This report presents a solution to the problem of optimal residual generation for discrete time nonlinear systems. Sufficient conditions for a (sub-) optimal Fault Detection Filter are derived which simultaneously produce robustness to disturbances and enhances sensitivity to faults. The results are derived for general class of input affine nonlinear systems and then it is also shown that these results reduce to the well known results derived for mixed ¿-/¿_¿ fault detection filter for linear discrete time systems.