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Journal ArticleDOI

An alternative sensitivity measure for designing low-sensitivity digital biquads

TL;DR: In this article, a sensitivity measure for determining the optimum set of machine-representable multiplier constants in the derivation of low-sensitivity digital biquadratic filters was proposed.
Abstract: A sensitivity measure is proposed for determining the optimum set of machine-representable multiplier constants in the derivation of low-sensitivity digital biquadratic filters. A comparison of this measure with two other sensitivity measures of this class is then undertaken using four different design examples. The four sixth-order filters considered are a Butterworth low-pass, a Chebyshev high-pass, an elliptic bandstop, and an elliptic bandpass filter. It is shown that the three sensitivity measures usually give slightly different low-sensitivity designs and that the new sensitivity measure often gives the best design. >
Citations
More filters
01 Jul 1997
TL;DR: An attempt is made to review and systematize all known structures and methods of design of variable digital filters with variable characteristics for different applications.
Abstract: There has been a constant interest in the design and implementation of digital filters with variable characteristics for different applications. In this article an attempt is made to review and systematize all known structures and methods of design of such filters. First the basic theory of the variable digital filters is introduced. Then FIR and IIR realizations with real and complex coefficients are considered, the known results for multidimensional variable filters are discussed and finally, typical implementations are overviewed. Recommendations for applications in different situations are given and unresolved problems are pointed out. This work is basically a review, but some of our original results are also included.

118 citations


Cites methods from "An alternative sensitivity measure ..."

  • ...Low-sensitivity allpass and LP sections can be selected in [49]-[51] or might be developed by using some sensitivity minimization techniques, like those in [52] and [53]....

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Proceedings ArticleDOI
01 Jan 1998
TL;DR: In this paper, an approach to minimize the two main disadvantages of the truncated Taylor series expansion of the allpass sections coefficients is proposed, which is shown that the degradation of the stop-band characteristics could be considerably decreased by minimizing the sensitivities of all-pass sections in the parallel structure over some critical frequency ranges.
Abstract: The best and simplest method to realize variable IIR digital filters is to apply frequency transformations on a parallel-allpass-structures-based circuits, followed by truncated Taylor series expansion of the allpass sections coefficients. In this work an approach to minimize the two main disadvantages of this method is proposed. It is shown first, after analyzing the sensitivity of the realization, that the degradation of the stop-band characteristics could be considerably decreased by minimizing the sensitivities of the allpass sections in the parallel structure over some critical frequency ranges. Then the tuning accuracy is improved by minimizing the sensitivities of the allpass sections used to apply the frequency transformations. Appropriate first- and second-order allpass sections are proposed for the most typical cases. The effectiveness of the proposed approach is demonstrated by simulation examples.

17 citations

Book ChapterDOI
11 Apr 2011

13 citations


Cites methods from "An alternative sensitivity measure ..."

  • ...9a) and DF (Eswaran et al., 1991)....

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  • ...The orthogonal complex LS2 filter section is compared with two other often-studied secondorder orthogonal complex sections: DF-section (Direct Form) (Eswaran et al., 1991) and MNsection (Minimum Norm) (Nie et al....

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Journal ArticleDOI
01 Jan 1994-Frequenz
TL;DR: In this article, all known first-order allpass sections with single multiplier and delay and limited to four adders are investigated, and general recommendations are formulated and families of curves are provided to be used for the selection of best circuit for given pole location and critical frequency band.
Abstract: In this paper all known first-order allpass sections with single multiplier and delay and limited to four adders are investigated. It is shown that most of the known sections are of a bridge (lattice) type and some new circuits of this type arc proposed. The sections are compared with respect to their multiplier coefficient sensitivities and roundoff noises, and general recommendations are formulated and families of curves are provided to be used for the selection of best circuit for given pole location and critical frequency band. It is shown that the roundoff noise cannot be used as a criterion for this selection. The obtained results are very important for the design of low sensitivity digital (liters based on parallel allpass structures. Übersicht: In diesem Beitrag werden alle bekannten Allpässe ersten Grades mit einem Multiplizierer, einem Verzögerungselement und bis zu vier Addierern untersucht. Die meisten dieser Schaltungen sind durch Krcuzglicdcr realisiert; einige neue Schaltkreise dieses Typs werden vorgeschlagen. Neben dem Vergleich der Allpässe hinsichtlich ihrer Kocffizientcncmpfindlichkcit und des Rundungsrauschcns enthält der Beitrag allgemeine Empfehlungen und Kurvenscharen, die sich zur Auswahl des besten Schaltkreises bei gegebener Polverteilung und gegebenem kritischen Frequenzband verwenden lassen. Es wird gezeigt, daß das Rundungsrauschcn nicht als Kriterium für diese Auswahl benutzt werden kann. Die gewonnenen Ergebnisse sind von großer Bedeutung für den Entwurf von Digitalfiltern geringer Empfindlichkeit, die auf parallclgeschaltctcn Allpaßstrukturen beruhen. Für die Dokumenta t ion : Digitale Filter / Allpaßstrukturen / Empfindlichkeit gegen Parameteränderungen / Rundungsrauschcn

13 citations


Cites background from "An alternative sensitivity measure ..."

  • ...First, it is clear that the sensitivity is lower when the multiplier coefficient value is smaller, as it was pointed out in [18] for biquadratic circuits....

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  • ...Besides, some new measures of sensitivities were suggested [18] in order to avoid the cumbersome and time consuming calculations especially in frequency domain....

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Proceedings ArticleDOI
01 Dec 1997
TL;DR: Very low magnitude sensitivity first and second-order bandpass and bandstop complex coefficient orthogonal digital filter structures are derived by developing appropriate prototype sections and applying on them a circuit transformation as discussed by the authors.
Abstract: Very low magnitude sensitivity first- and second-order bandpass and bandstop complex coefficient orthogonal digital filter structures are derived by developing appropriate prototype sections and applying on them a circuit transformation. The bandstop and the multioutput universal orthogonal sections are proposed for first time. Then, a comparative study together with other known structures is conducted and it is shown that while having a canonic (minimum) number of multipliers and delay elements (many times less than those of the other known structures), the new structures have tens or hundreds of times lower sensitivity for narrow-band realizations. A method of approximation and design of higher orthogonal filters employing the new sections also is proposed. The lower sensitivity of the new structures is demonstrated experimentally.

9 citations

References
More filters
Journal ArticleDOI
TL;DR: For poles close to the unit circle and near z = 1, the usual realizations of recursive or IIR digital filters are highly sensitive to the coefficient quantization and have large roundoff noise as mentioned in this paper.
Abstract: For poles close to the unit circle and near z = 1 , the usual realizations of recursive or IIR digital filters are highly sensitive to the coefficient quantization and have large roundoff noise. As the sampling rate is increased the poles approach z = 1 and the problems become more severe. For these situations several new digital filter structures are presented for which the above errors remain constant and generally insignificant as the sampling rate is increased. Results on sensitivity and the roundoff errors for these new structures are presented and compared with conventional realizations. Some numerical results are also presented showing order of magnitude improvements.

161 citations

Journal ArticleDOI
TL;DR: In this article, the authors investigate the effect of digital ladder structures on the performance of low-coefficient word length and conclude that the digital ladder structure in many cases can be implemented with lower coefficient word lengths than conventional structures.
Abstract: Recently, there has been a great deal of interest in the implementation of digital filter structures with low-coefficient word length. A conjecture has been made by Fettweis that if digital filter structures are modeled after analog ladder structures, which are known to have desirable coefficient sensitivity properties, then the digital ladder structures will also have these properties and could be implemented with low-coefficient word lengths. To investigate this conjecture, a seventh-order Chebyshev low-pass filter was realized as a digital ladder structure and the coefficient sensitivity was analyzed experimentally under coefficient rounding in floating-point representation. To serve as a comparison similar examples of cascade structures of direct and coupled form sections were also analyzed in the same manner. The conclusions drawn are that, indeed, the digital ladder structures in many cases can be implemented with lower coefficient word lengths than the conventional structures.

74 citations

Journal ArticleDOI
TL;DR: In this paper, three classes of digital-filter structures, namely two classes of cascade structures and one class of wave structures, are compared with regards to the number of arithmetic operations, the inherent speed capability, the output noise due to product quantization, and the sensitivity to multiplier-coefficient quantization.
Abstract: Three classes of digital-filter structures, namely two classes of cascade structures and one class of wave structures, are compared with regards to the number of arithmetic operations, the inherent speed capability, the output noise due to product quantization, and the sensitivity to multiplier-coefficient quantization Four types of filters are considered, namely a Butterworth low-pass filter, a Chebyshev high-pass filter, an elliptic bandstop filter, and an elliptic band-pass filter The arithmetic is assumed to be of the fixed-point type, numbers are assumed to be in two's complement representation, and number quantization is assumed to be by rounding

30 citations

Journal ArticleDOI
TL;DR: In this article, a systematic and exhaustive procedure is used to generate a class of new low-sensitivity second-order digital-filter structures which are amenable to error-spectrum shaping (ESS).
Abstract: A systematic and exhaustive procedure is used to generate a class of new low-sensitivity second-order digital-filter structures which are amenable to error-spectrum shaping (ESS). Collectively, these structures can realize any stable second-order transfer function. For every transfer function, a choice of at least two structures is available but, through a sensitivity analysis, the optimum one can always be identified. The paper concludes with sensitivity and roundoff-noise comparisons which show that the new structures are usually superior relative to corresponding direct canonic structures and also relative to the state-space section-optimal structure.

22 citations