In many fields the transmission of information from one point to another involves a source of excitation in some region, space-time propagation of the excitation through a medium, and calculation of the response in another region. The space-time dependent source may have an arbitrary form and may be viewed as a wavepacket, i.e. a superposition of elementary waveforms. The space-time dependent medium may be homogeneous or non-homogeneous. An efficient method of calculation of the space-time structure of the response to a prescribed source is sought. Since such problems are posed mathematically by partial differential wave equations descriptive of a particular field, their solution preferably requires a balanced mix of analytical and numerical techniques and an appropriate choice of mathematical representation. In the following we contrast the relative ease of solution of a class of wave propagation by examining representations of problems in
Fourier Transform (k,t) Space,
Wigner Transform (k,x,t) Phase Space
with the intent of enhancing conceptual insights into the basic processes underlying these different representations.