  We prove the Plancherel formula for a four-parameter family of discrete
Fourier transforms and their multivariate generalizations stemming from
corresponding generalized Schur polynomials. For special choices of the
parameters, this recovers the sixteen classic discrete sine- and cosine
transforms DST-1,...,DST-8 and DCT-1,...,DCT-8, as well as recently studied
(anti-)symmetric multivariate generalizations thereof.
