Conventional hardware for arbitrary waveform formation uses Digital-to-Analog Converters (DAC) and linear amplifiers. Proposed here are methods for encoding a tri-state pulser to approximate arbitrary waveforms. Algorithms are evaluated by simulation and experiment using the Verasonics, Inc. Vantage research ultrasound system, which transmits with 4 ns edge resolution. Two problems were considered: 1) matching the waveform produced by an ideal DAC given a particular transducer, and 2) compensating for the impulse response of a given transducer to reproduce a signal. The problems require the transducer impulse response in one-way and two-way propagation geometries, estimated here in water using a hydrophone and the ATL L7-4 transducer. Within measured nonlinear propagation effects, error in these four scenarios for an LFM waveform was consistent with simulated performance. In another test, a Gaussian pulse is encoded for transducer compensation, and compared to equivalent-bandwidth monopulse excitation in planewave imaging on a phantom. Here, a pin-trailing pedestal artifact is reduced by 3 dB over a span equal to the peak resolution (FWHM).