Design of high-order digital differentiators using L/sub 1/ error criteria

Chen, C.-K.; Lee, J.-H.

doi:10.1109/82.378044

Cited by 40 publications

(30 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Step Size Selection: The step size, , is determined according to the Armijo rule given by (25) such that a sufficient decrease of is guaranteed. The algorithm is summarized in Table I.…”

Section: A Algorithm Descriptionmentioning

confidence: 99%

“…However, it has not received much attention and serious treatment in the filter design literature. In fact, we are aware of very few works dealing with the criterion [25]- [27]. In [25], the design of high-order differentiators was considered, and in [27] an arbitrary amplitude function was designed using the discrete norm.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, we are aware of very few works dealing with the criterion [25]- [27]. In [25], the design of high-order differentiators was considered, and in [27] an arbitrary amplitude function was designed using the discrete norm. A general algorithm for the approximation under was proposed in [26], but convergence is not guaranteed for , and when it exists, it is often very slow.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

An $L_1$-Method for the Design of Linear-Phase FIR Digital Filters

Grossmann

Eldar

2007

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

Abstract-This paper considers the design of linear-phase finite impulse response digital filters using an 1 optimality criterion. The motivation for using such filters as well as a mathematical framework for their design is introduced. It is shown that 1 filters possess flat passbands and stopbands while keeping the transition band comparable to that of least-squares filters. The uniqueness of 1 -based filters is explored, and an alternation type theorem for the optimal frequency response is derived. An efficient algorithm for calculating the optimal filter coefficients is proposed, which may be viewed as the analogue of the celebrated Remez exchange method. A comparison with other design techniques is made, demonstrating that the 1 approach may be a good alternative in several applications.

show abstract

“…Step Size Selection: The step size, , is determined according to the Armijo rule given by (25) such that a sufficient decrease of is guaranteed. The algorithm is summarized in Table I.…”

Section: A Algorithm Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

An $L_1$-Method for the Design of Linear-Phase FIR Digital Filters

Grossmann

Eldar

2007

IEEE Trans. Signal Process.

View full text Add to dashboard Cite

show abstract

“…We consider a sampling period (given without unit) of T s = 1/200 which corresponds to 1000 samples in the interval [0,5]. The samples of the noise are simulated from a zero-mean white Gaussian iid sequence.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…See also [19,22,34] for other approaches from the control litterature. In signal processing, it is very common to cast the problem in terms of frequency domain digital filter design [31], [29], [5]. This is motivated by the observation that an ideal n th order differentiator has a frequency response of magnitude ω n .…”

Section: Introductionmentioning

confidence: 99%

Numerical differentiation with annihilators in noisy environment

2008

View full text Add to dashboard Cite

Numerical differentiation in noisy environment is revised through an algebraic approach. For each given order, an explicit formula yielding a pointwise derivative estimation is derived, using elementary differential algebraic operations. These expressions are composed of iterated integrals of the noisy observation signal. We show in particular that the introduction of delayed estimates affords significant improvement. An implementation in terms of a classical finite impulse response (FIR) digital filter is given. Several simulation results are presented.

show abstract

Algebraic Estimation in Partial Derivatives Systems: Parameters and Differentiation Problems

Ushirobira

Korporal

Perruquetti

2020

Algebraic and Symbolic Computation Methods in Dynamical Systems

View full text Add to dashboard Cite

Two goals are sought in this paper: namely, to provide a succinct overview on algebraic techniques for numerical differentiation and parameter estimation for linear systems and to present novel algebraic methods in the case of several variables. The state-of-art in the introduction is followed by a brief description of the methodology in the subsequent sections. Our new algebraic methods are illustrated by two examples in the multidimensional case. Some algebraic preliminaries are given in the appendix.

show abstract

Design of high-order digital differentiators using L/sub 1/ error criteria

Cited by 40 publications

References 9 publications

An $L_1$-Method for the Design of Linear-Phase FIR Digital Filters

An $L_1$-Method for the Design of Linear-Phase FIR Digital Filters

Numerical differentiation with annihilators in noisy environment

Algebraic Estimation in Partial Derivatives Systems: Parameters and Differentiation Problems

Contact Info

Product

Resources

About