The 900 MHz upper limit implies a sinc(t) width of 2.2 ns. A 256 point complex to 512 point real FFT will provide a long enough trace to reach the end of a ~50 m cable. The screen pixel count is not large enough to display all of that in time in a single screen.
The 1500 MHz upper frequency implies a 1.33 ns sinc(t). In that case the distance will be limited to ~30 m by only having 256 complex points. While more points would interpolate the sinc(t) and make it easier to pick the correct time looking at the TDR response, calculating the shift in the frequency domain will be *much* more accurate.
The screen resolution makes more than 256 samples not especially useful. Better to display the time to the cursor with picosecond resolution calculated in the frequency domain by a linear fit to the phase.
To reiterate. The sampling in time determines the maximum frequency. The sampling in frequency determines the maximum time. The maximum frequency and the numerical precision govern the achievable resolution picking a TDR trace.
The initial spike is a bug. It is a real constant added at all frequencies to the correct magnitude, but with no change in the phase angle. One can determine what that is by zeroing out everything after that initial spike and transforming back to frequency. I suspect that it is the result of a naive attempt to set the DC value in the frequency domain. If the frequency sampling were were infinitesimally fine (and the series length infinitely long), then setting that would be easy, but because it is discrete, that DC value is smeared out across the low frequency components. I did the smearing in frequency as a result of limited series length in grad school. I'll leave the problem one faces going the other way to the reader, at least for now. If you've taken a course in integral transforms or at least the Fourier transform, it's a very valuable exercise. The transform is symmetric, so once you've done one you know the other.
I haven't looked at the code, but I do know the mathematics well enough to be very sure of the preceding statement. "The Fourier Transform and Its Applications" by Ronald Bracewell will fill in all the details anyone might desire. At least until you want all the important theorems about the Fourier transform. For that, "A Handbook of Fourier Theorems" by D.C. Champeney is what you want. However, the latter is only really of use if you're concerned about whether doing the transform is valid.
Have Fun!
Reg
