Hadamard and Other Discrete Transforms in Spectroscopy

Sloane, N. J. A.

doi:10.1007/978-1-4899-0336-5_2

Cited by 10 publications

(1 citation statement)

References 32 publications

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“…The weights of individual objects are then derived by combining the four weighings according to the four columns of this matrix, for example, column four corresponds to W 1 Ϫ W 2 Ϫ W 3 ϩ W 4 and gives four times the weight D. However, compared to four individual weighings, the accuracy of the measurement is doubled because we have measured 4D but the random errors are only doubled. In the general case of N objects and N weighings, the improvement in accuracy would be the square root of N, a significant advantage when N is large.…”

Section: Hadamard Matrixmentioning

confidence: 99%

Beg, borrow, or steal. finding ideas for new NMR experiments

Freeman¹

2003

Concepts Magnetic Resonance

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ABSTRACT:Inspiration for new NMR experiments can sometimes come from other disciplines, far removed from magnetic resonance. Five disparate examples are presented: optimum weighing strategies, radar technology, Darwin's theory of evolution, quantum computers, and simulation of brain function. The applications range from multiple selective irradiation experiments that retain the multiplex advantage, radiofrequency oscillators that "follow" the magnetic field, a solvent suppression scheme, a pulse sequence for the "universal swap" operation, and "designer" radiofrequency pulses.

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Section: Hadamard Matrixmentioning

confidence: 99%

Beg, borrow, or steal. finding ideas for new NMR experiments

Freeman¹

2003

Concepts Magnetic Resonance

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Single Pixel Quadrature Imaging with Metamaterials

Nadell

Watts

Montoya

et al. 2015

Advanced Optical Materials

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Multi‐band Adiabatic Inversion Pulses for Use with the 8th‐order Hadamard Spectroscopic Imaging Technique

Goelman

Leigh

1992

Israel Journal of Chemistry

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Rf pulses with frequency responses which correspond to the rows of the 8th‐order Hadamard matrix are developed. These pulses can be used in the B1 insensitive Hadamard Spectroscopic Imaging multi‐volume localization technique. It is shown how any adiabatic rf pulse, which inverts spin population at a well defined frequency band, can be modified to invert populations at several frequency bands simultaneously. Conditions on the frequency and amplitude functions which allow such modifications are defined. For increasing amplitude the interaction between the bands produces nonlinear irradiation at several frequencies. By using an integrated form of the Floquet formalism and perturbation theory, the interaction between the bands is described analytically by an effective Hamiltonian. From this description the conditions which guarantee minimization of the unwanted irradiation are defined. The experimental results agree very well with the theoretical predications.

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Hadamard and Other Discrete Transforms in Spectroscopy

Cited by 10 publications

References 32 publications

Beg, borrow, or steal. finding ideas for new NMR experiments

Beg, borrow, or steal. finding ideas for new NMR experiments

Single Pixel Quadrature Imaging with Metamaterials

Multi‐band Adiabatic Inversion Pulses for Use with the 8th‐order Hadamard Spectroscopic Imaging Technique

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