Improving resolution and sensitivity will widen possible medical applications of magnetic particle imaging. Pulsed excitation promises such benefits, at the cost of more complex hardware solutions and restrictions on drive field amplitude and frequency. State-of-the-art systems utilize a sinusoidal excitation to drive superparamagnetic nanoparticles into the non-linear part of their magnetization curve, which creates a spectrum with a clear separation of direct feed-through and higher harmonics caused by the particles response. One challenge for rectangular excitation is the discrimination of particle and excitation signals, both broad-band. Another is the drive-field sequence itself, as particles that are not placed at the same spatial position, may react simultaneously and are not separable by their signal phase or shape. To overcome this potential loss of information in spatial encoding for high amplitudes, a superposition of shifting fields and drive-field rotations is proposed in this work. Upon close view, a system matrix approach is capable to maintain resolution, independent of the sequence, if the response to pulsed sequences still encodes information within the phase. Data from an Arbitrary Waveform Magnetic Particle Spectrometer with offsets in two spatial dimensions is measured and calibrated to guarantee device independence. Multiple sequence types and waveforms are compared, based on frequency space image reconstruction from emulated signals, that are derived from measured particle responses. A resolution of 1.0 mT (0.8 mm for a gradient of (-1.25,\,-1.25,\,2.5) T/m) in x- and y-direction was achieved and a superior sensitivity for pulsed sequences was detected on the basis of reference phantoms.