  Neuromorphic architectures achieve low-power operation by using many simple
spiking neurons in lieu of traditional hardware. Here, we develop methods for
precise linear computations in spiking neural networks and use these methods to
map the evolution of a linear dynamical system (LDS) onto an existing
neuromorphic chip: IBM's TrueNorth. We analytically characterize, and
numerically validate, the discrepancy between the spiking LDS state sequence
and that of its non-spiking counterpart. These analytical results shed light on
the multiway tradeoff between time, space, energy, and accuracy in neuromorphic
computation. To demonstrate the utility of our work, we implemented a
neuromorphic Kalman filter (KF) and used it for offline decoding of human vocal
pitch from neural data. The neuromorphic KF could be used for low-power
filtering in domains beyond neuroscience, such as navigation or robotics.
