Stack smoothers have received considerable attention in signal processing i
n the past decade. Stack smoothers define a large class of nonlinear smooth
ers based on positive Boolean functions (PBF) applied in the binary domain
of threshold decomposition. Although stack smoothers can offer some advanta
ges over traditional linear FIR filters, they are in essence smoothers lack
ing the flexibility to adequately address a number of signal processing pro
blems that require bandpass or highpass filtering characteristics. In this
paper, mirrored threshold decomposition is introduced, which, together with
the associated binary PBF, define the significantly richer class of stack
filters. Using threshold:,logic representation, a number of properties of s
tark filters are derived; Notably, stack filters defined in the binary doma
in of mirrored threshold decomposition require the use of double:weighting
of each sample in the integer domain. The class of recursive stack filters
and the corresponding recursive weighted median (RWM) filters in the intege
r domain admitting negative weights are introduced. The new stack filter fo
rmulation leads to a more powerful class of estimators capable of effective
ly addressing a number of fundamental problems in signal processing that co
uld not adequately be addressed by prior stack smoother structures.