An Efficient Method for Recovering the Optimal Unbiased Linear Spectrum-Estimate from Hadamard Transform Spectrometers Having Nonideal Masks

1989 ◽  
Vol 43 (5) ◽  
pp. 746-750 ◽  
Author(s):  
T. W. Johnson ◽  
J. B. Park ◽  
S. A. Dyer ◽  
B. K. Harms ◽  
R. A. Dyer
Keyword(s):  
Spectral Resolution ◽  
Efficient Method ◽  
Hadamard Transform ◽  
Computationally Efficient ◽  
Arithmetic Operations ◽  
Recovery Method ◽  
Linear Spectrum ◽  
Recovery Techniques ◽  
Spectrum Recovery ◽  
Conventional Methods

A spectrum-recovery method is presented which efficiently computes an optimal unbiased linear spectrum-estimate for measurements obtained with Hadamard transform (HT) spectrometers having nonideal masks. This method has the following advantages over other spectrum-recovery techniques: it is computationally efficient, it requires no additional measurements, and it computes an optimal spectrum-estimate. In the method presented, after the mask of the HT spectrometer has been characterized, approximately 3 N preliminary arithmetic operations are performed once for a given spectrometer, where N is both the number of spectral resolution-elements desired and the number of measurements required. Each spectrum-estimate to be recovered then requires only an additional O[ N(log2 N + 4)] arithmetic operations. In contrast, conventional methods for obtaining an optimal unbiased linear spectrum-estimate require O( N3) preliminary operations, and O(2 N2) operations during each spectrum-recovery.

A Fast Spectrum-Recovery Method for Hadamard Transform Spectrometers Having Nonideal Masks

1989 ◽  
Vol 43 (3) ◽  
pp. 435-440 ◽  
Author(s):  
S. A. Dyer ◽  
B. K. Harms ◽  
J. B. Park ◽  
T. W. Johnson ◽  
R. A. Dyer
Keyword(s):  
Point Spectrum ◽  
Hadamard Transform ◽  
Arithmetic Operations ◽  
Inexpensive Method ◽  
Recovery Method ◽  
Conventional Procedure ◽  
Preliminary Work ◽  
Spectrum Recovery

A computationally inexpensive method is presented for the recovery of spectra from measurements obtained with Hadamard transform spectrometers having nonideal masks. Normally, N measurements are required in order to recover an N-point spectrum; this method requires N + N0 measurements to be taken, where, typically, N0 ≤ 10. Once the additional measurements have been taken, only O( N[log2 N + 2]) arithmetic operations—mostly additions or subtractions—are needed in order to recover the spectrum; a conventional procedure requires O(2 N2) operations. Preliminary work for this method is minimal, requiring O( N) operations as opposed to O( N3) for a conventional procedure; this work needs to be done only once for a given spectrometer. The spectrum-estimate obtained is unbiased.

On the Mean-Square Error of Various Spectrum-Recovery Techniques in Hadamard Transform Spectrometry

1990 ◽  
Vol 44 (2) ◽  
pp. 219-228 ◽  
Author(s):  
J. B. Park ◽  
T. W. Johnson ◽  
S. A. Dyer ◽  
B. K. Harms ◽  
R. A. Dyer
Keyword(s):  
Mean Square Error ◽  
Hadamard Transform ◽  
Mean Square ◽  
Recovery Techniques ◽  
Spectrum Recovery ◽  
The Mean

On the Use of Fast Hadamard Transforms for Spectrum Recovery in Hadamard Transform Spectroscopy

1992 ◽  
Vol 46 (9) ◽  
pp. 1358-1361 ◽  
Author(s):  
B. K. Harms ◽  
J. B. Park ◽  
S. A. Dyer
Keyword(s):  
Equivalence Class ◽  
Efficient Method ◽  
Hadamard Matrix ◽  
Hadamard Matrices ◽  
Hadamard Transform ◽  
Spectrum Recovery ◽  
Hadamard Transforms ◽  
Permutation Scheme

The spectrum-recovery step in Hadamard transform spectroscopy is commonly implemented with a fast Hadamard transform (FHT). When the Hadamard or simplex matrix corresponding to the mask does not have the same ordering as the Hadamard matrix corresponding to the FHT, a modification is required. When the two Hadamard matrices are in the same equivalence class, this modification can be implemented as a permutation scheme. This paper investigates permutation schemes for this application. The investigation clarifies inaccurate claims about the applicability of existing methods; reveals a new, more efficient method; and leads to an extension that allows a permutation scheme to be applied to any Hadamard or simplex matrix in the appropriate equivalence class.

scholarly journals An Effective Potential for Frenkel Excitons

2020 ◽  
Author(s):  
Bartosz Błasiak ◽  
Wojciech Bartkowiak ◽  
Robert Władysław Góra
Keyword(s):  
Energy Transfer ◽  
Excitation Energy ◽  
Efficient Method ◽  
Effective Potential ◽  
Excitation Energy Transfer ◽  
Computationally Efficient ◽  
Frenkel Excitons

Excitation energy transfer (EET) is a ubiquitous process in life and materials sciences. Here, a new and computationally efficient method of evaluating the electronic EET couplings between interacting chromophores is...

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