In this paper, we study the tolerance of a new approach to produce coherent x-ray by cascading several stages of a High-Gain Harmonic Generation (HGHG) Free-Electron Laser (FEL). Being a harmonic generation process, a small noise in the initial fundamental signal will lead to a significant noise-to-signal (NTS) ratio in the final harmonic, so the noise issue is studied in this paper. We study two sources of noise: the incoherent undulator radiation, which is a noise with respect to the seed laser; and the noise of the seed laser itself. In reality, the electron beam longitudinal current profile is not uniform. Since the electron beam is the amplification medium for the FEL, this non- uniformity will induce phase error in the FEL. Therefore, this effect is studied.