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Right-cyclic Hadamard coding schemes and fast Fourier transforms for use in computing spectrum estimates in Hadamard-transform spectrometry

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3 Author(s)
Dyer, R.A. ; Dept. of Electr. & Comput. Eng., Kansas State Univ., Manhattan, KS, USA ; Ouattara, S. ; Dyer, S.A.

Two computationally efficient spectrum-recovery schemes were recently developed for use by Hadamard-transform spectrometers that have static and dynamic nonidealities in their encoding masks. These methods make use of a left-cyclic Hadamard encodement scheme and the ability to express the left-cyclic WD matrix in factored form as WD =STD. The matrix WD describes the dynamic characteristics of and the encodement scheme for the mask. This paper focuses on the use of a right-cyclic Hadamard pattern to encode the mask and computationally efficient methods that can be used to obtain the spectrum-estimate. The major advantage of right-cyclic over left-cyclic encodement schemes is due to the resulting right-cyclic nature of both W D and WD-1. Fast algorithms, such as a fast Fourier transform (FFT) or a Trench algorithm, that take advantage of the right-cyclic nature of WD can be used to obtain WD-1 directly. In general, the number of mask elements is not an integer power of two, and non-radix-2 FFT's must be used to compute WD-1. Since WD-1 is right-cyclic, the vector-matrix product of WD-1 and the measurement vector can be expressed as a circular correlation and implemented indirectly via FFT's. With appropriate zero-padding of the vectors, radix-2 FFT's can be used for this computation. Various algorithms were used at each step in the overall computation of the spectrum-estimate, and the total computation times are presented and compared. The size of the mask is important in determining which algorithms are the most efficient in recovering the spectrum-estimate

Published in:

Instrumentation and Measurement, IEEE Transactions on  (Volume:45 ,  Issue: 5 )

Date of Publication:

Oct 1996

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