By E. Hinton, et al.,
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Proceeding fum the top, and producing an output data vector whose components, also proceeding fran the top, are pairwise summations or differences of the elements in the input data vector which are separated by a span of T. As an example. we use Vetterli's constroetion to calculate HaX in Figure 2. Note that HaX appears in Sylvester ordering, top to bottom. at the extreme right of the tree. R. K. R. x o 1 :I' 3 4 • • 7 X+X+X .. X o :I' 4 • x+x+x+x 1 e 3 1 x . x . x . x • • xox , 7 x ••• o t x .
Table 3 Probability Density Functions and Their Transforms Pattern PA p. A PB p. 13 0 0 0 1/4 1 1/8 1 0 0 1 0 -1/4 3/8 -1/4 0 1 0 1/8 0 1/8 1/2 0 1 1 1/4 1/4 0 ·1/4 1 0 0 0 1/4 1/8 1/4 1 0 1 1/4 1/2 1/8 0 1 1 0 0 -1/4 0 1/4 1 1 1 1/8 1/2 1/8 -1/2 H we wished to calculate the average Hamming distance. DAB. between an A-vector pattern and a B-vector pattern. we could straightforwardly sum the appropriately weighted components of the 2n . 2n = 22n possible products. For the case of Table 3 this direct approach yields DAB = 23/16.
2"-1 L X~n) = (170) Hn .