Efficient and multiplierless design of FIR filters with very sharp cutoff via maximally flat building blocks

Vaidyanathan, P.P.

doi:10.1109/tcs.1985.1085695

Cited by 43 publications

(15 citation statements)

References 9 publications

(5 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to Proposition 1, the only two problematic vectors are and . Since the value of is decreased in each iteration, avoiding non-differentiable points can be accomplished if the initial vector satisfies, (21) As a good initial guess, we choose such that the corresponding interpolates the desired response at the points (22) see [36]. Thus, is the solution of the linear system…”

Section: A Algorithm Descriptionmentioning

confidence: 99%

“…Simulations show that this is an excellent choice, since it is usually very close to the optimal solution and also satisfies (21). If some of the points in (22) lie in the transition band , then intermediate values between zero and one are chosen as the value of the desired response .…”

Section: A Algorithm Descriptionmentioning

confidence: 99%

“…Another possible initial vector is the solution of the weighted least-squares approximation given by where and are described in [12]. This guess also appears to be a good choice that satisfies (21), however simulations show that the vector corresponding to (23) often performs better.…”

Section: A Algorithm Descriptionmentioning

confidence: 99%

“…The maximally flat filters are easy to compute and several closed form formula exist for their design [21]- [23]. However, the resulting transition bandwidth is usually very hard to control, which often makes them less attractive.…”

Section: Introductionmentioning

confidence: 99%

See 3 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

Section: A Algorithm Descriptionmentioning

confidence: 99%

Section: A Algorithm Descriptionmentioning

confidence: 99%

Section: A Algorithm Descriptionmentioning

confidence: 99%

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

show abstract

“…If we denote the minimum values of the objective functions in problems (39) and (40) by and , respectively, then because the feasible region of the problem in (39) is a subset of the feasible region of the problem in (40), we have . Furthermore, it has been shown [45] that if the diagonal elements of are all zero and the off-diagonal elements of are all nonnegative, then…”

Section: B a Semidefinite Programming Relaxation Of Problem (36)mentioning

confidence: 99%

A unified approach for the design of 2-D digital filters via semidefinite programming

2002

IEEE Trans. Circuits Syst. I

View full text Add to dashboard Cite

Abstract-This paper attempts to demonstrate that a modern optimization methodology known as semidefinite programming (SDP) can be served as the algorithmic core of a unified design tool for a variety of two-dimensional (2-D) digital filters. Representative SDP-based designs presented in the paper include minimax and weighted least-squares designs of FIR filters with continuous and discrete coefficients, and minimax design of stable separable-denominator IIR filters. Our studies are motivated by the fact that SDP as a subclass of convex programming can be solved efficiently using recently developed interior-point methods and, more importantly, constraints on amplitude/phase responses in certain frequency regions and on stability (for IIR filters), that are often encountered in many filter design problems, can be formulated in a natural way as linear matrix inequalities (LMI) which allow SDP to apply. Design examples for each class of filters are included to demonstrate that SDP-based methods can in many cases be useful in producing optimal or near-optimal 2-D filters with reduced computational complexity.

show abstract

Realization of multirate digital filters with powers‐of‐two coefficients

Todaka

Kambayashi

1992

Electron Comm Jpn Pt III

View full text Add to dashboard Cite

With a view to reducing the amount of hardware in the lowpass filter (LPF), bandpass filter (BPF), and band‐elimination filter (BEF) processing important in digital signal processing, this paper presents a method for configuration of the multirate digital filters with powers‐of‐two coefficients only. The proposed filters are constructed with the sampling rate increaser, the reference LPF and the sampling rate decreaser. The reference LPF consists of the stopband‐forming filter and the pass‐band compensating filter. The stopband‐forming filter consists of a cascade of RRSs while the linear phase FIR or IIR configuration is used for the passband‐compensating filter. First, a method of configuration is presented for the reference LPF based on the sampling rate increaser with powers‐of‐two coefficients. Next, it is shown that the multirate LPF, HPF (high‐pass filter), BPF and BEF with an arbitrary cutoff frequency can be constructed easily from the reference LPF. The present method is particularly effective for narrowband LPF and HPF. Since no multiplier is used, they have zero coefficient sensitivity. It is shown by means of a design example that the present method is effective in reducing the amount of hardware.

show abstract

Efficient and multiplierless design of FIR filters with very sharp cutoff via maximally flat building blocks

Cited by 43 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

A unified approach for the design of 2-D digital filters via semidefinite programming

Realization of multirate digital filters with powers‐of‐two coefficients

Contact Info

Product

Resources

About