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After processing a 50/60 Hz AC measurement through a 10 Hz low-pass filter, you get zero signal. For an accurate real power
measurement, you have to acquire at least the voltage and current fundamental frequency by amplitude and phase with sufficient
accuracy (assuming the voltage waveform is almost an undistorted sine). Practically, you would oversample the input signal at least
by a factor of four. State-of-the-art energy metering chips, e.g. from Analog Devices, are providing a sample rate, that gives correct
real power measurement also with distorted voltage waveforms, which requires kHz bandwidth.
Measuring real power actually doesn't require digital processing of sampled signals (although the method becomes more and more popular).
But it either requires measurement of RMS current and voltage and power factor or alternatively averaging the product of current
and voltage momentary values. A peak detector can't measure real power.
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