  A quantum anomalous Hall (QAH) insulator breaks reciprocity by combining
magnetic polarization and spin-orbit coupling to generate a unidirectional
transmission of signals in the absence of an external magnetic field. Such
behavior makes QAH materials a good platform for the innovation of circulator
technologies. However, it remains elusive as to how the wavelength of the
chiral edge plasmon relates to its frequency and how the plasmon wave packet is
excited in the time domain in a QAH insulator. Here, we investigate the edge
magnetoplasmon (EMP) resonances in Cr-(Bi,Sb)$_2$Te$_3$ by frequency and time
domain measurements. From disk shaped samples with various dimensions, we
obtain the dispersion relation of EMPs and extract the drift velocity of the
chiral edge state. From the time-resolved transport measurements, we identify
the velocity of the plasmon wave packet and observe a transition from the edge
to bulk transport at an elevated temperature. We show that the frequency and
time domain measurements are well modeled by loss from the microwave induced
dissipative channels in the bulk area. Our results demonstrate that the EMP
decay rate can be significantly reduced by applying a low microwave power and
fabricating devices of larger diameter $\ge100~\mu$m. In a $R=125~\mu$m sample,
a non-reciprocity of 20 dB has been realized at 1.3 GHz, shining light on using
QAH insulators to develop on-chip non-reciprocal devices.
