Search for EKG and EEG circuits and you'll get lotsa examples from hobby to pro. The good ones rely on a well designed instrumentation or differential amp front end for most of the noise rejection, but some have lowpass or notch filters downstream. All filters introduce phase distortions that alter the waveshape of the signal of interest, but the frequencies of interest are so low that they are a couple of octaves away from the corner frequencies. AG is right, the line-induced noise has harmonics, but those frequencies are even farther away and can be handled by a gentle lowpass.
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