Absolutely. It's called TDT, Time Domain Transmission measurement. If
you put a fast step into port1 of a 2-port box, and scope what comes
out of port2, that's the time domain equivalent to S21. The port-1
TDR, which you can do simultaneously, is (almost) just a Fourier
transform away from S11.
Once I'd thought about this some more, I realized I'd done this
stuff 25ish years ago. I had a Tek Digital Processing System (A
Tek 7704 with an A/D sampler in the middle, hooked to a DEC PDP-
11/34) and was looking for interesting things to do with it in my
"spare" time.
I "found (in my livingroom ;-)" this "HBO filter" and decided to
analyze it. I used 7S11 and 7S12 (IIRC) plugins in the DPO and a
HP pulse generator to excite the widget. I then took the input
and output waveforms, averaged the hell out of 'em and did an
FFT/convolution to find what was inside (simply a sharp notch
filter).
A Tek SD-24 (DC-20 GHz) sampling head does dual-channel TDR and is
cool for stuff like this; just turn on the TDR step of one channel and
use the other channel in pure sampling mode. If you attenuate the
step, you can use this to test the time-domain response of wideband RF
amplifiers and things like that.
I found that an "impulse" as narrow as I could get it (and as
small - averaged thousands of times) was better than the TDR head
on the 7S11. It's been a long time since I've had the "need" to
make an HBO filter though. ;-)
(Oh, are the statute of limitations up yet? Honestly, it was all
about intellectual curiosity! *I* didn't manufacture them!)