Accuracy vs speed tradeoffs in the estimation of fixed-point errors on Linear Time-Invariant systems

Fixed-point format is essential to most efficient Digital Signal Processing (DSP) implementations. The conversion of an algorithm specification to fixed-point precision targets the minimization of the implementation cost while guaranteeing a minimal processing accuracy. However, measuring such processing accuracy can be extremely time consuming and lead to long design cycles. In this paper, we study reference approaches to measure fixed-point errors of Linear Time-Invariant (LTI) systems without feedback. Unsurprisingly, we find the existing analytical approach significantly faster than a straightforward simulation-based estimation. However, we also show that such analytical approach can incur high estimation errors for some particular bitwidth configurations. Accordingly, we propose a new hybrid approach, which is able to reduce by up to 4 times the error of the analytical estimation, while still being more than 10 times faster than the simulation-based estimation.