On the approximation problem in nonrecursive digital filter design

Herrmann, O.E.

doi:10.1109/tct.1971.1083275

Cited by 184 publications

(81 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Lowpass filter design based on Taylor series has been considered in [39] and later in [25]. The proposed method is also closely related to the complex orthogonal symmetric wavelet design method given recently by Han [40].…”

Section: Paper's Contributionmentioning

confidence: 99%

See 1 more Smart Citation

Symmetric tight frame wavelets with dilation factor M=4

Abdelnour

2011

Signal Processing

View full text Add to dashboard Cite

In this paper we discuss a new set of symmetric tight frame wavelets with the associated filterbank outputs downsampled by four at each stage. The frames consist of seven generators obtained from the lowpass filter using spectral factorization, with the lowpass filter obtained via a simple method using Taylor polynomials. The filters are simple to construct, and offer smooth scaling functions and wavelets. Additionally, the filterbanks presented in this paper have limited redundancy while maintaining the smoothness of underlying limit functions. The filters are linear phase (symmetric), FIR, and the resulting wavelets possess vanishing moments.

show abstract

Section: Paper's Contributionmentioning

confidence: 99%

“…We base the proposed design method on the earlier work by Herrmann [39]. The proposed method is also closely related to the complex orthogonal symmetric wavelet design method…”

Section: Lowpass Filter Designmentioning

confidence: 99%

Symmetric tight frame wavelets with dilation factor M=4

Abdelnour

2011

Signal Processing

View full text Add to dashboard Cite

show abstract

“…i (67) nn Since P is positive-definite, I,,,, in (67) are evidently nonzero. Using (67), we first solve for uk+i (0) and solve recursively for all uk+i(n) for 1~ n < N-1, where N is the dimension of L. (In (67), xk(n) denotes the nth element of vector xk.) It takes N(N -1)/2 multiplications, N divisions, and N( N -1)/2 additions to compute vk 't i.…”

Section: Eigenvectorcomputationandrelated Issuesmentioning

confidence: 99%

Eigenfilters: A new approach to least-squares FIR filter design and applications including Nyquist filters

Vaidyanathan

Nguyen

1987

IEEE Trans. Circuits Syst.

318

View full text Add to dashboard Cite

Abstract-A new method of designing linear-phase FIR filters is proposed by minimizing a quadratic measure of the error in the passband and stopband. The method is based on the computation of an eigenvector of an appropriate real, symmetric, and positive-definite matrix. The proposed design procedure is general enough to incorporate both time-and frequency-domain constraints. For example, Nyquist filters can be easily designed using this approach. The design time for the new method is comparable to that of Remez exchange techniques. The passband and stopband errors in the frequency domain can be made eqniripple by an iterative process, which involves feeding back the approximation error at each iteration. Several numerical design exahples and comparisons to existing methods are presented, which demonstrate the usefulness of the present approach.

show abstract

“…It can be shown, based on the results in [7] that such a low-pass function is given by 1.000 '0. l/a2 and is, therefore, much larger than for an equiripple filter approximation with 26 dB (0.05) stopband loss.…”

Section: Maxflat Fir Filtersmentioning

confidence: 99%

“…The main disadvantage of such techniques is that the resulting filters generally require larger number of multiplications for implementation as compared to the filters based on optimization techniques. Examples of this type of design procedure are the windowmg technique [5], the Chebyshev-function based technique,s [6], and the MAXFLAT techniques [7]. In this paper, we are primarily concerned with the maximally flat (MAXFLAT) FIR filters which can be designed "quickly" using Kaiser's method [8], without the use of iterative algorithms.…”

Section: Introductionmentioning

confidence: 99%

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

Vaidyanathan

1985

IEEE Trans. Circuits Syst.

View full text Add to dashboard Cite

Ahsrract -A new design technique for linear-phase FIR filters, based on maximally flat building blocks, is presented. The design technique does not involve iterative approximations and is, therefore, fast. It gives rise to filters that have a monotone stopband response, as required in some applications. The technique is partially based on an interpolative scheme. Implementation of the obtained filter designs requires a much smaller number of multiplications than maximally flat (MAXFLAT) FIR filters designed by the conventional approach. A technique based on FIR spectral transformations to design new multiplierless FIR filter structures is then advanced, and multiplierless implementations for sharp cutoff specifications are included.

show abstract

On the approximation problem in nonrecursive digital filter design

Cited by 184 publications

References 1 publication

Symmetric tight frame wavelets with dilation factor M=4

Symmetric tight frame wavelets with dilation factor M=4

Eigenfilters: A new approach to least-squares FIR filter design and applications including Nyquist filters

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

Contact Info

Product

Resources

About