Optimal measurement of signal over noise ratio with constrained filter transfer functions

The problem of optimal measurement of a signal in presence of noise is treated in detail by Baldinger and Franzen (Adv. Electron. Electron Phys. 8 (1956) 225), Radeka and Karlovac (Nucl. Instr. and Meth. 52 (1967) 86) and Gatti and Manfredi (La Rivista Nuovo Cimento 9(1) (1986) 1), and the filter transfer function optimizing the signal over noise ratio is well known. These calculations deals with unconstrained optimization, that is the filter transfer function may assume any value. In this paper functional analysis techniques are applied to optimize the filter transfer function in presence of linear constraints.