Real to complex and complex to real in place FFTs are very popular because the negative frequencies are the complex conjugate of the positive frequencies. Back when room size computer had 4 MB of memory and multiple users, these were essential to seismic processing. But there are lots of FFTs which do *not* fill in the complex conjugate part. So it matters what algorithm you use.
I'll post TDR to 20 GHz BW using an 11801 & SD-24 later. Setup will be SMA-M to BNC-F cable open, same with Chinese 50 ohm BNC-M terminator, then SMA-F to BNC-F cable to BNC-M to SMA-M cable to SMA-F to N-F adapter and Anritsu 50 ohm N-M calibrator load. The cables are very high quality made for me by a friend. So it will be a canonical test case. I can also sweep them to 3 GHz on an 8560A w/ TG option in addition to my nanoVNA results.
The SMA to BNC cables are about 10-12" so it gives good separation in the time domain.
For testing software, multiply a complex series with a real part of 1.0 and an imaginary part of 0.0 by exp(j*2*pi*f*t) for t equal to 1/2 the reciprocal of the frequency spacing. Do this with the DC part [0,0] and with the DC part [1.0,0]. In both cases you should get a spike in the middle of the TDR trace. Without the DC, the base of the spike will be offset from zero.
Another canonical test is a cosine in frequency. That will be a pure real spike in time. A sine wave will be a pure imaginary spike in time.
I've got some headaches to take care of, so it might be a day or two before I have time to do the physical tests.
Attached below are a few pages from Bracewell with pictures of important transforms in both domains. Most of these are excellent test cases as both domains are obvious. Some are more complex, but I thought I'd leave them.
What matters are impulse, sine, cosine, "boxcar" (sinc) and some of the variations.