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Timo I. Laakso, Helsinki University of Technology (Finland)
Vesa Valimaki, Helsinki University of Technology (Finland)
A measure for the effective length of the impulse response of a stable recursive digital filter based on accumulated energy is proposed. A general definition and a simple algorithm for its evaluation are introduced, and closed-form expressions are derived for first-order IIR filters. The effect of zeros on the effective length is analyzed. An upper bound for the effective length of higher-order filters is derived using results for low-order filters. The new measure finds applications in several fields of digital signal processing, including estimation of the extent of attack transients for filters with dynamically varying inputs, elimination of transients in variable recursive filters, and design and implementation of linear-phase IIR systems.
ic981501.pdf (From Postscript)
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Guergana S Mollova, UACG-Sofia
Rolf Unbehauen, University of Erlangen-Nurnberg (Germany)
This article presents some new results concerning recursive filters design with approximately linear phase and Chebyshev stopband attenuation. The denominator polynomial D(z) of the transfer function H(z)=N(z)/D(z) is used to obtain amaximally flat behavior for the delay in the passband, whereas N(z) describes equiripple amplitude in the stopband. The approach under consideration is based on z-domain concepts. At the end, the paper concludes with several detailed examples and graphics showing the efficacy of the proposed technique.
ic981097.pdf (Scanned) TOPAki Härmä, Helsinki University of Technology (Finland)
Certain types of recursive filters have been considered as non-realizable because they contain delayless recursive loops. Usually the problem is rather technical than theoretical. In this paper a method of implementing such filters is introduced. The general procedure is to split a delay free recursive filter to a non-delay free and a pure delay free structure.As a combination of these, the filter can be implemented directly and efficiently. In addition, following from the same formulation, a generic procedure to convert any such filter to an equivalent directly realizable structure is also given. As an example, a set of frequency warped all-pole filters is considered. The new warped all-pole lattice introduced in this paper completes the family of warped filters.
ic981114.pdf (From Postscript) TOP
Fabrizio Argenti, University of Florence (Italy)
Enrico Del Re, University of Florence (Italy)
In this study, the eigenfilter approach is applied to designing Infinite Impulse Response (IIR) filters having an arbitrary magnitude frequency response. A causal rational transfer function having an arbitrary number of poles and zeros is achieved. The procedure works in the frequency domain. Some numerical examples showing the application of the presented method to the design of multiband filters with different gains and different magnitude shape in each band are presented.
ic985221.pdf (Scanned) TOP
Hai H Dam, Curtin University (Australia)
Sven Nordebo, Curtin University (Australia)
Kok L Teo, Curtin University (Australia)
Antonio Cantoni, Curtin University (Australia)
In this paper, we consider a class of FIR filters defined by the first order different routing digital filter (DRDF) structure and sums of two powers of two coefficients. A novel design method is developed for constructing high quality filters with reference to the min-max error criterion. This method is highly efficient in terms of computational time. Simulation studies show a large improvement over existing methods such as quantization. In some cases, the peak ripple magnitute over the stop and pass bands is reduced up to 13 dB over the quantization method. These results are achieved for even small number of delays.
ic981550.pdf (From Postscript) TOP
Roy Chapman, University of Strathclyde, Scotland (U.K.)
Tariq S Durrani, University of Strathclyde, Scotland (U.K.)
This paper presents a new technique which exploits constrained optimization methods to derive optimal two dimensional filters in the cumulant domain for processing signals in non Gaussian noise, or signals with corrupting interferences which have non symmetrical probability density functions. The approach proposed here for enhancing signals in such noise is important, as increasingly practical engineering application areas are identifying occasions where the perceived wisdom of modelling signals in additive noise simply does not hold. Since the bispectrum of non Gaussian noise and interference is not zero, it corrupts the bispectrum of the signal. Thus filters that suppress the bispectral component of the noise and enhance the signal bispectrum are required. The two dimensional filters proposed in this paper have the property of concentrating the filter energy into a hexagonal region in the bispectral domain. This leads to an impulse response for these filters which represents a new form of two dimensional discrete prolate spheriodal sequence. The sensitivity of cumulant determination for non Gaussian noise has been noted in the area of array processing. However this paper presents one of the first attempts to remove non Gaussian noise by cumulant filtering.
ic981821.pdf (From Postscript) TOP
Subhash Challa, Queensland University of Technology (Australia)
Farhan A Faruqi, Queensland University of Technology (Australia)
Chebechev's inequality theorem from the theory of probability and statistics provides an upperbound for the amount of probability in the ""tails"" of any given probability density function. This theorem has interesting applications in the numerical solution of the Fokker-Planck-Kolmogorov Equation (FPKE) as shown in this paper. Numerical solution of FPKE is an essential component of the design of optimal nonlinear filters. The solution of the FPKE in conjunction with the Bayes' conditional density lemma provides optimal (minimum variance) state estimates of any general stochastic dynamic system (SDS).
ic981873.pdf (From Postscript) TOPSalim Ibrir, Laboratoire des Signaux et Systemes (France)
This paper is dealing with a numerical method for data-fitting and estimation of the continuous higher derivatives of a given signal from its non-exact sampled data. The proposed algorithm is a generalization of the algorithm proposed by C. H. Reinsch[1967]. This algorithm is conceived as being a key element in the structure of the numerical observer discussed in our last papers. The presented algorithm seems to be flexible because of the introduction of equivalent conditions of smoothness derived from finite difference methods. Detailed steps of the computational method will be given to evaluate the continuous approximates of higher derivatives of a signal given by its noisy discrete values together with the filtered continuous signal. Satisfactory results have been obtained showing the efficiency of such an algorithm. Keywords: Spline functions, Numerical differentiation, Observers, Smooth filters.
ic982005.pdf (From Postscript) TOP