A microwave photonic signal processor that is capable of simultaneously realizing sub-harmonic frequency down conversion and IF signal phase shifting operation is presented. The IF signal generated by the frequency down conversion process is obtained by the beating of the second-order local oscillator (LO) sideband with the fundamental RF signal sideband at the photodetector. The phase of the IF signal can be tuned continuously from 0° to 360° by controlling the optical phase of the RF signal sideband. The optical carrier is eliminated at the signal processor output to achieve high conversion efficiency mixing operation. The signal processor can be designed to have a very wide bandwidth as it only involves optical components. Experimental results are presented that demonstrate frequency down conversion with > 8.8 dB conversion efficiency over 6 to 40 GHz RF signal bandwidth and 0.05 to 10 GHz IF signal bandwidth, and a continuous 0° to 360° phase shift on the output IF signal.