Lower bounds on the MSE in Nth order multi-bit multi-loop ΣΔ modulation with DC inputs

In ΣΔ modulation, optimal decoding is defined from the intrinsic behavior of the encoder which is to induce a partition of the space of discrete-time signals. It is shown, in the multi-loop configuration, that this partition has some particular lattice properties which constitute potential tools for the analysis of mean square error (MSE) lower bounds in the general case of time-varying bandlimited signals. Their immediate application in the case of constant inputs is shown. An analysis of the intrinsic behavior of an encoder, based on signal partitioning is presented, thus providing a basic tool for the theoretical analysis of optimal decoding MSE