We characterized and analyzed the effect of intracavity spectral filtering in the Er:fiber laser mode-locked with a semiconductor saturable absorber mirror (SESAM). We studied the dispersive properties of bandpass filters and their influence on the characteristics of generated soliton pulses. Our analysis showed that various sideband structures were induced by the filter dispersion profiles and shaped through the interaction of the soliton with the dispersive wave. In addition, intracavity filtering improved the intensity and phase noise of the laser significantly, and we showed optimal filtering conditions for both types of noise. By adding a 10 nm bandpass filter to the laser resonator, the intensity and phase noise were improved 2- and 2.6 times, respectively.