Fourier-based Error Analysis for Computing with Asynchronous Sigma-Delta Streams

We analyze error versus observation time for numerical computing under the stochastic computing paradigm, where operands are encoded with asynchronous sigma-delta modulators. Such encoding offers dramatic savings in energy consumption and/or latency, relative to traditional stochastic computing, at equal RMS error. The paper presents a Fourier analysis of the error with sigma-delta computing for the product of two numerical operands, and presents Matlab error/latency tradeoffs for example operands.