop (IIR FLL), which is based on the time measurement and processing of both, the input and output periods. A general form of the difference equation describing this type of IIR FLL of any order is developed and compared with the corresponding difference equation of classical digital filters. The mathematical analyses in the time domain were performed using the Z transform approach and the theory of linear discrete systems. An analysis of the IIR digital filter was performed in the time and frequency domain. The transfer functions and Z transform of the third-order IIR FLL outputs are developed. The main part of the article is devoted to designing the appropriate IIR FLL digital filter using the corresponding IIR FLL. For this purpose, the theory of IIR digital filter and the corresponding MATLAB tools are used, but taking into account the differences between these systems. The filtering abilities of the designed IIR FLL digital filter are demonstrated. Computer simulation of the designed IIR FLL is made in the time domain to enable precise insight into its properties.

Estimation of phase distortions of the photoplethysmographic signal in digital IIR filtering

Pre-processing of the photoplethysmography (PPG) signal plays an important role in the analysis of the pulse wave signal. The task of pre-processing is to remove noise from the PPG signal, as well as to transmit the signal without any distortions for further analysis. The integrity of the pulse waveform is essential since many cardiovascular parameters are calculated from it using morphological analysis. Digital filters with infinite impulse response (IIR) are widely used in the processing of PPG signals. However, such filters tend to change the pulse waveform. The aim of this work is to quantify the PPG signal distortions that occur during IIR filtering in order to select a most suitable filter and its parameters. To do this, we collected raw finger PPG signals from 20 healthy volunteers and processed them by 5 main digital IIR filters (Butterworth, Bessel, Elliptic, Chebyshev type I and type II) with varying parameters. The upper cutoff frequency varied from 2 to 10 Hz and the filter order—from 2nd to 6th. To assess distortions of the pulse waveform, we used the following indices: skewness signal quality index (SSQI), reflection index (RI) and ejection time compensated (ETc). It was found that a decrease in the upper cutoff frequency leads to damping of the dicrotic notch and a phase shift of the pulse wave signal. The minimal distortions of a PPG signal are observed when using Butterworth, Bessel and Elliptic filters of the 2nd order. Therefore, we can recommend these filters for use in applications aimed at morphological analysis of finger PPG waveforms of healthy subjects.

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.

Filtering Eye-Tracking Data From an EyeLink 1000: Comparing Heuristic, Savitzky-Golay, IIR and FIR Digital Filters.

In a prior report (Raju et al., 2023) we concluded that, if the goal was to preserve events such as saccades, microsaccades, and smooth pursuit in eye-tracking recordings, data with sine wave frequencies less than 75 Hz were the signal and data above 75 Hz were noise. Here, we compare five filters in their ability to preserve signal and remove noise. We compared the proprietary STD and EXTRA heuristic filters provided by our EyeLink 1000 (SR-Research, Ottawa, Canada), a Savitzky- Golay (SG) filter, an infinite impulse response (IIR) filter (low-pass Butterworth), and a finite impulse filter (FIR). For each of the non-heuristic filters, we systematically searched for optimal parameters. Both the IIR and the FIR filters were zero-phase filters. All filters were evaluated on 216 fixation segments (256 samples), from nine subjects. Mean frequency response profiles and amplitude spectra for all five filters are provided. Also, we examined the effect of our filters on a noisy recording. Our FIR filter had the sharpest roll-off of any filter. Therefore, it maintained the signal and removed noise more effectively than any other filter. On this basis, we recommend the use of our FIR filter. We also report on the effect of these filters on temporal autocorrelation.

Enhancing IIR system identification: Harnessing the synergy of gazelle optimization and simulated annealing algorithms

In the field of digital filter design and system identification, accurately modeling Infinite Impulse Response (IIR) systems is of utmost importance. This paper introduces a new adaptive algorithm that combines the gazelle optimization algorithm with simulated annealing to achieve superior optimization performance for digital IIR filters used in system identification. To evaluate the algorithm's effectiveness, extensive experiments were conducted on two fronts: the challenging CEC2020 benchmark functions and a fifth order IIR system identification problem. The proposed algorithm proves its effectiveness by achieving optimal solutions on the CEC2020 benchmark functions when compared to other well-known optimization algorithms such as arithmetic optimization, particle swarm optimization, differential evolution, sine cosine algorithm, gray wolf optimizer, biogeography-based optimization, salp swarm algorithm, and the original gazelle optimization algorithm. The algorithm's performance is measured by its ability to find the best solutions for these benchmark functions. For the IIR system identification problem, the study considers both the same order and reduced order cases. The system to be identified is represented by a fifth order plant. The algorithm's statistical analysis and convergence behavior are compared to the original gazelle optimization algorithm, artificial hummingbird algorithm, mountain gazelle optimization algorithm, and the widely used artificial bee colony algorithm. These comparisons demonstrate the proposed algorithm's superior capability and efficiency in accurately identifying the parameters of IIR systems.

Kalman filter/smoother-based design and implementation of digital IIR filters

Recently, a unified framework was proposed for forward-backward filtering and penalized least-squares optimization. It was shown that forward-backward filtering can be presented as instances of penalized least-squares optimization. In other words, the output of a zero-phase digital infinite-impulse response (IIR) filter can be computed by solving a constrained optimization problem, in which the weight controlling the constraint is directly related to cutoff frequencies with closed-form equations. It was also shown that a zero-phase digital IIR filter can be formed as an optimal smoothing Wiener filter for a random process obtained from an autoregressive (AR) or AR-moving average (ARMA) model driven by input (innovation) noise in presence of an observation noise.In this paper, the problem of zero-phase digital IIR filtering is re-examined using Kalman filter/smoother. The paper shows that every zero-phase digital IIR filter can be viewed as a special case of an optimal smoothing Wiener filter. Based on the fact that the formulations of the optimum filter by Wiener and Kalman are equivalent in steady state, we present a Kalman filter/smoother framework to the design and implementation of digital IIR filters. As an example, the zero-phase digital Butterworth filter is designed using Kalman smoother and compared with the traditional design (forward filtering and backward smoothing) method.

DESIGN AND IMPLEMENTATION OF EFFICIENT DIGITAL FILTERS USING LABVIEW

In digital signal processing, the purpose of a filter is to remove unnecessary components in the signal, such as random noise. An infinite impulse response (IIR) filter is an iteration-type filter. The current pattern resulting from the IIR filter is based on the current input and output patterns. Several methods are available to detect digital IIR filters. Filters are widely used in signal processing and communication device approaches such as in channel equalization; noise reduction; radar systems; audio, speech signal, video, and biomedical signal processing, and economical, electrocardiogram, electroencephalogram, electromyography, and electrical circuit analyses. In this study, we used the Laboratory Virtual Instrument Engineering Workbench (LabVIEW) software program to analyze the design and implementation of an efficient digital filter, the results of which are presented in this paper. The important objective of this task was to design and examine different IIR filters-namely, Chebyshev, Butterworth, and Elliptic filters-using LabVIEW for the simulation processes. LabVIEW is used by graphical programming environmental engineers to implement automated research, certification, and product testing systems. In this work, the LabVIEW graphical programming tool was used because it gives accurate results in real time compared to other available simulation tools.

A field-programmable gate array (FPGA)-based data acquisition system for closed-loop experiments.

We describe a custom and open source field-programmable gate array (FPGA)-based data acquisition (DAQ) system developed for electrophysiology and generally useful for closed-loop feedback experiments. FPGA acquisition and processing are combined with high-speed analog and digital converters to enable real-time feedback. The digital approach eases experimental setup and repeatability by allowing for system identification and in situ tuning of filter bandwidths. The FPGA system includes I2C and serial peripheral interface controllers, 1 GiB dynamic RAM for data buffering, and a USB3 interface to Python software. The DAQ system uses common HDMI connectors to support daughtercards that can be customized for a given experiment to make the system modular and expandable. The FPGA-based digital signal processing (DSP) is used to generate fourth-order digital infinite impulse response filters and feedback with microsecond latency. The FPGA-based DSP and an analog inner-loop are demonstrated via an experiment that rapidly steps the voltage of a capacitor isolated from the system by a considerable resistance using a feedback approach that adjusts the driving voltage based on the digitized capacitor current.

A novel hybrid of chimp with cuckoo search algorithm for the optimal designing of digital infinite impulse response filter using high-level synthesis

A novel hybrid of chimp with cuckoo search algorithm for the optimal designing of digital infinite impulse response filter using high-level synthesis

Solution of Basset integro-differential equations by IIR digital filters

A new O(n) time complexity numerical method for computing the solutions of Basset integro-differential equations is presented. The method is based on the use of Laplace and bilinear transformations, leading after a precise Chebyshev rational interpolation, to the construction of first order infinite impulse response (IIR) filters. The resulting recurrence relations allow for a very accurate O(n) resolution of Basset equations. Different numerical examples are presented in order to demonstrate the applicability of the method to the study of the transient creeping flow motion of a rigid spherical particle. The results are compared on the one hand to those provided by the Talbot inversion method and on the other hand to those provided by an iterative method specially elaborated here to solve the Basset problem.

ADOPTION OF VIBRATION OF FUZZY PARTIAL FRACTIONAL-ORDER EQUATION IN MONITORING OF NOISE BIG DATA UNDER INFINITE IMPULSE RESPONSE DIGITAL FILTER ALGORITHM

In order to study the application of fuzzy partial fractional-order equation based on infinite impulse response (IIR) digital filter in noise big data monitoring, in this study, first, the noise level is calculated through IIR filter to obtain the sound signal sequence after C weight and A weight; the weight equivalent continuous sound level of C, A, and Z is calculated. Then, the vibration condition of fuzzy partial fractional-order equation is studied; the vibration acceleration signal is converted into the vibration velocity and displacement signal; the corresponding effective values are calculated according to the root mean square (RMS), and the noise monitoring platform is designed from hardware and software aspects. Finally, the calibrated sound level value is compared with the standard signal value generated by the digital signal generator; the sequence of sound signal after weight of the original signal, the actual acceleration signal, velocity signal, and displacement signal are calculated; the acceleration signal, velocity signal, and theoretical signal values are compared at different frequencies. The results show that the error between the calculated and calibrated sound level and the standard signal value is very small, and the results of weight counting of C and A are good and meet the requirement of calculation; the error between the measured value of actual acceleration, velocity, and displacement signal and the theoretical value is small, which can realize the accurate acquisition of vibration signal; the error between the actual measured value and the theoretical value of acceleration and velocity at different frequencies is small, about 1% and 10%, respectively. Therefore, the fuzzy partial fractional-order equation based on IIR digital filter can effectively monitor the big noise data.

Convergence Rate For Low-Pass Infinite Impulse Response Digital Filter

The hybrid optimization technique is used to design a low-pass infinite impulse response (IIR) digital filter, to improve the coefficients of adaptive IIR digital filter, thus ensure stability. In this paper, the newly technique of hybrid particle swarm optimization (PSO) algorithm is proposed. This technique is a dynamic and static topology with a PSO algorithm, which called dynamic and static PSO (DS-PSO) algorithm. In the simulation, the low-pass IIR digital filter 8th order is designed. The fitness function problem is discussed based on values of the ripple of the passband, a ripple of the stopband, and a transition band. Thus, the proposed algorithm results are compared with previous studies results. From results comparison, results have shown the convergence rate with the DS-PSO algorithm outperformed the convergence rates using fuzzy gravitational search algorithm (FGSA), gravitational search algorithm (GSA), and differential evolution (DE) with mean values of 55.21%, 57.80%, and 70.40%, respectively.

Filtering-induced time shifts in photoplethysmography pulse features measured at different body sites: the importance of filter definition and standardization

Objective. The waveform of a photoplethysmography (PPG) signal depends on the measurement site and individual physiological conditions. Filtering can distort the morphology of the original PPG signal waveform and change the timing of pulse feature points on PPG signals. We aim to quantitatively investigate the effect of PPG signal morphology (related to measurement site) and type of pulse feature on the filtering-induced time shift (TS). Approach. 60 s PPG signals were measured from six body sites (finger, wrist under (volar), wrist upper (dorsal), earlobe, and forehead) of 36 healthy adults. Using infinite impulse response digital filters which are common in PPG signal processing, PPG signals were prefiltered (band-pass, pass and stop bands: >0.5 Hz and <0.2 Hz for high-pass filter, <20 Hz and >30 Hz for low-pass filter) and then filtered (low-pass, pass and stop bands: <3 Hz and >5 Hz). Four pulse feature points were defined and extracted (peak, valley, maximal first derivative, and maximal second derivative). For each subject, overall TS and intra-subject TS variability in feature points were calculated as the mean and standard deviation of TS between prefiltered and filtered PPG signals in 50 cardiac cycles. Statistical testing was performed to investigate the effect of measurement site and type of pulse feature on overall TS and intra-subject TS variability. Main results. Measurement site, type of pulse feature, and their interaction had significant impacts on the overall TS and intra-subject TS variability (p < 0.001 for all). Valley and maximal second derivative showed higher overall TS than peak and maximal first derivative. Finger had higher overall TS and lower intra-subject TS variability than other measurement sites. Significance. Measurement site and type of pulse feature can significantly influence the timing of feature points on filtered PPG signals. Filtering parameters should be quoted to support the reproducibility of PPG-related studies.

Performance Investigation of Digital Lowpass IIR Filter Based on Different Platforms

The work presented in this paper illuminates the design and simulation of a recursive or Infinite Impulse Response (IIR) filter. The proposed design algorithm employs the Genetic Algorithm to determine the filter coefficients to satisfy the required performance. The effectiveness of different platforms on filter design and performance has been studied in this paper. Three different platforms are considered to implement and verify the designed filter’s work through simulation. The first platform is the MATLAB/SIMULINK software package used to implement the Biquad form filter. This technique is the basis for the software implementation of the designed IIR filter. The HDL – Cosimulation technique is considered the second one; it inspired to take advantage of the existing tools in SIMULINK to convert the designed filter algorithm to the Very high-speed integrated circuit Hardware Description Language (VHDL) format. The System Generator is employed as the third technique, in which the designed filter is implemented as a hardware structure based on basic unit blocks provided by Xilinx System Generator. This technique facilitates the implementation of the designed filter in the FPGA target device. Simulation results show that the performance of the designed filter is remarkably reliable even with severe noise levels.

Performance Analysis in Higher-Order IIR Filter Structures with Application to EEG Signal

This paper investigates the analysis of critical path delay in various infinite impulse response (IIR) digital filter structure implementations. The critical path delay increases with the order of filter increasing in all conventional structures. So, it is needed to reduce the critical path delay for the faster realization of a digital filter in real-time processing. This paper proposed the rules for taking efficient cutset to retime the higher-order IIR filter structure. By applying this proposed retiming/pipelining techniques to EEG preprocessing filter, the critical path delay is $$28\%$$ , $$23\%$$ and $$18\%$$ more reduced as compared to the traditional retiming in direct form, parallel and lattice-ladder structure, respectively. These newly retimed structures are simulated in MATLAB Simulink and converted to fixed-point arithmetic for the synthesis of structures on Virtex-5 implementation. The results in different structures show that the allpass-based IIR structures has the lowest critical path delay and lowest computational complexity as compared to the conventional structures. Also, the proposed retimed structure has a smaller slice-delay product and support the largest maximum sampling frequency but requires more slice lookup tables (LUTs) than a conventional structure.