On the design of linear phase, FIR integrators for midband frequencies

Kumar, Bipin; Choudhury, Deepankar; Kumar, Ashwani

doi:10.1109/78.539024

Cited by 33 publications

(25 citation statements)

References 8 publications

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“…The response curves in Figure 2 obviously resemble those in Figure 2 of [2], because we have used the same criteria of optimality (viz. maximal flatness of Hn(co, 1) at co = rr/2) in this paper as well as in [2].…”

Section: Performancementioning

confidence: 81%

“…In [2], the optimality criteria adopted is the maximal flatness of Hn (co, 1) at co = 7r/2. This requires the constraints H,}v)(co, l)loj=~/2 =/J(u)(co, 1)lw=~r/2 = (-1)Vv!p v+I,…”

Section: Approximation Of Amplitude Response/q(co 1)mentioning

confidence: 99%

“…The weights b~ n) derived in [2] are computed by using involved mathematical formulas. Here we consider an alternative form (Taylor structure) of the approximation given by…”

Section: Approximation Of Amplitude Response/q(co 1)mentioning

confidence: 99%

“…Also, in biomedical measurements, autofollow control systems, and servomechanism, etc., higher degrees of integration are usually necessary. For many other applications of digital integrators of degree r _> 2, references [2]- [6] are relevant.…”

Section: Introductionmentioning

confidence: 99%

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Efficient linear-phase FIR, maximally flat error approximations for the amplitude response |1/? r |,r,r=1, 2, 3,..., and a versatile realization

Kumar

2000

Circuits Systems and Signal Process

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Abstract. In this paper, designs of linear-phase finite impulse response (FIR) filters approximating the ideal frequency response H(o), r)All/corl r = 1, 2, 3 ..... by using maximally flat error criteria have been proposed. Exact weights required for the realizations have been derived and are shown to be independent of the filter order N. The suggested designs are particularly suitable for operation in the midband frequency range of 0.107r-0.90Jr radians.

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Section: Performancementioning

confidence: 81%

“…In [2], the optimality criteria adopted is the maximal flatness of Hn (co, 1) at co = 7r/2. This requires the constraints H,}v)(co, l)loj=~/2 =/J(u)(co, 1)lw=~r/2 = (-1)Vv!p v+I,…”

Section: Approximation Of Amplitude Response/q(co 1)mentioning

confidence: 99%

“…The weights b~ n) derived in [2] are computed by using involved mathematical formulas. Here we consider an alternative form (Taylor structure) of the approximation given by…”

Section: Approximation Of Amplitude Response/q(co 1)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Efficient linear-phase FIR, maximally flat error approximations for the amplitude response |1/? r |,r,r=1, 2, 3,..., and a versatile realization

Kumar

2000

Circuits Systems and Signal Process

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“…The Fourier transform of Equation (1) yields the analytic relation between displacement and acceleration in the frequency domain [9,10].…”

Section: Analysis Of the Displacement Reconstruction Scheme In The Frmentioning

confidence: 99%

Design of an FIR filter for the displacement reconstruction using measured acceleration in low‐frequency dominant structures

Lee

Hong

Park

2009

Numerical Meth Engineering

157

142

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SUMMARYThis paper presents a new class of displacement reconstruction scheme using only acceleration measured from a structure. For a given set of acceleration data, the reconstruction problem is formulated as a boundary value problem in which the acceleration is approximated by the second-order central finite difference of displacement. The displacement is reconstructed by minimizing the least-squared errors between measured and approximated acceleration within a finite time interval. An overlapping time window is introduced to improve the accuracy of the reconstructed displacement. The displacement reconstruction problem becomes ill-posed because the boundary conditions at both ends of each time window are not known a priori. Furthermore, random noise in measured acceleration causes physically inadmissible errors in the reconstructed displacement. A Tikhonov regularization scheme is adopted to alleviate the ill-posedness. It is shown that the proposed method is equivalent to an FIR filter designed in the time domain. The fundamental characteristics of the proposed method are presented in the frequency domain using the transfer function and the accuracy function. The validity of the proposed method is demonstrated by a numerical example, a laboratory experiment and a field test.

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Linear phase FIR approximation of magnitude response |1/?| for maximal flatness at an arbitrary frequency ?0, 0<?0<?*

Kumar

1999

Circuits Systems and Signal Process

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Abstract. In many signal processing situations, the desired (ideal) magnitude response of the filter is a rational function:/4(~o) = I1/col (a digital integrator). The requirements of a linear phase response and guaranteed stable performance limit the design to a finite impulse response (FIR) structure. In many applications we require the FIR filter to yield a highly accurate magnitude response for a narrow band of frequencies with maximal flatness at an arbitrary frequency coo in the spectrum (0, zr). No techniques for meeting such requirements with respect to approximation of/4(w) are known in the literature. This paper suggests a design by which the linear phase magnitude response I/4(w)[ can be approximated by an FIR configuration giving a maximally fiat (in the Butterworth sense) response at an arbitrary frequency wo, 0 < coo < n. A technique to compute exact weights for the design has also been given.

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On the design of linear phase, FIR integrators for midband frequencies

Cited by 33 publications

References 8 publications

Efficient linear-phase FIR, maximally flat error approximations for the amplitude response |1/? r |,r,r=1, 2, 3,..., and a versatile realization

Efficient linear-phase FIR, maximally flat error approximations for the amplitude response |1/? r |,r,r=1, 2, 3,..., and a versatile realization

Design of an FIR filter for the displacement reconstruction using measured acceleration in low‐frequency dominant structures

Linear phase FIR approximation of magnitude response |1/?| for maximal flatness at an arbitrary frequency ?0, 0<?0<?*

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