Piecewise linear circuits operating on first-order multi-level and second-order binary sigma-delta modulated signals

This paper describes piecewise linear circuits operating directly on first-order multi-level and second-order binary sigma-delta modulated signals. The sigma-delta modulated signal sequences contain subsequences which reflect whether the inputs to sigma-delta modulators are positive or negative. We build circuits performing absolute operation with detectors of the subsequences. Using the absolute circuits, we build various piece- wise linear circuits, such as Min/Max circuits. These piecewise linear circuits can be built of a smaller number of logic gates and perform more precise piecewise linear operation at a high oversampling ratio than multi-bit Nyquist rate circuits.