  Varied signature splitting phenomena in odd proton rare earth nuclei are
investigated. Signature splitting as functions of $K$ and $j$ in the angular
momentum projection theory is explicitly shown and compared with those of the
particle rotor model. The observed deviations from these rules are due to the
band mixings. The recently measured $^{169}$Ta high spin data are taken as a
typical example where fruitful information about signature effects can be
extracted. Six bands, two of which have not yet been observed, were calculated
and discussed in detail in this paper. The experimentally unknown band head
energies are given.
