A signal processing system is taught to be formed by combining a crossbar array with programming circuitry and signal input circuitry so as to provide a linear transformation from a set of input signals to a set of output signals. Applications of such a system to waveform generation, signal filtering, communications, and pattern recognition are explained. In one embodiment the crossbar array of the signal processing system may be a molecular nanowire crossbar array in which the crossbar interconnects are addressed via dual arrays of scanning probe tips so as to provide an interface between the molecular crossbar electronics and conventional solid state electronics used in the programming and signal processing circuitry.