Broad-band evoked potentials (BBEPs) are responses to non-periodic stimuli, evoked in reponse to carefully chosen pseudo-random noise-sequences (PRNS). In this chapter, a generative method called reconvolution is discussed. Reconvolution is a method that decomposes BBEPs in response to PRNS into transient responses to the individual events. With reconvolution, one can then generate responses to any other novel PRNS. In this chapter, we discuss three approaches to reconvolution: (1) a sequential approach, (2) an integrated approach, and (3) a zero-training approach. Reconvolution enables Brain Computer Interfaces to be trained with little or even no data, and provides a generative model to accurately predict responses to novel stimuli.