 A Z-transform implementation of an all-pass filter with a complex pole at formula_11 is
which has a zero at formula_13, where formula_14 denotes the complex conjugate.The pole and zero sit at the same angle but have reciprocal magnitudes (i.e., they are "reflections" of each other across the boundary of the complex unit circle).The placement of this pole-zero pair for a given formula_11 can be rotated in the complex plane by any angle and retain its all-pass magnitude characteristic.