I sense a little confusion about the differences between time and
frequency domain analysis. This is really common.

Impedance is a frequency domain concept, and works in the time domain
only in a very limited way. Impedance consists of two parts, a magnitude
and phase or a resistance and reactance. Reactance is a function of
frequency, so it has no simple equivalent meaning in the time domain
which encompasses a very wide range of frequencies all at once. Likewise
for magnitude and phase. So only resistance is really useful in time
domain analysis. Some impedances, like a low loss transmission line's
Z0, are essentially purely resistive, so they're useful. But complex
impedances, in general, are not.

With a TDR system you can readily see and interpret frequency-dependent
resistances like skin effect, "capacitive" and "inductive" regions
(where the Z0 of the transmission path is lower or higher than the
reference respectively), and a lot of other features. But it's difficult
to get an intuitive feel for the relationship between a TDR and
frequency domain analysis of a lot of circuits which change
characteristics rapidly with frequency (in other words, which have a
reasonably high Q).

A TDR generally produces a fast rising step or its derivative, a narrow
pulse. Viewed in the frequency domain, this step or pulse has energy
over a very wide range of frequencies, but very little in any narrow
range of frequencies. So if a circuit has high Q, there's usually not
enough energy at or near the resonant frequency to get the circuit to
ring at any appreciable amplitude, and you often won't even see the
circuit with a TDR. (By this I mean that, for example, a high Q series
resonant circuit looks like an open and a parallel resonant circuit like
a short, which are essentially their impedances except near resonance.)
A dipole is a pretty low Q circuit in the frequency domain, so you can
see a periodic time domain response that corresponds to its basic
resonance. It looks like a lossy, open circuited transmission line whose
characteristic impedance increases from the feed point outward. The
response, which I'm sure you can also find somewhere on the web, looks
something like a distorted (due to the changing Z0) square wave whose
amplitude diminishes with time (due to the radiative "loss").

Roy Lewallen, W7EL