The synthesis of a feedforward unit for $H_2$ optimal decoupling of measurable or previewed signals in discrete-time linear time-invariant systems is considered. It is shown that an $H_2$ optimal compensator can be achieved by connecting a finite impulse response (FIR) system and a stable dynamic unit. To derive the FIR system convolution profiles an easily implementable computational scheme based on pseudoinversion (possibly nested to avoid computational constraints) is proposed, while the dynamic unit...