A signal $x(t)=|\sin(2π(1000)t)|$ ($|x|$ is the absolute value function) is fed to an ideal low-pass filter with cutoff frequency of 1500Hz to produce an output $y(t)$, what is the RMS voltage of $y(t)$?
My initial belief is that it will be zero since the absolute value doubles the frequency of the signal and so the frequency of $y(t)$ will be 2000 Hz which is beyond the cut-off frequency of the ideal low pass filter.
However, upon reflecting on the Fourier transform of $y(t)$, I believe it will have a DC component with zero frequency which will give it an RMS voltage. Moreover, $y(t)$ is a fully rectified signal which, when passed through low pass filters in reality (i.e. capacitors) will yield a smooth DC signal. How do I find the RMS voltage of the resulting y(t)? Is it really nonzero? Will it be just the same as the RMS voltage of $x(t)$?