  The orthogonal delay-Doppler (DD) division multiplexing (ODDM) modulation has
recently been proposed as a promising solution for ensuring reliable
communications in high mobility scenarios. In this work, we investigate the
time-frequency (TF) localization characteristics of the DD plane orthogonal
pulse (DDOP), which is the prototype pulse of ODDM modulation. The TF
localization characteristics examine how concentrated or spread out the energy
of a pulse is in the joint TF domain. We first derive the TF localization
metric, TF area (TFA), for the DDOP. Based on this result, we provide insights
into the energy spread of the DDOP in the joint TF domain. Then, we delve into
the potential advantages of the DDOP due to its energy spread, particularly in
terms of leveraging both time and frequency diversities, and enabling
high-resolution sensing. Furthermore, we determine the TFA for the recently
proposed generalized design of the DDOP. Finally, we validate our analysis
based on numerical results and show that the energy spread for the generalized
design of the DDOP in the joint TF domain exhibits a step-wise increase as the
duration of sub-pulses increases.
