Infinite Impulse Response Digital Filters Research Articles

A Characterized Method for the Real-Time Compensation of Power System Measurement Transducers

This paper presents a real-time compensation method for the improvement of the frequency behavior of measurement transducers already operating or to be installed in transmission and distribution grids. The developed technique relies on the identification of an infinite impulse response digital filter with complex frequency response equal to the inverse of the transducer, whose parameters are evaluated through a hybrid scheme based on the combination of a stochastic and a deterministic procedure. Attention is focused on the algorithm identification capability, on the sensitivity to the weighting array introduced in the optimization cost function, and on the propagation uncertainty associated with the algorithm input quantities. Such investigation has been carried out on a circuit model of a resistive divider thought for medium-voltage (MV) measurements. To estimate the uncertainty associated with the identified filter frequency behavior, the Monte Carlo method has been implemented. The overall improvement varies with the frequency; at 10 kHz, the improvement for both the ratio as well as phase error is of two orders of magnitude. The uncertainty, estimated with 10 500 draws, associated with the filter is lower or equal to the input ones all over the 10 Hz–50 kHz frequency range. The algorithm is finally applied to a laboratory resistive capacitive divider, which is the low-voltage stage of an MV divider. The obtained improvement is of two orders of magnitude for the ratio and phase errors over all the considered frequency range.

High‐Order Recursive Filtering of Non‐Uniformly Sampled Signals for Image and Video Processing

AbstractWe present a discrete‐time mathematical formulation for applying recursive digital filters to non‐uniformly sampled signals. Our solution presents several desirable features: it preserves the stability of the original filters; is well‐conditioned for low‐pass, high‐pass, and band‐pass filters alike; its cost is linear in the number of samples and is not affected by the size of the filter support. Our method is general and works with any non‐uniformly sampled signal and any recursive digital filter defined by a difference equation. Since our formulation directly uses the filter coefficients, it works out‐of‐the‐box with existing methodologies for digital filter design. We demonstrate the effectiveness of our approach by filtering non‐uniformly sampled signals in various image and video processing tasks including edge‐preserving color filtering, noise reduction, stylization, and detail enhancement. Our formulation enables, for the first time, edge‐aware evaluation of any recursive infinite impulse response digital filter (not only low‐pass), producing high‐quality filtering results in real time.

A generalized design framework for IIR digital multiple notch filters

Digital multiple notch filters are used in a variety of applications to remove or suppress multiple sinusoidal or narrow-band interference in digital signals. In this paper, we propose an all-pass filter-based design framework for infinite impulse response (IIR) multiple notch filters. Our approach aims to overcome the limitations of former techniques through greater design capacity and performance. The proposed framework has versatility and enables the tailored use of design constraints thus providing a family of possible multiple notch filter design methods. The design performance and practicality of the proposed framework are verified empirically by a series of experimental results and different applications.

Fractional Euler analog-to-digital transform

In this paper, the design of fractional Euler transform which is the regular Euler transform where the digital delay operator z−1 is replaced by the ideal digital fractional delay operator z−α is presented. This introduced transform will be used in analog-to-digital transform to improve the accuracy of a digital filter equivalent to a given analog filter. However, because of the fractional delay operator z−α the proposed fractional Euler transform cannot be exactly implemented; only a limited implementation by means of infinite impulse response (IIR) digital filter can be achieved using approximation techniques. First, the fractional order α of the digital fractional delay operator z−α, for 0<α<0.5, is selected such that the relative error between the analog differentiator s and its equivalent digital one obtained by the fractional Euler transform is minimum. Then, the ideal digital fractional delay operator z−α is approximated by a digital IIR filter based on approximation of analog fractional order system leading to an IIR digital filter implementation of the fractional Euler transform. Illustrative examples are given to show the effectiveness of the fractional Euler analog-to-digital transform design. Finally, the design of low order digital differentiator using the proposed fractional Euler transform has been compared to the most recent designed analog-to-digital transforms.

&lt;italic&gt;In Vivo&lt;/italic&gt; Ultrasound Thermography in Presence of Temperature Heterogeneity and Natural Motions

Real-time ultrasound thermography has been recently demonstrated on commercially available diagnostic imaging probes. In vitro experimental results demonstrate high sensitivity to small, localized temperature changes induced by subtherapeutic focused ultrasound. Most of the published results, however, are based on a thermally induced echo strain model that assumes infinitesimal change in temperature between imaging frames. Under this assumption, the echo strain is computed using a low-pass axial differentiator, which is implemented by a finite-impulse response digital filter. In this paper, we introduce a new model for temperature estimation, which employs a recursive axial filter that acts as a spatial differentiator-integrator of echo shifts. The filter is derived from first principles and it accounts for a nonuniform temperature baseline, when computing the spatial temperature change between two frames. This is a major difference from the previously proposed infinitesimal echo strain filter ( δ-ESF) approach. We show that the new approach can be implemented by a first-order infinite-impulse response digital filter with depth-dependent spatial frequency response. Experimental results in vitro demonstrate the advantages over the δ-ESF approach in terms of suppressing the spatial variations in the estimated temperature without resorting to ad hoc low-pass filtering of echo strains. The performance of the new recursive echo strain filter (RESF) is also illustrated using echo data obtained during subtherapeutic localized heating in the hind limb of Copenhagen rat in vivo. In addition to the RESF, we have used an adaptive spatial filter to remove motion and deformation artifacts during real-time data collection. The adaptive filtering algorithm is described and comparisons with uncompensated estimated spatio-temporal temperature profiles are given. The results demonstrate the feasibility of in vivo ultrasound thermography with high sensitivity and specificity.

Design of digital filters for frequency weightings (A and C) required for risk assessments of workers exposed to noise.

Many workers are exposed to noise in their industrial environment. Excessive noise exposure can cause health problems and therefore it is important that the worker’s noise exposure is assessed. This may require measurement by an equipment manufacturer or the employer. Human exposure to noise may be measured using microphones; however, weighting filters are required to correlate the physical noise sound pressure level measurements to the human’s response to an auditory stimulus. IEC 61672-1 and ANSI S1.43 describe suitable weighting filters, but do not explain how to implement them for digitally recorded sound pressure level data. By using the bilinear transform, it is possible to transform the analogue equations given in the standards into digital filters. This paper describes the implementation of the weighting filters as digital IIR (Infinite Impulse Response) filters and provides all the necessary formulae to directly calculate the filter coefficients for any sampling frequency. Thus, the filters in the standards can be implemented in any numerical processing software (such as a spreadsheet or programming language running on a PC, mobile device or embedded system).

Implementation and characterization of a fibre-optic colour sensor

In this paper the implementation of a fibre-optic sensor for colour detection based on reflective colour sensing is proposed. The sensor consists of three plastic optical fibres emitting red, green and blue components and one optical fibre collecting light reflected from the object. Red, green and blue LEDs are excited at different frequencies. In this way detection of the reflected signal is achieved with only one photodetector and three bandpass filters. Bandpass filters are implemented as digital IIR (infinite impulse response) filters on the microcontroller. Results obtained from the proposed sensor are compared with commercial available colour sensors and the results are satisfactory. Analyses of the sensor performance both in RGB and HSV colour space are done. The proposed solution shows that in specific applications by using the HSV model the sensor can be used both as a colour and distance sensor.

Design of Digital IIR Filters using Integrated Cat Swarm Optimization and Differential Evolution

This paper aims to establish a solution methodology for the optimal design of digital infinite impulse response (IIR) filters by integrating the features of cat swarm optimization (CSO) and differential evolution algorithm (DE). DE is a population based stochastic optimization technique which optimizes real valued functions. It requires negligible control parameter tuning but sometimes causes instability problem. CSO is a heuristic optimization algorithm based on the observations and imitation of the natural behavior of cats. CSO algorithm possesses local as well as global search capabilities. Although, CSO possesses better capability to search optimal point but it requires a higher computation time because the local and global searches are carried out independently in each iteration. A hybrid algorithm is proposed using the CSO algorithm and the DE optimization algorithm for the robust and stable design of digital IIR filter. To start with a better solution set, opposition based learning strategy is incorporated. The proposed method explores and exploits the search space locally as well as globally. The design criterion undertakes the minimization of magnitude approximation error and ripple magnitudes of both pass-band and stop-band satisfying the stability requirements. The developed hybrid algorithm is effectively applied for designing the digital low-pass, high-pass, band-pass and band-stop filters. The computational results demonstrate that the proposed algorithm is capable of creating designs that are competitive with reference to other design processes and can efficiently be applied for higher order filter design.

2-D-IIR Time-Delay-Sum Linear Aperture Arrays

A uniform linear array (ULA) digital beamformer with enhanced selectivity (interference rejection) over conventional true-time delay-sum (TTDS) beamforming is proposed for scanned aperture applications. Conventional TTDS transfer function, which contains only zero-manifolds, is modified by introducing complex pole-manifolds based on 2-D infinite impulse response (IIR) digital beam filters, thereby achieving enhanced selectivity for the same number of antennas in the ULA. For a ULA of 64 antennas, desired direction of arrival (DOA) 30° and interference DOA -60° from array broadside, a relative improvement in signal-to-interference ratio (SIR) of 7 dB is verified. For 128-element ULA, interference DOA -10°, a relative improvement in SIR of 5-10 dB is obtained for the desired DOA in the range 10°-90°. The projected improvements are independent of the weights of the conventional phased-array, TTDS, or filter-sum beamformer used because the method does not change the zero-manifolds of the original array pattern.

Space-Time Spectral White Spaces in Cognitive Radio: Theory, Algorithms, and Circuits

Space-time spectral white spaces in a cognitive radio environment are defined based on multidimensional spatio-temporal spectral properties of radio waves received by a planar array of antennas. Spectral occupancy of a given carrier frequency pertaining to a particular direction in space is expressed by the volume of a semi-cone shaped geometrical region in the 3-D spatio-temporal frequency space ω. A combined approach employing low complexity array processing and conventional time-frequency spectrum sensing is proposed towards the detection of space-time white spaces in ω. The detection scheme employs four subsystems; antenna array, front-end processing, 3-D spatio-temporal array processing, and 1-D spectrum sensing. Key components in the antenna array and front-end processing subsystems are described including an example of a broadband Vivaldi antenna simulated in the frequency range 1.25-2 GHz. The array processing subsystem employs 3-D infinite impulse response digital beam filters, as a low complexity alternative to conventional phased arrays. One potential realization of the 1-D spectrum sensing subsystem is described by using a tunable bandpass filter followed by an energy detector. Simulation examples are provided by considering different directions of arrival, effect of multi-path replicas, signal to noise ratio changes and both narrow band and wideband signals in the normalized temporal frequency range (0,π).

AN OPTIMAL DESIGN OF IIR DIGITAL FILTER USING PARTICLE SWARM OPTIMIZATION

In this article, a novel approach for infinite-impulse response (IIR) digital filters using particle swarm optimization (PSO) is presented. IIR filter is essentially a digital filter with recursive responses. Because the error surface of digital IIR filters is generally nonlinear and multimodal, so global optimization techniques are required in order to avoid local minima. This study is based on a heuristic way to design IIR filters. PSO is a powerful global optimization algorithm introduced in combinatorial optimization problems. This study finds the optimum coefficients of the IIR digital filter through PSO. It is found that the calculated values are more optimal than the FDA tool and GA available for the design of the filter in MATLAB. Design of low-pass and high-pass IIR digital filters is proposed in order to provide an estimate of the transition band. The simulation results of the employed examples show an improvement on the transition band. The stability of designed filters is described by the position of Pole-Zeros.

A bit too precise? Verification of quantized digital filters

Fixed-point digital filters are simple yet ubiquitous components of a wide variety of digital processing and control systems. Common errors in fixed-point filters include arithmetic round-off (truncation) errors, overflows and the presence of limit cycles. These errors can potentially compromise the correctness of the system as a whole. Traditionally, digital filters have been verified using a combination of design techniques from control theory and extensive testing. In this paper, we examine the use of formal verification techniques as part of the design flow for fixed-point digital filters. We study two classes of verification techniques involving bit-precise analysis and real-valued error approximations, respectively. We empirically evaluate several variants of these two fundamental approaches for verifying fixed-point implementations of digital filters. We design our comparison to reveal the best possible approach towards verifying real-world designs of infinite impulse response (IIR) digital filters. Our study compares the strengths and weaknesses of different verification techniques for digital filters and suggests efficient approaches using modern satisfiability-modulo-theories solvers (SMT) and hardware model checkers. This manuscript extends our previous work evaluating bounded verification, where a limited number of iterations of the system are explored, with unbounded verification, where an unlimited number of iterations of the system are considered. Doing so allows us to evaluate techniques that can prove the correctness of fixed-point digital filter implementations.

Digital IIR Filter Design using Real Coded Genetic Algorithm

The paper develops a technique for the robust and stable design of digital infinite impulse response (IIR) filters. As the error surface of IIR filters is generally multi-modal, global optimization techniques are required to design efficient digital IIR filter in order to avoid local minima. In this paper a real-coded genetic algorithm (RCGA) with arithmetic- average-bound-blend crossover and wavelet mutation is applied to design the digital IIR filter. A multicriterion optimization is employed as the design criterion to obtain the optimal stable IIR filter that satisfies the different performance requirements like minimizing the Lp-norm approximation error and minimizing the ripple magnitude. The proposed real-coded genetic algorithm is effectively applied to solve the multicriterion, multiparameter optimization problems of low-pass, high-pass, band-pass, and band-stop digital filters design. The computational experiments show that the proposed method is superior or atleast comparable to other algorithms and can be efficiently used for higher order filter design.

Design of Digital IIR Filter with Conflicting Objectives

Infinite impulse response (IIR) filter design is a highly constrained multiobjective optimization problem involving conflicting objectives. In this paper, particle swarm optimization (PSO) is purposed to efficiently and effectively handle multiple conflicting objectives of IIR filter design. The weighted sum approach is used to minimize magnitude response and phase response of digital IIR filter simultaneously. The value of weights are searched using PSO along with filter coefficients thus assigning different weight vector to each individual particle. The order of the filter is controlled by a control gene whose value is also optimized along with the filter coefficients to obtain optimum order of designed IIR filter. The proposed algorithm shows competitive results with improved diversity and convergence

An application of swarm intelligence for the design of IIR digital filters

This paper presents the swarm intelligence (SI)-based particle swarm optimisation (PSO) in context of designing infinite-impulse response (IIR) digital filters. IIR filters are the part of digital filters with recursive responses. Since the error surface of IIR digital filters is generally non-linear and multimodal, global optimisation techniques are required in order to avoid local minima. The particle swarm optimisation algorithm is then applied for calculating optimal coefficients of IIR digital filters and comparison is done preferably with filter design tool and other heuristic techniques. The simulation results of benchmark filter are discussed in this paper and can be efficiently used for IIR digital filter design.

Vibration Analysis Based on Time-Frequency Analysis with Digital Filter

The primary aim of this study is to model and identify vibrations in mechanical systems subject to arbitrary external excitations. We propose a method based on infinite impulse response digital filter technology—termed time-frequency analysis—to analyze transient and steady-state vibrations. First, we introduce the time-frequency analysis procedure and the algorithm that implements it. Second, we analyze typical discrete signal inputs, such as impulse, sinusoidal and swept sine signals, and present time-frequency characteristics for transient and steady-state signals. Third, we apply our analysis method to the mechanical vibration behavior of a single-degree-of-freedom system subjected to various types of external excitations. The results of our analysis for steady-state vibration are verified as being equivalent to those from a Fast Fourier Transform (FFT) analysis. Moreover, the proposed analysis has the advantage over FFT analysis that we can also use it to analyze transient vibration phenomena.

A comparative study on the active power filter control strategy for independent and small power system

Aiming at the serious influence on the power frequency stabilisation for independent power system when its loads are largely changed, a control strategy of active power filter is presented. Firstly, the principle of second-order direct type IIR (infinite impulse response) digital notch filter is described, and the frequency real-time detection model is established based on least mean power (LMP, p = 3) adaptive algorithm to track the notch filter parameters. Then, combining the instantaneous reactive power theory and hysteresis current method, the simulation model of active filter control strategy with power frequency’s change is established. Finally, the simulation results proved that the active power filter model can track the changing frequency quickly and compensate harmonic current accurately. Therefore, the power quality and reliability of the small power grid are enhanced.

Design and Determination of Optimum Coefficients of IIR Digital Highpass Filter using Analog to Digital Mapping Technique

Digital Signal Processing (DSP) , there two types of filters are used to perform the filtering operations and they are the Infinite Impulse Response (IIR) filter and the Finite Impulse Response (FIR) filter. The present output sample of an IIR filter depends on the present input samples, past input samples and past output samples, i.e IIR filter is of recursive type. Now to design the Digital IIR filter, the coefficients are essentially required. There are a numbers of techniques available for designing the IIR filter. In this paper, the design and determination of the IIR filter coefficients are introduced using computer based approach. The program based on the algorithm proposed in this paper is simulated in Matlab which provides with the satisfactory results.

Design of One-Dimensional Linear Phase Digital IIR Filters Using Orthogonal Polynomials

In the present paper, we discuss a method to design a linear phase 1-dimensional Infinite Impulse Response (IIR) filter using orthogonal polynomials. The filter is designed using a set of object functions. These object functions are realized using a set of orthogonal polynomials. The method includes placement of zeros and poles in such a way that the amplitude characteristics are not changed while we change the phase characteristics of the resulting IIR filter.

Elimination of noise on transcranial Doppler signal using IIR filters designed with artificial bee colony – ABC-algorithm

Biomedical signals are usually contaminated by noise generated from sources such as power line interference and disturbances produced by the movement of the recording electrodes. Also the signal-to-noise ratio of biomedical signals is usually quite low. In addition, biomedical signals often interfere with each other. Therefore, the filters employed for eliminating noise and interference are significant in the medical practice. Digital infinite impulse response (IIR) filters have shorter filter length than the finite impulse response (FIR) filters with the same frequency characteristic. Therefore, in this work, an approach based on digital IIR filters are described for the elimination of noise on transcranial Doppler by using artificial bee colony (ABC) which is a popular swarm based optimization algorithm introduced recently. Moreover, the performance of the proposed approach is compared to particle swarm optimization algorithm.