The paper investigates theoretically the sensitivities of ignition capsule implosion performance on the hard x-ray spectral distribution of hohlraum. In the simulation, the hohlraum radiation is represented by a Planckian spectrum for the main drive plus a gaussian bump centered at energy Ec for preheating x-rays. Simulation results show that with the increasing of center energy Ec, the Atwood number at the fuel-ablator interface increases rapidly due to the preheating and expanding of the inner undoped CH layer. The growing of Atwood number indicates the hydrodynamic instability (HI) growth and mixing at this interface. On the other hand, the increasing of Ec results in a large density gradient scale length of ablation front and stabilizes the HI growth at ablation front. The changes of the hard x-ray spectrum have significant influences on other important implosion parameters including the ablator mass remaining, shock timing, implosion velocity, and yield as well. High-precision results on the hard x-ray spectral distribution of hohlraum are thus critical for optimizing the ignition capsule design to limit the HI growth.