This paper presents a method for the overdesign of gain-shaping filter
s in an optimal way. The passband minima and the stopband maxima of a
filter approximation are adjusted using an iterative method, with the
objective of obtaining a circuit that satisfies exactly the specificat
ions when the statistical deviation in the filter transfer function du
e to errors on its components is considered. The result is a filter th
at can be significantly more selective than what is obtained by a simp
ler overdesign method that results in an equal-ripple ideal design. Tw
o different approaches are examined, one based in the development of a
special approximation followed by synthesis, and the other by direct
optimization of an initial classical design.