Reduced-hardware digital filter design via joint quantization and multiple constant multiplication optimization

The focus of this paper is to provide a framework for the joint optimization of both the coefficient quantization and multiple constant multiplication (MCM) problems. It is known that while the MCM problem is complete in the subspace of integer constants, it is incomplete and not optimal in the real world where the MCM constants are often noninteger. In these situations there is flexibility in how constants are quantized in digital circuits that can be leveraged. There is a gap in the current literature between the methods of optimally quantizing constants into integers and the methods of optimizing circuits when integer constants are given. Here we show a potential for tremendous benefit when both of these problems are solved using one unified problem framework.