Wordlength determination algorithms for hardware implementation of linear time invariant systems with prescribed output accuracy

This paper proposes two novel algorithms for optimizing the hardware resources in finite wordlength implementation of linear time invariant systems. The hardware complexity is measured by the exact internal wordlength used for each intermediate data. The first algorithm formulates the design problem as a constrained optimization, from which an analytic closed-form solution of the internal wordlengths subject to a prescribed output accuracy can be determined by the Lagrange multiplier method. The second algorithm is based on a discrete optimization method called the marginal analysis method, and it yields the desired wordlengths in integer values. Both approaches are found to be very effective and they are well-suited to large scale systems such as software radio receivers. Design examples show that the proposed algorithms offer better results and a lower design complexity than conventional methods.