Magnetic particle imaging (MPI) is a promising new tracer-based imaging modality. The steady-state, nonlinear magnetization physics most fundamental to MPI typically predicts improving resolution with increasing tracer magnetic core size. For larger tracers, and given typical excitation slew rates, this steady-state prediction is compromised by dynamic processes that induce a significant secondary blur and prevent us from achieving high resolution using larger tracers. Here, we propose a new method of excitation and signal encoding in MPI we call pulsed MPI to overcome this phenomenon. Pulsed MPI allows us to directly encode the steady-state magnetic physics into the time-domain signal. This in turn gives rise to a simple reconstruction algorithm to obtain images free of secondary relaxation-induced blur. Here, we provide a detailed description of our approach in 1D, discuss how it compares with alternative approaches, and show experimental data demonstrating better than 500- $\mu \text{m}$ resolution (at 7 T/m) with large tracers. Finally, we show experimental images from a 2D implementation.