  Medical ultrasound imaging is the most widespread real-time non-invasive
imaging system and its formulation comprises signal transmission, signal
reception, and image formation. Ultrasound signal transmission modelling has
been formalized over the years through different approaches by exploiting the
physics of the associated wave problem. This work proposes a novel
computational framework for modelling the ultrasound signal transmission step
in the time-frequency domain for a linear-array probe. More specifically, from
the impulse response theory defined in the time domain, we derived a parametric
model in the corresponding frequency domain, with appropriate approximations
for the narrowband case. To validate the model, we implemented a numerical
simulator and tested it with synthetic data. Numerical experiments demonstrate
that the proposed model is computationally feasible, efficient, and compatible
with realistic measurements and existing state-of-the-art simulators. The
formulated model can be employed for analyzing how the involved parameters
affect the generated beam pattern, and ultimately for optimizing measurement
settings in an automatic and systematic way.
