The present invention provides methods and apparatus to encode substrates (e.g., paper, synthetics, etc.) with information. In one implementation a method is provided including: receiving data that corresponds to a two-dimensional signal that encodes plural bits of data; receiving data that corresponds to a frequency-domain signal, the data corresponding to a representation in a spatial domain through inverse transforming the frequency-domain signal; and defining characteristics for an element of a substrate-making process, the characteristics including at least a pattern representing the spatial domain representation and the two-dimensional signal.