19 research outputs found
On the eigenfilter design method and its applications: a tutorial
The eigenfilter method for digital filter design involves the computation of filter coefficients as the eigenvector of an appropriate Hermitian matrix. Because of its low complexity as compared to other methods as well as its ability to incorporate various time and frequency-domain constraints easily, the eigenfilter method has been found to be very useful. In this paper, we present a review of the eigenfilter design method for a wide variety of filters, including linear-phase finite impulse response (FIR) filters, nonlinear-phase FIR filters, all-pass infinite impulse response (IIR) filters, arbitrary response IIR filters, and multidimensional filters. Also, we focus on applications of the eigenfilter method in multistage filter design, spectral/spacial beamforming, and in the design of channel-shortening equalizers for communications applications
Design of FIR digital filters with prescribed flatness and peak error constraints using second-order cone programming
This paper studies the design of digital finite impulse response (FIR) filters with prescribed flatness and peak design error constraints using second-order cone programming (SOCP). SOCP is a powerful convex optimization method, where linear and convex quadratic inequality constraints can readily be incorporated. It is utilized in this study for the optimal minimax and least squares design of linear-phase and low-delay (LD) FIR filters with prescribed magnitude flatness and peak design error. The proposed approach offers more flexibility than traditional maximally-flat approach for the tradeoff between the approximation error and the degree of design freedom. Using these results, new LD specialized filters such as digital differentiators, Hilbert Transformers, Mth band filters and variable digital filters with prescribed magnitude flatness constraints can also be derived. © 2005 IEEE.published_or_final_versio
Critical analysis of the eigenfilter method for the design of FIR filters and wideband beamformers
The least squares based eigenfilter method has been
applied to the design of both finite impulse response (FIR) filters
and wideband beamformers successfully. It involves calculating
the resultant filter coefficients as the eigenvector of an appropriate
Hermitian matrix, and offers lower complexity and less
computation time with better numerical stability as compared
to the standard least squares method. In this paper, we revisit
the method and critically analyze the eigenfilter approach by
revealing a serious performance issue in the passband of the designed
FIR filter and the mainlobe of the wideband beamformer,
which occurs due to a formulation problem. A solution is then
proposed to mitigate this issue, and design examples for both FIR
filters and wideband beamformers are provided to demonstrate
the effectiveness of the proposed method
Optimum design of discrete-time differentiators via semi-infinite programming approach
In this paper, a general optimum full band high order discrete-time differentiator design problem is formulated as a peak constrained least square optimization problem.
That is, the objective of the optimization problem is to minimize the total weighted square error of the magnitude response subject to the peak constraint of the weighted
error function. This problem formulation provides a great flexibility for the tradeoff between the ripple energy and the ripple magnitude of the discrete-time differentiator.
The optimization problem is actually a semi-infinite programming problem. Our recently developed dual parametrization algorithm is applied for solving the problem. The main advantage of employing the dual parameterization algorithm for solving the problem is the guarantee of the convergence of the algorithm and the obtained solution being the global optimal solution that satisfies the corresponding continuous constraints. Moreover, the computational cost of the algorithm is lower than that of algorithms implementing the semi-definite programming approach
Unified eigenfilter approach: with applications to spectral/spatial filtering
The eigenfilter approach is extended to solve general least-squares approximation problems with linear constraints. Such extension unifies previous work in eigenfilters and many other filter design problems, including spectral/spatial filtering, one-dimensional or multidimensional filters, data independent or statistically optimal filtering, etc. With this approach, various filter design problems are transformed into problems of finding an eigenvector of a positive definite matrix that is determined by filter design specifications. This approach has the advantage that many filter design constraints can be incorporated easily. A number of design examples are presented to show the usefulness and flexibility of the proposed approach
Revisit of the eigenfilter method for the design of FIR filters and wideband beamformers
The least squares-based eigenfilter method has been applied to the design of both finite impulse response (FIR) filters and wideband beamformers successfully. It involves calculating the resultant filter coefficients as the eigenvector of an appropriate Hermitian matrix, and offers lower complexity and less computation time with better numerical stability as compared to the standard least squares method. In this paper, we revisit the method and critically analyse the eigenfilter method by revealing a serious performance issue in the passband of the designed FIR filter and the mainlobe of the wideband beamformer, which occurs due to a formulation problem. A solution is then proposed to mitigate this issue by imposing an additional constraint to control the response at the passband/mainlobe, and design examples for both FIR filters and wideband beamformers are provided to demonstrate the effectiveness of the proposed method
Design and frequency analysis of continuous finite-time-convergent differentiator
In this paper, a continuous finite-time-convergent differentiator is
presented based on a strong Lyapunov function. The continuous differentiator
can reduce chattering phenomenon sufficiently than normal sliding mode
differentiator, and the outputs of signal tracking and derivative estimation
are all smooth. Frequency analysis is applied to compare the continuous
differentiator with sliding mode differentiator. The beauties of the continuous
finite-time-convergent differentiator include its simplicity, restraining
noises sufficiently, and avoiding the chattering phenomenon