We use a Fabry-Perot cavity to optically filter the output of a Ti:sapphire frequency comb to integer multiples of the original 1 GHz mode spacing. This effectively increases the pulse repetition rate, which is useful for several applications. In the case of low-noise microwave signal generation, such filtering leads to improved linearity of the high-speed photodiodes that detect the mode-locked laser pulse train. The result is significantly improved signal-to-noise ratio at the 10 GHz harmonic with the potential for a shot-noise limited single sideband phase noise floor near -168 dBc/Hz.