Here’s the opposite of a cheap solution, but much better suited for lab use – a Siglent SDG7102A Arbitrary Waveform Generator programmed to output a 10 ns wide pulse at 10 MHz repetition rate with 1 ns transition time for both edges.
A quick check with a high bandwidth SDS7404A DSO reveals that the pulse shaper in the SDG isn’t quite accurate anymore at faster edges like this, hence the actual rise time is more like 900 ps:
SDS7404A H12_PR_W10ns_RT1ns_4GHz_Dots
A 500 MHz (actually 570 MHz) SDS2504X HD DSO by contrast, shows a bit of overshoot – this is the price we pay for analog AA-filtering, even when it’s still not very effective:
SDS2504X HD_PR_W10ns_RT1ns_570MHz_Dots
These measurements were taken in Dots display mode, in order to rule out any reconstruction artefacts. But of course, a properly implemented Sinc reconstruction does an equally flawless job:
SDS2504X HD_PR_W10ns_RT1ns_570MHz_Sinc
If you want to see Gibbs Ears, this won’t be achieved with a regular analog filter (as long as it is a minimal phase system). But it’s easily produced with a digital FIR filter, as in the variable bandwidth limiter provided by the SDS7404A. Here’s an example with 600 MHz acquisition bandwidth:
SDS7404A H12_PR_W10ns_RT1ns_600MHz_Dots