Implementation problems in Hadamard spectrometry

The multiplexing offered by Hadamard-transform spectrometry can improve the signal-to-noise ratio at the output of a spectrometer. Traditionally, the inverse Hadamard transform (IHT) has been used to recover the individual spectral components, but the IHT does not take into account the nonidealities associated with the multiplexing process. A system model has been developed which addresses nonidealities in the multiplexer, noise introduced at the detector, and choice of method for spectrum recovery. A computer simulation of the model has been developed and can be used to examine the effect of certain nonidealities that may typically be encountered. Three different spectrum-recovery schemes are examined, and their relative performance is compared with regard to mean-square error and to the computational efficiency of the algorithms necessary to implement them. An example application is described, and the performance of the three spectrum-recovery schemes is discussed.