🚀 go-pugleaf

In the computer-music literature, I've seen the term "complementary"
used to describe a pair of filters.  For example, in the waveguide
clarinet model proposed by Julius Smith, the signal traveling down the
bore is partly transmitted and partly reflected; the reflected version
is lowpass, the transmitted version is highpass.  These filters are
described as complementary, which I take to mean that, at any given
frequency, the sum of the energy coming out of the two filters is equal
to the energy going down the bore.

Is there a recipe for generating the "complement" of a given filter?  Or
for generating a pair of filters which are complementary in this sense? 
I've seen the basic transformations between lowpass and highpass
filters, and I don't think they qualify.