For the negative input, the first part acts as a closed-loop inverter (A = -1) and the second stage is a buffer for the positive output. When the input signal is positive, the first op amp output is in a saturated state close to ground, and the diode becomes high impedance, thus allowing the signal to pass directly to the buffer stage without inversion. The result of the combination is to provide a full-wave rectified waveform at the output of the buffer.
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