jIIR2HW

This repository contains scripts and julia packages that permit to design second-order IIR filters for multiplierless hardware.

Context: multiplierless implementations of products by constants using shift-and-add architectures.

Problem: determine the coefficients of an IIR filter in fixed-point arithmetic such that the total cost of the shift-and-add architecture is minimal in terms of number of adders.

Techniques: our approach is based on a formalization of the problem as an instance of a Mixed Integer Linear Programming problem, which is subsequently solved using a third-party solver.

Input:

• frequency specifications
• wordlength

Output:

• filter coefficients
• adder graph structure for the optimal solution

Guarantees (in case of successful exit):

• optimality of the proposed solution
• a posteriori validation of frequency specifications

Options:

• bounded/unbounded adder depth
• avoid internal shifts in the adder graph structure