Cascade (juggling) for a complete cycle of throws. However, in order to keep the number of props in the juggler's hands to a minimum, it is necessary to begin the pattern by throwing, from alternating hands, all but one prop (in the same hand as the first throw, which started with one more prop than the other) before any catches are made. The reverse cascade, or outside cascade, is a juggling pattern in which the props follow the same path as the cascade, but with time going backwards, hence the 'reverse'. One throws every ball with, "an outward instead of an inward
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