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Crowdsourced vehicle trajectory data, eg, from connected vehicles or ride-hailing service providers such as Uber in the US or Didi in China, are increasingly available. These trajectory data would potentially revolutionize traffic signal operation. Different from conventional detector data, trajectory data could serve as a low-cost, continuous and reliable data source, which could advance conventional detector-based signal control to a detector-free signal control scheme. Using trajectory data as the only input, this research develops a system that can optimize fixed-time traffic signal systematically. The proposed system is an integrated platform for performance evaluation and parameter optimization, with three main components: 1. traffic demand estimation, 2. performance visualization and 3. parameter optimization. It optimizes a set of signal parameters, including Time of Day (TOD) schedule, cycle length, offset and green split. The system has been implemented in the City of Jinan, China, using vehicle trajectory data collected from Didi vehicles. Two case studies on arterial signal optimization are presented. In both cases, the system considerably improved the performance of signal operation, reducing delay by 5-20%. During peak-hour periods with severe oversaturation, the number of spillover vehicles on main street during red signal also decreased substantially, indicating reduction of likelihood of intersection gridlock. The effectiveness of the developed system demonstrates the potential for large scale deployment.