Mills' Mess variant of the Boston Mess in which every catch from one hand is clawed. Eric's Extension, invented by Eric Uhrhane, is a variation on Mills Mess in which the arms cross twice on each side instead of just once. The extra throws may add to the visual appeal of the pattern. Eric's Extension requires the juggler's arms to be slender or flexible to cross two times, a requirement which makes this variation physically impossible for some. It is especially difficult with clubs. When combined with chops (a "chop" is a downward sweep or flourish of the hand that has just
All-pass filter 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_9 can be rotated in the complex plane by any angle and retain its all-pass magnitude characteristic. Complex pole-zero pairs in all-pass filters help control the frequency where phase shifts occur. To create an all-pass implementation with real coefficients, the complex all-pass filter can be cascaded with an all-pass that substitutes formula_14 for formula_9, leading to the Z-transform implementation which is equivalent to the difference equation where formula_18 is the