Transient emissions occur throughout normal engine operation and can significantly contribute to overall system emissions. Such transient emissions may originate from various sources including cold start, varying load and exhaust-gas recirculation (EGR) rates; all of which are dynamic processes in the majority of engine operation applications. Alternatively, there are systems which are inherently dynamic even at steady-state engine-operation conditions. Such systems include catalytic exhaust-emissions treatment devices with self-initiated and sustained oscillations and NOX adsorber systems. High-speed diagnostics, capable of temporally resolving such emissions transients, are required to characterize the process, verify calculated system inputs, and optimize the system.