The intense noise radiated by jet aircraft exhaust nozzles causes structural vibration, fatigue, carrier deck personnel operational difficulties, and community environmental concerns. Prior work into the physics and control of jet noise have identified several important sound sources, including wavepackets, screech, Mach wave radiation, and broadband shock associated noise, to name a few. Reducing the loudest sources of jet noise, without sacrificing propulsive performance, has thus-far relied on intuition, parametric survey, or optimal control techniques. With the aim of developing a more general and robust method of jet noise reduction (JNR), we seek a physics-based JNR approach that is built upon a linear resolvent analysis appropriate for mean flows with strong shocks. The effect of flow discontinuities on linear analysis, including the optimal forcing and response modes that arise from resolvents, is investigated.