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105
Linear phase lowpass IIR digital differentiators
 IEEE Trans. Signal Process
"... Abstract—A novel approach to designing approximately linear phase infiniteimpulseresponse (IIR) digital filters in the passband region is introduced. The proposed approach yields digital IIR filters whose numerators represent linear phase finiteimpulseresponse (FIR) filters. As an example, lowp ..."
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Abstract—A novel approach to designing approximately linear phase infiniteimpulseresponse (IIR) digital filters in the passband region is introduced. The proposed approach yields digital IIR filters whose numerators represent linear phase finiteimpulseresponse (FIR) filters. As an example, lowpass IIR differentiators are introduced. The range and highfrequency suppression of the proposed lowpass differentiators are comparable to those obtained by higher order FIR lowpass differentiators. In addition, the differentiators exhibit almost linear phases in the passband regions. Index Terms—AlAlaoui operator, analog filters, bilinear transformation, digital differentiators, finiteimpulseresponse (FIR) filters, infiniteimpulseresponse (IIR) filters, linear phase, lowpass digital differentiators. I.
Approximate Fekete points for weighted polynomial interpolation
, 2009
"... We compute approximate Fekete points for weighted polynomial interpolation, by a recent algorithm based on QR factorizations of Vandermonde matrices. We consider in particular the case of univariate and bivariate functions with prescribed poles or other singularities, which are absorbed in the basis ..."
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We compute approximate Fekete points for weighted polynomial interpolation, by a recent algorithm based on QR factorizations of Vandermonde matrices. We consider in particular the case of univariate and bivariate functions with prescribed poles or other singularities, which are absorbed in the basis by a weight function. Moreover, we apply the method to the construction of real and complex weighted polynomial filters, where the relevant concept is that of weighted norm.
Exchange algorithms that complement the ParksMcClellan algorithm for linearphase FIR filter design
 IEEE Trans. Circuits Syst. II, Analog Digit. Signal Process.g
, 1997
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The Asymptotics of Optimal (Equiripple) Filters
, 1999
"... fFor equiripple filters, the relation among the filter length N +1, the transition bandwidth 1!, and the optimal passband and stopband errors ffi p and ffi s has been a secret for more than 20 years. This paper is aimed at solving this mystery. We derive the exact asymptotic results in the weightfre ..."
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Cited by 5 (2 self)
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fFor equiripple filters, the relation among the filter length N +1, the transition bandwidth 1!, and the optimal passband and stopband errors ffi p and ffi s has been a secret for more than 20 years. This paper is aimed at solving this mystery. We derive the exact asymptotic results in the weightfree case ffi p = ffi s = ffi, which enables us to interpret and improve the existing empirical formulas. Our main results are finally combined into formula (17). In the transition band, the filter response is discovered to be asymptotically close to a scaled error function. The main tools are potential theory in the complex plane and asymptotic analysis.
Hierarchical Watermarking for Protection of DSP Filter Cores
 IN PROCEEDINGS OF THE CUSTOM INTEGRATED CIRCUITS CONFERENCE. PISCATAWAY, NJ: IEEE
, 1999
"... A hierarchical watermarking approach is developed that incorporates an ownership identification .directly into the design development process. This approach oftrs a high degree of tamper resistance and provides easy, noninvasive copy detection. We present two FIR digital filter cores, one watermarke ..."
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A hierarchical watermarking approach is developed that incorporates an ownership identification .directly into the design development process. This approach oftrs a high degree of tamper resistance and provides easy, noninvasive copy detection. We present two FIR digital filter cores, one watermarked at the algorithm level and the second at the algorithm and architecture levels. A unique ownership signature (watermark) is placed at each level. At the algorithm level, the watermark is embedded in the filter coefficients during the development of the transfer function. At the architecture level, we use circuit transformations to watermark the design. Experimental results show approximately 7% area overhead of the algorithmlevel watermarked design over a nonwatermarked design. The cost of area for the design watermarked at both the algorithm and architecture levels is less than 40%.
Nonlinear Phase FIR Filter Design according to the L 2 Norm with Constraints for the Complex Error
, 1994
"... We examine the problem of approximating a complex frequency response by a realvalued FIR filter according to the L 2 norm subject to additional inequality constraints for the complex error function. Starting with the KuhnTucker optimality conditions which specialize to a system of nonlinear equati ..."
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We examine the problem of approximating a complex frequency response by a realvalued FIR filter according to the L 2 norm subject to additional inequality constraints for the complex error function. Starting with the KuhnTucker optimality conditions which specialize to a system of nonlinear equations we deduce an iterative algorithm. These equations are solved by Newton's method in every iteration step. The algorithm allows arbitrary tradeoffs between an L 2 and an L1 design. The L 2 and the L1 solution result as special cases. Wir untersuchen das Problem der Approximation eines komplexen Frequenzganges mittels eines reellwertigen nichtrekursiven Filters nach der L 2 Norm mit zusatzlichen Ungleichungsbedingungen fur die komplexe Fehlerfunktion. Ausgehend von den KuhnTucker Optimalitatsbedingungen, die auf ein nichtlineares Gleichungssystem fuhren, leiten wir einen iterativen Algorithmus her. Diese Gleichungen werden in jedem Iterationsschritt mittels des NewtonVerfahrens gelost. D...
Theory and Design of Multirate Sensor Arrays
"... Abstract—This paper studies the basic design challenges associated with multirate sensor arrays. A multirate sensor array is a sensor array in which each sensor node communicates a lowresolution measurement to a central processing unit. The objective is to design the individual sensor nodes and the ..."
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Abstract—This paper studies the basic design challenges associated with multirate sensor arrays. A multirate sensor array is a sensor array in which each sensor node communicates a lowresolution measurement to a central processing unit. The objective is to design the individual sensor nodes and the central processing unit such that, at the end, a unified highresolution measurement is reconstructed. A multirate sensor array can be modeled as an analysis filterbank in discretetime. Using this model, the design problem is reduced to solving the following two problems: a) how to design the sensor nodes such that the timedelay of arrival (TDOA) between the sensors can be estimated and b) how to design a synthesis filterbank to fuse the lowrate data sent by the sensor nodes given the TDOA? In this paper, we consider a basic twochannel sensor array. We show that it is possible to estimate the TDOA between the sensors if the analysis filters incorporated in the array satisfy specific phaseresponse requirements. We then provide practical sample designs that satisfy these requirements. We prove, however, that a fixed synthesis filterbank cannot reconstruct the desired highresolution measurement for all TDOA values. As a result, we suggest a fusion system that uses different sets of synthesis filters for even and odd TDOAs. Finally, we use the optimality theory to design optimal synthesis filters. Index Terms—Delay estimation, filterbanks, FIR filters, optimization, multirate systems, multisensor systems, sensor fusion, sensor networks. I.
Conjugate Quadrature Filters
"... Conjugate quadrature filters (CQF's) have applications to wavelet construction and signal processing. We show that any continuous frequency response (Fourier transform) P of a CQF p can be uniformly approximated by the frequency response Q of CQF q having finite length. Our first proof uses Ha ..."
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Conjugate quadrature filters (CQF's) have applications to wavelet construction and signal processing. We show that any continuous frequency response (Fourier transform) P of a CQF p can be uniformly approximated by the frequency response Q of CQF q having finite length. Our first proof uses Hardy space theory and the parametrization of CQF's by the infinite dimensional Lie group of paraunitary matrices. Our second proof uses a differential equation method to approximate CQF's by CQF's having factorial decay, followed by a phase retreival method to approximate CQF's having factorial decay by CQF's having finite support. 1 Introduction We let Z; R; C; and T denote the integers, reals, complex numbers, and unit circle. A conjugate quadrature filter (CQF) is a sequence p whose Fourier transform P is a measurable function that satisfies jP (w)j 2 + jP (\Gammaw)j 2 = 1; w 2 T : (1.1) These filters, having either finite or infinite support, have applications to wavelet construction and...
BARYCENTRICREMEZ ALGORITHMS FOR BEST POLYNOMIAL APPROXIMATION IN THE Chebfun System
 BIT NUMERICAL MATHEMATICS (2008)46
, 2008
"... The Remez algorithm, 75 years old, is a famous method for computing minimax polynomial approximations. Most implementations of this algorithm date to an era when tractable degrees were in the dozens, whereas today, degrees of hundreds or thousands are not a problem. We present a 21stcentury update ..."
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The Remez algorithm, 75 years old, is a famous method for computing minimax polynomial approximations. Most implementations of this algorithm date to an era when tractable degrees were in the dozens, whereas today, degrees of hundreds or thousands are not a problem. We present a 21stcentury update of the Remez ideas in the context of the chebfun software system, which carries out numerical computing with functions rather than numbers. A crucial feature of the new method is its use of chebfun global rootfinding to locate extrema at each iterative step, based on a recursive algorithm combining ideas of Specht, Good, Boyd, and Battles. Another important feature is the use of the barycentric interpolation formula to represent the trial polynomials, which points the way to generalizations for rational approximations. We comment on available software for minimax approximation and its scientific context, arguing that its greatest importance these days is probably for fundamental studies rather than applications.
Second order volterra inverses for compensation of loudspeaker nonlinearity
 in Proceedings of the IEEE ASSP Workshop on applications of
, 1995
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