High-pass filters are circuits that allow relatively high frequency  signals to be transmitted through the input to the output while  attenuating relatively low frequency signals. Conversely, low-pass  filters are circuits that allow relatively low frequency signals to be  transmitted through the input to the output while attenuating relatively  high frequency signals.  Common-emitter BJTs have both characteristics  of low pass and high pass filters.

Coupling capacitors and bypass  capacitors (external capacitors) do affect input and output  characteristics of amplifier circuits.  For example, both voltage gain  and phase shift of amplifier circuits can be affected by these  capacitors.  We can see from the equation for capacitive reactance Xc =  1/(2 pi * f * c) that frequency is inversely proportional to capacitive reactance.   Therefore, low frequencies cause high capacitive reactance values and  vice versa.  High capacitive reactance cause less current to flow and  therefore reduce voltage gain (i.e. the voltage gain of a common-  collector amplifier).  In the common-collector amplifier there is an  ideal phase shift of 180°, which is a direct result of the coupling  capacitors in the circuit.  Also, the bypass capacitor in a CE  configuration blocks DC but allows AC to pass and thereby further  stabilizing the circuit.  Internal transistor capacitance has an adverse  effect as input signal frequencies increase causing less than ideal  characteristics such as phase shift and reduction in voltage gain.

The  bandwidth is the range of frequencies in which an amplifier is designed  to operate. This range falls between the dominant upper and lower  critical frequencies. The following equation expresses this bandwidth:                                                                  
BW =f’cu(dom)-f’cl(dom)

• Having  two cut off frequencies that are the same in an amplifier causes  different outcomes depending on whether or not the critical frequencies  are lower or upper critical frequencies. If they are dominant lower  critical frequencies, the overall dominant lower critical frequency is  increased by a factor of 1/ sqrt[(2^1/n) -1] as shown by the equation  f’cl(dom=fcl(dom)/sqrt[(2^1/n) -1], where n is equal to the number of  stages of the amplifier. If they are dominant upper critical  frequencies. the overall dominant upper critical frequency is reduced by  a factor of sqrt[(2^1/n) -1], as shown by the equation   f’cu(dom)=fcu(dom)sqrt[(2^1/n) -1].

References

Floyd,  Thomas L. Electronic Devices (Conventional Current Version). Available  from: ECPI, (10th Edition). Pearson Education (US), 2017.