The classic Envelope Detector is very old and very cheap and very simple .Sure there are now better schemes like synchronous detection ,PLL etc.The circuit is responding to the peak of the Amplitude modulated carrier .The decay time constant is arranged to ensure that the highest audio frequency can be reproduced and there is reasonable carrier ripple attenuation .For Medium wave Broadcast AM the carrier frequency to be demodulated would most likely be 455KHz and the highest Audio frequency would be 9KHz .These frequencies are geometricly far enough apart for the simple circuit to work well enough for most receivers.My Question is would an averaging type of detector with an averaging time constant large enough to attenuate the 455KHz ripple and small enough to pass 9 KHz give a signal to noise advantage over the peak scheme that could hang up on impulse noise ?
Impulse noise is demodulated on an AM radio. Snap, crackle and POP are common sounds. If you smooth impulse sounds then speech and some music will sound weird. AM radio does not pass 9kHz sounds, but only 4kHz if you are lucky. Most AM radios cut frequencies above only 2.5kHz, which is why FM radio was made to sound much better.