Diode demodulation for AM
Because of the diode at the input, you get a DC offset at the output. Notice that a single diode is already a primitive rectifier, because it blocks the negative half wave. 

But you usually will want a purely AC output, that's why you put a HPF with very low cutoff frequency after the LPF. It will block the DC and yield a pure AC output signal. You can see it either as part of the demodulator or as part of the following circuit, usually some kind of amplifier or buffer, but it is always required.