Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design

Stanković, Radomir S.; Moraga, Claudio; Astola, Jaakko

doi:10.1002/047174543x

Cited by 39 publications

(17 citation statements)

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“…Proof. Notice that the inverse matrix R −1 a,b has necessarily the structure of the matrix M S in (20). The uniqueness of the expansion with respect to a basis gives the interpolation property.…”

Section: G-compatible Left-inversesmentioning

confidence: 99%

Knit Product of Finite Groups and Sampling

2019

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A finite sampling theory associated with a unitary representation of a finite non Abelian group G on a Hilbert space is stablished. The non Abelian group G is a knit product N ⊲⊳ H of two finite subgroups N and H. Sampling formulas where the samples are indexed by either N or H are obtained. Using suitable expressions for the involved samples, the problem is reduced to obtain dual frames in the Hilbert space ℓ 2 (G) having a unitary invariance property; this is done by using matrix analysis techniques. An example involving dihedral groups illustrates the obtained sampling results.

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Section: G-compatible Left-inversesmentioning

confidence: 99%

Knit Product of Finite Groups and Sampling

2019

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“…We invoke the Schur's orthogonality relations, see [12], for example. With notation as in Theorem 2.1, we observe, using the Schur's orthogonality relations 1 ; 12 ; 13…”

Section: Proofmentioning

confidence: 99%

Some Remarks on the Non-Abelian Fourier Transform in Crossover Designs in Clinical Trials

Zizler¹

2014

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“…The motivation behind Walsh-Fourier analysis was the need to approximate stationary time series, which display square waveforms with abrupt switches (e.g. in communications and engineering), see Stankovic et al (2005) for instance. We introduce the concept of local stationarity but based on the orthogonal system of Walsh functions to account for such phenomena that exhibit, in addition, non-stationary behaviour.…”

Section: Introductionmentioning

confidence: 99%

“…We study important general classes of time series, similar in concept with the time varying ARMA (tvARMA) process-see Dahlhaus (2012). We anticipate that our theory and methods will be applicable to non-stationary data observed in diverse applications like pattern recognition for binary images, linear system theory and other (see Stankovic et al (2005), for more).…”

Section: Introductionmentioning

confidence: 99%