We extend the current theory of stack filters by determining fixed points for the infmite length signals using positive Boolean functions. Fixed point analysis is basically determining root structure. We describe the fixed point structure for three and four variable positive Boolean functions and describe how one may generate larger positive Boolean functions and simultaneously generate their fixed point structure. We give two explicit formulations for the stack filter that correspond to any positive Boolean function. We then discuss explicit algorithms for generalizing positive Boolean functions that will "stack" on each other. We define a generalized stack filter as the filter that has varying positive Boolean function at various levels. We provide sufficient conditions so that positive Boolean functions in a generalized stack filter can be varied at levels and still uphold threshold decomposition and stacking properties. We also describe a rule which must be followed in the stacking of rank order filters if the stacking property is to be satisfied. Design of stack filters is also presented.