On the space of orthonormal wavelets

Sherlock, Barry G.; Monro, D.M.

doi:10.1109/78.678504

Cited by 48 publications

(53 citation statements)

References 9 publications

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“…The M -shift orthogonality error moe(F) is displayed as a function of the number of lattice angles J = N/2 for the SRORA(N ;2;1) filters computed with either the original algorithm (curve with '+' markers) or the corrected algorithm (curve with 'o' markers). The original algorithm orthogen was not tested, and thus never validated, for J ≥ 4 by the original authors [9]. The results displayed in Figure 1.1 demonstrate clearly that the original algorithm does not generate orthogonal wavelets for J ≥ 4 whereas the corrected algorithm [13] resolves the problem.…”

Section: Tests On Filter Banks Generated By Computational Algorithmsmentioning

confidence: 96%

“…This instability impacted the orthogonal spectral factor filters but not the nonorthogonal product filter. Finally, with regard to the discrepancies depicted in Figure 1.1, it is apparent as established by the corrected algorithm [13] that the original algorithm orthogen was not consistent with the original authors' mathematical and diagrammatical specification [9].…”

Section: Discussionmentioning

confidence: 99%

“…Instead, conclusions were merely assumed to be true based on theoretical expectations (analytic design and algorithm specification) without experimental observation and verification. For example, if Sherlock and Monro [9] had performed independent tests of orthogonality for all J including J ≥ 4, it is probable that they would have detected the implementation error in their algorithm orthogen. Analogously, if Rioul and Duhamel [8] had computed the orthogonal spectral factors and numerically evaluated their orthogonality, it is probable that they would have detected the interpretation error for their algorithm remezwav.…”

Section: Discussionmentioning

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: 96%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

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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“…Therefore, the ECG signals were broken up into the details D1 − D4 and one final estimate, DWT design can take many forms. Sherlock and Monro [8] developed a way to determine the coefficients of a filter bank. They derive an orthonormal perfectreconstruction finite impulse response (FIR) filter of arbitrary length.…”

Section: Butterworth Low Pass and High Pass Filtermentioning

confidence: 99%

Cardiac arrhythmia detection in ECG signals by feature Extraction and support vector machine

Malik¹,

Kumar²,

Panda³

2017

Annals of Computer Science and Information Systems

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Abstract-Purpose of this work is to develop an automated physiologihal signal diagnostih tool that han help us to early determination of arrhythmia for proper medihal attention. This paper presents a simple automated approahh for hlassifihation of normal and abnormal ECG based on arrhythmia. The proposed method validated by the data MIT BIH arrhythmia database. The performanhe in terms of ahhurahy for hlinihal dehision must be very high. This method uses fourth order wavelet dehomposition, wavelet dehomposition used for time frequenhy representation and feature extrahtion. For hlassifihation support vehtor mahhine is used for detehtion kinds of ECG signals.

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