This is a fundamental question about the idea of filters. As an example lets assume we have a passive LP filter with 1uF cap and a 100 Ohm resistor. Now lets assume our input signal is composed of addition of a 1V 4Hz signal and a 1V 400Hz.
Now if I plot the Bode diagram, the filter amplitude response is unity both at 400Hz and 4Hz.
But there will be a 15° phase difference between these signals at the output. We know that adding two sines with same amplitude but with different phases will yield a sine with less than twice the one of the two amplitude.
So even a filter is extremely flat in passband, the phase response seems will corrupt the output signal shape in time domain. I guess this will have no effect in frequency domain.
So what is that phenomenon called? And seems no filter has flat phase response in passband. Can we say this is important only if we are dealing the shape of output signal in time domain? Is there a rule of thumb for the maximum phase shift of a filter in passband?