Sound radiation from a rectangular, baffled and perforated piston vibrating harmonically is investigated in the two dimensional wavenumber domain. The perforations are in the form of an array of uniformly distributed circular holes. Perforation ratios in the piston and the baffle are independently chosen and this generalization is later used to represent a more practical case of a perforated piston fixed in an unperforated baffle. It is found that there exists a 'coupling' of the different wavenumbers of the spatially averaged fluid particle velocity field. Analytical expressions for the radiated power and the radiation efficiency are derived in an integral form. The results are presented and compared with those from a finite element solver (COMSOL). The COMSOL results are different due to dissimilar perforate impedance and flow continuity models adopted in their solver. The effect of the perforation ratio on the radiation efficiency of a perforated piston is also discussed.