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Abstract—The shift operator, q, and the z-transform are used extensively in filter design. However, techniques involving forward shifts do not have sensible continuous-time counterparts. The delta operator and its corresponding transform, alternatives to the previous methods, converge to the underlying continuous- time result as the sampling period goes to zero. This unifies continuous and discrete time theory. It has also been shown mathematically that the delta operator is numerically superior to the shift operator. This document will examine the delta operator and its transform.