Abstract: A system and method for automatic differentiation are disclosed. The system and method provide automatic differentiation (AD) that accurately supports functions whose domains and/or ranges are functions. The system and method advantageously enable AD that is completely general and which can be applied in an unrestricted fashion to correctly compute the derivative of all programs that compute differentiable mathematical functions. This includes application to functions whose domain and/or ranges include the entire space of data types supported by programming languages, including not only aggregates but also functions. Moreover, the system and method advantageously remedy an insidious bug that would otherwise lead to incorrect results.

Abstract: Systems and methods for performing source separation are provided. Source separation is performed using a composite signal and a signal dictionary. The composite signal is a mixture of sources received by a sensor. The signal dictionary is a database of filtered basis functions that are formed by the application of directional filters. The directional filters approximate how a particular source will be received by the sensor when the source originates from a particular location. Each source can be characterized by a coefficient and a filtered basis function. The coefficients are unknown when the sources are received by the sensor, but can be estimated using the composite signal and the signal dictionary. Various ones of the sources may be selectively reconstructed or separated using the estimated value of the coefficients.