Assuming we have an audio with noise embedded in it, I was wondering what happens theoretically if we remove (filter out) too much frequency when we pass LPF with a cutoff frequency lower than the perfect cutoff frequency needed to reconstruct the signal perfectly? Practically after performing the necessary computations on MATLAB and running the audio, the sound level was somehow lower than that of the perfect reconstructed audio. However, I have no explanation as to why this phenomena occurs.
Theoretically, the error between the original and the reconstructed signal goes up. Practically, for actual audio, if you're lowpass filtering too much, the audio starts to sound muffled or muddy -- like you're trying to listen to the event through a pillow.
Again in theory, if you've got a bandlimited signal mixed with noise, the best processing for that signal is to low-pass filter it more than the signal is already bandlimited. There's a lot of theory out there on how to design optimal filters for this.