A Sigma-Delta Domain Lowpass Wave Filter

This paper presents a sigma-delta (SD) domain lowpass wave filter modeled after an analog distributed parameter filter (ADPF). The SD domain filter operating on SD modulated signals is built with two kinds of units, shift registers on which two-level-quantized waves propagate and sorter-based units that simulate reflection, transmission, and superposition of waves propagating on the transmission lines of the ADPF. The SD domain lowpass filter has the following advantages: First, design techniques for ADPFs can be applied directly to the SD domain filter. Secondly, the SD domain filter consists mainly of shift registers and sorting networks. Because the structures of the registers and the networks are spatially uniform and their internal connections are local, the filter architecture will mitigate difficulties in physical design and fabrication of filter circuits using nanometer-scale quantum effect devices. We confirmed by computer simulation that the designed SD domain filter possessed the same frequency response characteristics as the theoretical characteristics of the reference ADPF. Although internal units of SD domain filters generate SD modulation noise, it does not change to aliasing noise in the signal band because the operations of the units are linear. Therefore, the quantization noise contained in the outputs of SD domain filters is shaped like SD modulation noise.