Implementation problems in Hadamard transform spectrometry

The multiplex advantage offered by Hadamard transform spectrometry (HTS) can improve the signal-to-noise ratio (SNR) at the output of a spectrometer. However, additional processing of the spectrometer output is required to recover the individual spectral components. A block diagram description of HTS and the spectrum-recovery process is presented. A computer simulation of this model has been developed and can be used to examine the effects of certain nonidealities that may typically be encountered. Traditionally, the inverse Hadamard transform (IHT) has been used as the spectrum-recovery method, but the IHT does not take into account the nonidealities associated with the multiplexing process. Two spectrum-recovery methods that address the problems of nonidealities are presented. The relative performance of all three methods is compared with regard to mean square error (MSE) and the computational efficiency of the algorithms necessary to implement the schemes. An example application is described, and the performance of the three spectrum-recovery schemes is discussed