Is there any difference in Implementing sigma delta modulator using filters and state space model in FPGA?

Question

Sigma delta modulation is extensively used in quantization to reduce quantization noise.

In the literature one can see different architecture for example python-deltasigma to implement a modulator. One can learn the output of the modulator by implementing the filters or one can convert the problem into a state space model and design the modulator based on A,B,C,D parameters of the state space model. The question: is there a difference or advantage/disadvantage in working with state space model instead of implementing the filters as per the architecture, specifically for FPGA implementation.

Answer 1

Probably not much advantage either way, possibly unless you've got a really high-order modulator (in which case someone else will have to answer!)

If the state-space representation is a single-input single-output system, and if it's linear, and if it's running in steady-state, and if data path widths aren't an issue, then there's no difference between it and a "more traditional" IIR filter implementation such as a set of biquads.

If you've got some super-high-order modulator, or if someone's gone and invented a nifty nonlinear way to get more performance out of a sigma-delta modulator when I wasn't looking, then maybe -- but I doubt it.