Hadamard Matrix Analysis and Synthesis

Yarlagadda, R.; Hershey, John E.

doi:10.1007/978-1-4615-6313-6

Cited by 58 publications

(29 citation statements)

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“…Like the Hadamard transform [22], the PT can be calculated using only additions (no multiplications are required). As shown in Section III, each projection requires approximately operations, but the calculations required to project onto (say) overlap the calculations required to project onto in a nontrivial way, and these redundancies can undoubtedly be exploited in a more efficient implementation.…”

Section: Discussionmentioning

confidence: 99%

Periodicity transforms

Sethares

Staley

1999

IEEE Trans. Signal Process.

143

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Abstract-This paper presents a method of detecting periodicities in data that exploits a series of projections onto "periodic subspaces." The algorithm finds its own set of nonorthogonal basis elements (based on the data), rather than assuming a fixed predetermined basis as in the Fourier, Gabor, and wavelet transforms. A major strength of the approach is that it is linearin-period rather than linear-in-frequency or linear-in-scale. The algorithm is derived and analyzed, and its output is compared to that of the Fourier transform in a number of examples. One application is the finding and grouping of rhythms in a musical score, another is the separation of periodic waveforms with overlapping spectra, and a third is the finding of patterns in astronomical data. Examples demonstrate both the strengths and weaknesses of the method.

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Section: Discussionmentioning

confidence: 99%

Periodicity transforms

Sethares

Staley

1999

IEEE Trans. Signal Process.

143

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“…The only eigenvalues of the unnormalized Hadamard matrix of order N = 2 n are known to be 2 n/2 and −2 n/2 [18], hence the normalized Hadamard matrix H N has only the eigenvalues 1 and −1, each one has an eigenspace of dimension N/2. In [8] it was shown that the recursively computed eigenvectors with the formulas (5)- (7) are orthogonal and that the 2N eigenvectors of H 2N can be ordered in such a way that v k 2N has k sign-changes.…”

Section: Mathematical Backgroundmentioning

confidence: 99%

Fast algorithm for discrete fractional Hadamard transform

Cariow

Majorkowska-Mech

2014

Numer Algor

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“…Since tag 34 IDs usually contain object-specific information, we should 35 prevent such information from leakage when it is privacy 36 sensitive for tagged objects [6,17,18]. In an anonymous RFID 37 system, RFID readers are not expected to collect IDs from 38 tags or to access them on the server [19][20][21][22]. This way, 39 tag IDs achieve anonymity and protect their associated pri- 40 vacy.…”

Section: Introductionmentioning

confidence: 99%