In this paper, the noise filtering effect on a femtosecond laser source via a broadband passive cavity is analyzed in detail. The results show that a passive optical cavity not only can be used as a low-pass noise filter, but also can inter-convert the phase and amplitude fluctuations of a light beam after transmission or reflection. Therefore, by measuring the intensity noise of the light field under test after transmission and reflection from a passive cavity, its phase noise properties can be explored. Based on this theoretical model, an eight-mirror ring passive cavity with a finesse of 1500 and a free spectral range of 75 MHz is designed and built. With a commercial Ti:sapphire femtosecond laser as a source, its intensity noises after transmission and reflection from the above cavity are measured with home-made self-homodyne detection setup. Furthermore, with the help of the noise conversion model of the passive cavity, the phase noise of the femtosecond laser as well as its evolution through the cavity transmission and reflection is indirectly derived. The result shows that after transmission through the passive cavity, both the amplitude and phase noise of the femtosecond laser source are evidently suppressed and reach the shot noise limit at the analyzing frequency of 2 MHz.