We report a photonic integrated circuit implementation of an optical clock multiplier, or equivalently an optical frequency comb filter. The circuit comprises a novel topology of a ring-resonator-assisted asymmetrical Mach-Zehnder interferometer in a Sagnac loop, providing a reconfigurable comb filter with sub-GHz selectivity and low complexity. A proof-of-concept device is fabricated in a high-index-contrast stoichiometric silicon nitride (Si3N4/SiO2) waveguide, featuring low loss, small size, and large bandwidth. In the experiment, we show a very narrow passband for filters of this kind, i.e. a -3-dB bandwidth of 0.6 GHz and a -20-dB passband of 1.2 GHz at a frequency interval of 12.5 GHz. As an application example, this particular filter shape enables successful demonstrations of five-fold repetition rate multiplication of optical clock signals, i.e. from 2.5 Gpulses/s to 12.5 Gpulses/s and from 10 Gpulses/s to 50 Gpulses/s. This work addresses comb spectrum processing on an integrated platform, pointing towards a device-compact solution for optical clock multipliers (frequency comb filters) which have diverse applications ranging from photonic-based RF spectrum scanners and photonic radars to GHz-granularity WDM switches and LIDARs.