Some added performance tests accumulated over the past holidays using a "calibrated" RF generator HP 8640B. The 3B point of the 1054B is about 120 MHz versus my prior conservative test.
This is the maximum usable frequency of the unmodded scope. At near n/2 at the Nyquist limit the onboard counter quits just over 400 MHz then waveforms are wholly unstable at 430MHz. Down - 30dB.
IMHO, the practical limit of the scope, Down - 23dB. This is were all the math functions and on board calculations still are accurate and stable. YELLOW single channel, 363 MHz. Red math channel calculating derivates of CH1. Note Vpp and calculated RMS value, rise time of 821ps, Cursors are measuring rise time manually at 10-90 which is 1.15ns, or by 0.35/Tr ~ 304 MHz or 426 MHz using the automated rise time. Calculations were unstable on ungated mode, so these are based on using the 1054B gated to screen mode.
The stat function of the 1054B to show the level of stability at 363 MHz.
Close up of 1054B doing derivate of CH1 in real time. It will calculate cleanly even at 1kpts. Derivate of sin(x) is cos(x) but while the appearance is correct the phase shift is a bit prolonged.
Close up of the derivate of the rise time. This is also called the Dirac delta function.
Live 2 channels and math channel. Source is a Tek 284, Yellow CH1 is the pulse output and Blue CH2 is the trigger output, they are delayed by 5ns as shown on the cursors.