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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 piecewise 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.

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