“…Unfortunately, up to now, thxe is still no unified proof of the invariance for all of the o r lerings. The only proof available is of show-by-example t l ,e illustration [l], [2], [4], [5] which, though demonstrates tb ; invariant property, does not provide a rigorous treatment of the dyadic shift invariance. As an example, let { T } be an 12'-periodic sequence and { T , } be the sequence subjects to a J \ adic shift of size k , and { X } be the WHT of {x} and { X , } bc.…”