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An improvement to the realization of the linear-phase IIR filters
is described. It is based on the rearrangement of the numerator
polynomials of the IIR filter functions that are used in the real-time
realizations proposed in literature. The new realization has better
total harmonic distortion when a sine input is used, and it has smaller
phase and...
Contexts in source publication
Context 1
... a notable interest has been shown in real-time implementation of IIR filters having linear phase. Powell and Chau [1] have devised an efficient method for the design and realization of the real-time linear-phase IIR filters using suitable modification of the well-known time reversing technique [2]. In their method, which is shown in Fig. 1, the input signal is divided into L-sample segments, time-reversed, and twice filtered using two IIR filter blocks whose transfer functions are the same, e.g. H 1 (z) = H 2 (z) = H(z). The transfer function H(z) is usually of elliptic type, giving the best selectivity. It has been shown that the proposed procedure is much faster than ...
Context 3
... truncation noise, which is noise caused by truncation to Lsample segments, of several realizations will be examined. Since the truncation noise depends only on the realization of H1(z), the spectrum of the signal f (n) (at the output of the time-reversing part of the diagram in Fig. 1) will be analyzed. As in [1], the total harmonic distortion (THD) of the signal f (n) is measured in response to a single frequency input x(n) = sin(! 0 n); 0 n N 01. The input Finally, when B(z) is included in the time-reversed section H1(z), the noise is considerably decreased at lower frequencies (curve d). As can be seen in Fig. 2, ...
Context 4
... the numerator polynomials A(z) and B(z) and denominator polynomial D(z) are the same as in [1] or [3]. In Fig. 3(a) spectra of output signals y(n) [after the direct block H 2 (z) in Fig. 1] are shown, both for the original realization using (1) and (2) and for the new realization using (4) and (5). The input signal x(n) and the polynomials A(z); B(z); and D(z) are the same as in the previous example. The spectrum of the Powell-Chau technique is shown by the thin line, whereas the spectrum for the new realization is shown ...
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Citations
... This improvement results in improved amplitude response and reduced distortions to some extent. Furthermore, [7] proposes an improvement by reordering the polynomials on the numerator, which lowers the phase error and truncate length, with a tradeoff of a greater magnitude of L and more transistors used [7]. ...
... This improvement results in improved amplitude response and reduced distortions to some extent. Furthermore, [7] proposes an improvement by reordering the polynomials on the numerator, which lowers the phase error and truncate length, with a tradeoff of a greater magnitude of L and more transistors used [7]. ...
... Powell and Chau implementation block diagram[7] Overlap-add truncate block diagram and timing [ ...
Signal processing has become one of the most popular research topics. Researchers have designed a variety of digital filters to exclude unwanted random noises during the transmission or extract part of the signal in the desired range. There is a prevalent trend for digital filters to replace analog ones since they do not require hardwires. All the performances are operated on a single processor and are free from the effect of external factors. Finite impulse response (FIR) and infinite impulse response (IIR) filters in digital filters respectively provide infinite and finite impulse responses. In the application, it is preferred to have a linear phase digital filter, and FIR filters are naturally linear. However, FIR filters have higher orders and group delay than IIR filters, so researchers found various ways to implement linear phase IIR filters for improvement. This paper introduces and compares Powell and Chau Linear Phase IIR Filter, Kwan Linear Phase IIR Filter, and Xiao, Oliver, and Agathoklis Linear Phase IIR Filter.
... This special class of NR digital filters can offer highly magnitude characteristics with theoretically zero phase shift and optimal computational burdens per output sample [4][5][6]. Throughout the last four decades, Kormylo and Jain's design [2] was the most widespread used in designing NR filters [4][5][6][7][8][9][10][11][12][13]. This classical design requires specifications in the frequency domain. ...
This paper presents an optimal design for the special class of Non-Causal Recursive (NR) digital filters with zero phase shift. The design
is based on the Chebyshev approximation problem. It can be transformed to an equivalent linear program under linear constraints of the zero phase. The given design yields more interesting pole-zero patterns that are not necessarily restricted to the classical design of Kormylo and Jain. The proposed optimal design allows an accurate zero phase shift and better magnitude characteristics in passband and stopband.
... As is well known, Noncausal Recursive (NR) digital filters can be realized by a cascade connection of a causal IIR filter with an arbitrary transfer function Hz (forward pass) and an anticausal time reversed version of the same function 1 Hz (backward pass) [1][2][3][4][5][6][7]. The issue of designing this special class of digital filters has been discussed only slightly [1][2], and the most contributions have been focused on its real-time implementation [1][2][3][4], [6][7][8][9][10]. Kormylo and Jain [1] have proposed a classical design in the frequency domain based on bilinear transform and a well-known optimal design of analog elliptic filters, such that the magnitude characteristic of the causal recursive filter Hz has to agree with the square root of the desired ; while, its phase characteristic is inconsequential. ...
... Kormylo and Jain [1] have proposed a classical design in the frequency domain based on bilinear transform and a well-known optimal design of analog elliptic filters, such that the magnitude characteristic of the causal recursive filter Hz has to agree with the square root of the desired ; while, its phase characteristic is inconsequential. Over these four decades, this classical design was the most commonly used in several papers [3][4][5][6][7][8][9][10], where the design procedure is fast and simple. However, despite of using an optimal elliptic digital filter Hz, we are not sure that the squared magnitude response 2 j He is the optimal frequency response of the NR digital filters. ...
In this paper, an optimal design for the special class of Non-Causal Recursive (NR) digital filters with zero phase shift is presented. The approximation problem is formulated as a minimax optimization. It is transformed into a linear programming, which can be solved iteratively by a well-known binary search technique. We demonstrate that the optimal frequency response of the NR filter can be better than that of the classical squared magnitude response of an optimal elliptic filter; where, we get additional attenuation in the stopband. Two examples of filter design are illustrated in agreement with our contribution. Some details of the linear programming implementation and its limits are also discussed.
... Dans certains domaines d'application tels que : la parole, l'imagerie biomédicale, la géophysique, la cristallographie à rayon X,…etc., [Harasty88], [Raita94], [Rosten03], [Farsi06], [Willson94], [Djokic98], [Kurosu03]. ...
... Cette dernière catégorie présente l'avantage d'engendrer de meilleures performances en retard pur et quantité de mémoire. Ce qui l'a favorisé pour la mise en oeuvre des filtres PN [Powell91], [Willson94], [Djokic98] et [Kurosu03]. Les méthodes de la première catégorie [Czarnach82a], [Arias04], présentent des performances moins bonnes en retard pur et quantité de mémoire requise. ...
... Cependant, leur majeur avantage est la réduction de l'erreur de sectionnement à l'aide de l'état initial du filtrage non causal. Nous montrons que cette démarche s'avère difficile à intégrer pour les schémas en cascade II [Powell91], [Willson94], [Djokic98], [Kurosu03], [Rader06]. L'étude de l'impact du sectionnement sur la qualité de la réponse du filtre PN peut être effectuée dans le domaine temporel. ...
Le travail effectué dans le cadre de cette thèse consiste à étudier et élaborer de nouvelles techniques d’implémentation en temps réel de certaine classe particulière de systèmes, appelés filtres récursifs non causaux à phase nulle (PN). Ces filtres sont souvent utilisés en temps différé (off line). Ils s’implémentent avec des cellules élémentaires récursives, et nécessitent deux inversions temporelles. Ainsi, leur mise en œuvre se réalise par deux filtrages : l’un est causal et s’exécute dans le sens direct (forward filtering), l’autre est non causal, s’effectuant avec une entrée inversée (backward filtering). Ils sont appréciés pour leurs performances intéressantes et non conflictuelles en amplitude et en phase. Ils peuvent avoir à une phase exactement nulle avec une caractéristique d’amplitude très sélective et similaire à celle d’un filtre optimal elliptique. Ils présentent une bonne alternative par rapport aux filtres classiques RII à phase quasi-linéaire et RIF à phase linéaire.
Cependant, leur mise en œuvre en temps réel est délicate ; et rend leur utilisation peu intéressante pour le traitement des signaux de longueur importante. Il existe dans la littérature scientifique, quelques techniques de leur implémentation en temps réel. Celles-ci se basent, pour la plupart, sur des approches utilisant un sectionnement du signal traité. Ceci engendre des erreurs de calcul souvent importantes, avec des retards purs conséquents et qui exigent plus de ressources en mémoire. Notre contribution dans cette thèse portera sur une synthèse critique et une étude de performances des principales techniques de mise en œuvre des filtres PN en temps réel, à savoir : le sectionnement avec chevauchement sauvegardé (SCSauve), et chevauchement additionné (SCAdd), ou sans chevauchement (SSC). Les performances sont évaluées selon quatre critères : l’erreur de calcul, le retard pur engendré, la quantité de mémoire requise et la complexité algorithmique exigée. Une définition des différentes erreurs de calcul dues à la réalisation des filtres PN en temps réel est abordée. Une approche analytique est aussi élaborée dans le but de caractériser l’origine de ces erreurs de calcul. L’impact de sectionnement sur la qualité de la réponse d’un filtre PN est évalué dans les deux domaines temporel et fréquentiel, respectivement par la notion de l’erreur de sectionnement relative et le taux de distorsion harmonique (THD).
Une nouvelle technique s’appuie sur le sectionnement sans chevauchement est proposée. Elle se base sur un calcul récursif de l’état initial du filtrage non causal. Une pile de type FIFO (First In, First Out) est intégrée afin d’organiser les échantillons d’entrées. Les inversions temporelles sont implémentées par des piles de type LIFO (First Out, First In). La technique proposée offre une diminution de la complexité algorithmique et de la quantité de mémoire requise, avec une réduction du retard pur pour des erreurs de calcul acceptables.
Mots Clés :
phase nulle - phase linéaire - filtre RII - filtres RIF - filtre PN - sectionnement par chevauchement sauvegardé - sectionnement par chevauchement additionné - sectionnement sans chevauchement - complexité algorithmique – retard pur- FIFO- LIFO
... A notable interest to the Powell and Chau's backward/forward scheme has been shown in several papers [5,6], where improvements have been made on total harmonic distortions and phase linearity precision in passband using different IIR transfer functions. ...
A technique is presented to realize recursive digital filters with a linear phase and arbitrary magnitude characteristics. It is based on a well-known non-causal two-pass forward/backward filtering; where, a non-overlapping segmentwise processing is involved for a real-time implementation. Initial conditions of the backward pass are calculated recursively instead of a direct computation in the previous Arias-de-Reyna and Achaʼs non-overlapping method. Additionally, a single first in, first out memory (FIFO) is introduced to organize samples into a data queue structure, and it allows filtering in real-time sample-by-sample. These improvements over the prior non-overlapping method can reduce delays and data storage capacities, and get similar computational complexity and phase linearity precision in passband.We show through the proposed non-overlapping technique that the forward/backward scheme can be a good alternative and competitive over the Powell and Chauʼs backward/forward realization. We get better data storage capacities and phase linearity precision in passband, with approximately the same delays. Simulation of group delay precision in agreement with our contributions is illustrated.
... Noncausal filters are usually realized using a combination of 2-pass filtering and time reversal [1][2][3][4][5][6][7]. The first pass can be performed in a forward direction using a stable recursive digital filter, and the second pass can be performed in a backward direction using a noncausal subsystem implemented by 2 time reversal operations and a stable recursive digital filter, as shown in Figure 1. ...
... A continuous infinite-length input is divided into finite-length sections and each section is filtered separately by the 2-pass scheme. The final output can be built using output sections yielded from finite-length section processing and overlap-based approximations such as overlapand-save techniques [2,5], overlap-and-add techniques [3,4,6,7], or the nonoverlapping technique [1]. The final output is never achieved without errors; the magnitude of the systematic errors depends on section length and degrades the linearity of the overall system. ...
A novel method for implementing noncausal forward/backward 2-pass recursive digital filters in real time is presented. It is based on a segment-wise block processing scheme without overlapping. Factors that degrade the linearity of the overall system's transfer function are discussed. An analytical condition that corrects the system's linearity is elaborated upon using the state variable approach. A recursive algorithm is developed to compute an implementable condition for real-time filtering. A single first in, first out queue memory is introduced to ensure an organized and continuous data stream into the proposed system. This technique allows real-time, sample-by-sample filtering, and it yields reduced delay and data storage memory compared to previous works. Better performances in total harmonic distortion were also obtained. Experimental results are illustrated.
... bank design and the Nyquist filter design and different methods have been proposed for this design (Djokic et al., 1998;Powell & Chau, 1991;Surma-aho & Saramaki, 1999). A linear-phase lowpass IIR filter H(z) can be expressed in terms of complex allpass filters as (Zhang et al., 2001), ...
In this chapter, we have proposed a new general framework to designing real and complex allpole filters with given degree of flatness, and with phase and group delays at any desired set of frequency points. The filter coefficients are obtained by solving a set of linear equations. In the proposed allpole filter design, we can control the phase, group delay, and degree of flatness at different frequency points. Consequently, as demonstrated here, our proposal is useful for special IIR filter designs, i.e., linear-phase Butterworth-like filter, Butterworth-like filters with improved group delay, complex wavelet filters, fractional Hilbert transformers, and new IIR filters based on three allpass filters.
... However, Infinite Impulse Response (IIR) filters can have linear phase only in the noncausal case (Mitra, 2006;Vaidyanathan, 1993;Vaidyanathan and Chen, 1998), (the phase response can be 0 or π). It has been recently shown that filters with a linear phase property are useful in the filter bank design and Nyquist filter design (Argenti et al., 1996;Djokic et al.,1998;Powell and Chau, 1991;Selesnick, 1998;Willson and Orchard, 1994;Zhang et al., 2001Zhang et al., , 2000. ...
... As a difference to methods presented in (Djokic et al., 1998;Powell and Chau, 1991;Willson and Orchard, 1994), our goal is to propose here a new technique to design linear phase IIR filter with flat magnitude response based on complex allpole filters. Additionally, the design specification must be the same as in traditional IIR filter design based on analog filters, i.e., the passband and stopband frequencies, ω p and ω s , the passband droop A p , and the stopband attenuation A s , as shown in Fig. 1. ...
... The magnitude response of the designed filter is given in Fig. 4(a) in solid line. For comparison purpose, we design two filters using the methods (Djokic et al., 1998;Powell and Chau, 1991;Willson and Orchard, 1994). These designs are based on traditional Butterworth filter design. ...
This paper presents a new method for the design of linear phase IIR filters with flat magnitude response. The method is based on the design of flat digital allpole filters with complex coefficients. Depending on the parity of the allpole filter order the resulting IIR filter have either real or complex coefficients. The parameters of the design are the same as in traditional IIR filter design, i.e., passband and stopband frequencies, ωp and ωs, passband droop Ap , and stopband attenuation As . Several design examples are provided to illustrate the method. In addition, a design of linear phase modified twoband IIR filter banks and a design of stable IIR filter with an improved group delay are presented as two applications of the proposed method.
... For the filtering of the EEG data a forward-backward scheme using Butterworth filters was employed that is being applied in one step to the integrality of the ingoing signal. This choice was made for reasons of simplicity, however in order to enable realtime classification in online BCI systems, the filter should be realized either by using a windowed implementation of the forward-backward scheme (Djokic et al., 1998; Kurosu et al., 2003), or by using a traditional causal filtering scheme, for instance based on finite impulse response (FIR) filters. ...
A brain-computer interface (BCI) is a system that enables control of devices or communication with other persons, only through cerebral activity, without using muscles. The main application for BCIs is assistive technology for disabled persons. Examples for devices that can be controlled by BCIs are artificial limbs, spelling devices, or environment control systems. BCI research has seen renewed interest in recent years, and it has been convincingly shown that communication via a BCI is in principle feasible. However, present day systems still have shortcomings that prevent their widespread application. In part, these shortcomings are caused by limitations in the functionality of the pattern recognition algorithms used for discriminating brain signals in BCIs. Moreover, BCIs are often tested exclusively with able-bodied persons instead of conducting tests with the target user group, namely disabled persons. The goal of this thesis is to extend the functionality of pattern recognition algorithms for BCI systems and to move towards systems that are helpful for disabled users. We discuss extensions of linear discriminant analysis (LDA), which is a simple but efficient method for pattern recognition. In particular, a framework from Bayesian machine learning, the so-called evidence framework, is applied to LDA. An algorithm is obtained that learns classifiers quickly, robustly, and fully automatically. An extension of this algorithm allows to automatically reduce the number of sensors needed for acquisition of brain signals. More specifically, the algorithm allows to perform electrode selection. The algorithm for electrode selection is based on a concept known as automatic relevance determination (ARD) in Bayesian machine learning. The last part of the algorithmic development in this thesis concerns methods for computing accurate estimates of class probabilities in LDA-like classifiers. These probabilities are used to build a BCI that dynamically adapts the amount of acquired data, so that a preset, approximate bound on the probability of misclassifications is not exceeded. To test the algorithms described in this thesis, a BCI specifically tailored for disabled persons is introduced. The system uses electroencephalogram (EEG) signals and is based on the P300 evoked potential. Datasets recorded from five disabled and four able-bodied subjects are used to show that the Bayesian version of LDA outperforms plain LDA in terms of classification accuracy. Also, the impact of different static electrode configurations on classification accuracy is tested. In addition, experiments with the same datasets demonstrate that the algorithm for electrode selection is computationally efficient, yields physiologically plausible results, and improves classification accuracy over static electrode configurations. The classification accuracy is further improved by dynamically adapting the amount of acquired data. Besides the datasets recorded from disabled and able-bodied subjects, benchmark datasets from BCI competitions are used to show that the algorithms discussed in this thesis are competitive with state-of-the-art electroencephalogram (EEG) classification algorithms. While the experiments in this thesis are uniquely performed with P300 datasets, the presented algorithms might also be useful for other types of BCI systems based on the EEG. This is the case because functionalities such as robust and automatic computation of classifiers, electrode selection, and estimation of class probabilities are useful in many BCI systems. Seen from a more general point of view, many applications that rely on the classification of cerebral activity could possibly benefit from the methods developed in this thesis. Among the potential applications are interrogative polygraphy ("lie detection") and clinical applications, for example coma outcome prognosis and depth of anesthesia monitoring.
... Non-causal processing is not directly applicable to real-time applications, but can be approximated with block processing. The technique has been used for realization of linear-phase IIR filters [11,12]. The fundamental problem with the concept is the truncation noise that is caused by segmentation. ...
... The fundamental problem with the concept is the truncation noise that is caused by segmentation. The truncation error can be minimized using larger data blocks or rearranging the polynomials in the IIR filter [12]. However, the length of the impulse response used in reverberation filters makes the approach less attractive for reverberation use and is not discussed any further here. ...
In this paper we show several digital signal processing techniques that can be used for non-exponentially decaying artificial reverberation. Traditional recursive filter techniques used for simulating the diffuse part of reverberation produce an exponentially decaying reverberation. We show how traditional reverberation algorithms can be modified and combined to create non-exponentially decaying reverberation. The techniques presented here can be used for interesting musical effects and speech enhancement. As an application example, a real-time system using the Motorola DSP56002 digital signal processor is presented. 1 Introduction Artificial reverberation has been used for dozens of years to add reverberation to studio recordings. The first digital reverberator was developed by Schroeder [1] over 30 years ago. His solution was based on a recursive structure constructed of parallel comb filters in series with two allpass filters. Later, Moorer [2] improved Schroeder's algorith...
