h-w controlled rectification
I assume you mean a DSP function that is a half wave rectifier. But in the real analog world, a half wave rectifier has a freqeuncy response that is selectable by the designer. THis is because there are two parts to a physical half wave rectifier: 1) something that rectifies a sine wave to become a series of one-way current pulses (usually a diode), and 2) something that integrates (or stores) those rectified current pulses (usually a capacitor). The diode has a series resistance, so there is a R-C time lag in charging up the capacitor, and the capacitor has a load resistance across it, so there is another R'-C discharge time in the capacitor voltage drooping after the sine wave input goes away.
So, simplistically, a half wave rectifier can be thought of as a rectifier with a lowpass filter response. More precisely, it can be thought of as a rectifier with different rise and fall times--both user controlled.