  Broadband hyperspectral digital holography and Fourier transform spectroscopy
are important instruments in various science and application fields. In the
digital hyperspectral holography and spectroscopy the variable of interest are
obtained as inverse discrete cosine transforms of observed diffractive
intensity patterns. In these notes, we provide a variety of algorithms for the
inverse cosine transform with the proofs of perfect spectrum reconstruction, as
well as we discuss and illustrate some nontrivial features of these algorithms.
