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

Abstract

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.