The method and the circuit are much simpler than you suppose. But you must use your wits to figure it out. That's the beauty of electronics design: the ingenuity you use to solve a complicated problem with a simple solution.
OK, let's reason through it so at least we agree on the steps needed. Then I'll think about how hard it would be to build.
What changes is not the frequency of sampling. What changes is the TIME at which the sampling occurs. In the first cycle, (for example) it occurs 1 picosecond after the wave starts (zero crossing from bottom to top). The second sample is taken 2 picoseconds after the zero crossing, from bottom to top.
In many things there are different ways of describing the same thing. Often two very descriptions will boil down to the same thing. In this case, at a given signal (say our 100MHz) sampling as you describe will result in a sampling frequency just under the signal frequency, just by a different method. In this case the method is important, but the result may be considered in different ways.
And if you use 10000 samples to reconstitute the original waveform, and you have taken only one sample for each cycle, then the reconstituted signal will have a frequency 10000 times lower and you will be able to observe it on a cheap oscilloscope. The sampled voltage is charged into a capacitor. And on that capacitor a perfect sine wave is obtained, and a faithful copy of the sampled signal.
No A/D converters are needed. No need for counters. No need for memories.
OK, so to the meat of the problem. Someone correct me if I err. These are the issues, more or less in order. Assume a 100MHz input signal to be displayed at 10kHz.
1. You need a way to trigger on the zero crossing (or anywhere, I suppose) of the input signal.
2. You are sampling at 100MSa/s using an offset that cycles at 10kHz and has a range sufficient to cover one period.
3. If you want to display this as single period 10kHz signal on a scope, the scope should have a sweep time of 100 microseconds.
4. You need a method of offsetting samples of the input frequency from 0 to 10 nanoseconds, corresponding to one period.
5. To display the samples on the scope, they have to be correlated so that their positions in real time on the scope are proportional to the sample offset time. So the +5nS sample must appear at the 50uS position.
6. Since there is no storage, the samples have to occur in real time with the two values correlated. Thus you need a circuit that 'knows' where it is on the 100uS scale and offsets the sample by the corresponding amount.
So you need a trigger that operates on the 100MHz input signal, a 10kHz ramp signal followed by an offset delay circuit that corresponds to the ramp and then operates the sample circuit. You can trigger the display scope on the 10kHz ramp or on the sampled output. Anything else?
The most remarkable thing about all this talk is that
GlennSprigg , the original author of the query, has not even shown up here......
Time zones. We're all over the world and people pop in and out.