This paper presents a family of observers which has as particular cases the 'unknown input observers' and the 'linear quadratic/H-2/H-infinity optimal observers'. A smooth transition between these particular extreme cases through the general case is provided, corresponding to a transition of the disturbance patterns from entirely 'singular' to entirely 'regular' ones. Both 'hard' (arbitrary) and 'soft' (Gaussian or l(2) signals) disturbances are allowed. The methodology presented here, although developed for discrete time systems, may be extended to the continuous time case.