Time-domain filter bank analysis: a new design theory

Nayebi, K.; Barnwell, T.P.; Smith, M.J.T.

doi:10.1109/78.139245

Cited by 148 publications

(73 citation statements)

References 14 publications

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“…However, selectivity was poor at ς = −0.216 when compared with ς = 0.847 for DCOMS(22;11), while uncertainty was good at υ = 0.928 when compared with υ = 2.15 for RROMS(20;2). Table 1.6 presents a summary of test results for reconstruction error and delay for all filter banks tabulated in [5]. Despite the increased floating point precision with mantissa and exponent of these tabulated coefficients relative to the fixed precision of those tabulated in [3], only were not reconstructing with e ≥ 10 −1 .…”

Section: Tests On Filter Banks Generated By Computational Algorithmsmentioning

confidence: 99%

“…, M − 1} should equal the expected delay ∆ that has been designed for the filter bank. Finally, note that the original criterion described by Nayebi et al [5] was intended for use in a design and optimization algorithm rather than for use in independent tests of reconstruction error and system delay. Thus, the essential extension implemented here is the modification of the original criterion for use in evaluating the errors and delays of each of the bands in the M -band filter bank.…”

Section: -Band Reconstruction Error Mre(a S)mentioning

confidence: 99%

“…Those for the Heller Real Orthogonal M -band K-regular HROMK(8;4;2) filter bank were entered manually from the table in [3, pg:518]. Those for the various Nayebi-Barnwell-Smith filter banks were input from the tables in [5] by optical scanning and conversion to text characters with optical character recognition software. Coefficients published in [3] are tabulated in fixed precision to only four decimal places, whereas those in [5] are tabulated in full floating point precision with six digit mantissa and two digit exponent.…”

Section: Experiments With Test Evaluations Of Filter Banksmentioning

confidence: 99%

“…Those for the various Nayebi-Barnwell-Smith filter banks were input from the tables in [5] by optical scanning and conversion to text characters with optical character recognition software. Coefficients published in [3] are tabulated in fixed precision to only four decimal places, whereas those in [5] are tabulated in full floating point precision with six digit mantissa and two digit exponent. Accuracy of the coefficients input was double-checked by painstaking comparison of the data between the printed page and computerized file displayed on monitor.…”

Section: Experiments With Test Evaluations Of Filter Banksmentioning

confidence: 99%

“…Using the names and acronyms summarized here, these filters include the Daubechies Real Biorthogonal Balanced Regular (DRBBR) and Complex Orthogonal Most Symmetric (DCOMS) [12,16], Rioul Real Orthogonal Most Selective (RROMS) [8], Heller Real Orthogonal M -band K-regular (HROMK) [3], Sherlock Real Orthogonal 2-band 1-regular [9] parameterized with Random Angles (SRORA), Hermite Real Nonorthogonal Symmetric Binomial (HRNSB) [2], and a wide assortment of filter banks available from Nayebi et al [5]. The filter banks chosen as test examples were selected to represent a variety of different classes with contrasting features.…”

Section: Introductionmentioning

confidence: 99%

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Empirical Tests for Evaluation of Multirate Filter Bank Parameters

Taswell¹

2001

Computational Imaging and Vision

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Empirical tests have been developed for evaluating the numerical properties of multirate M -band filter banks represented as N × M matrices of filter coefficients. Each test returns a numerically observed estimate of a 1 × M vector parameter in which the m th element corresponds to the m th filter band. These vector valued parameters can be readily converted to scalar valued parameters for comparison of filter bank performance or optimization of filter bank design. However, they are intended primarily for the characterization and verification of filter banks. By characterizing the numerical performance of analytic or algorithmic designs, these tests facilitate the experimental verification of theoretical specifications.Tests are introduced, defined, and demonstrated for M -shift biorthogonality and orthogonality errors, M -band reconstruction error and delay, frequency domain selectivity, time frequency uncertainty, time domain regularity and moments, and vanishing moment numbers. These tests constitute the verification component of the first stage of the hierarchical three stage framework (with filter bank coefficients, single-level convolutions, and multi-level transforms) for specification and verification of the reproducibility of wavelet transform algorithms.Filter banks tested as examples included a variety of real and complex orthogonal, biorthogonal, and nonorthogonal M -band systems with M ≥ 2. Coefficients for these filter banks were either generated by computational algorithms or obtained from published tables. Analysis of these examples from the published literature revealed previously undetected errors of three different kinds which have been called transmission, implementation, and interpretation errors. The detection of these mistakes demonstrates the importance of the evaluation methodology in revealing past and preventing future discrepancies between observed and 1 2 expected results, and thus, in insuring the validity and reproducibility of results and conclusions based on those results.

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Section: Tests On Filter Banks Generated By Computational Algorithmsmentioning

confidence: 99%

Section: -Band Reconstruction Error Mre(a S)mentioning

confidence: 99%