Hello friends. I want to develop an ultra-low power counting system as the figure shown below. Is there a possible circuit scheme to achieve this? Thanks.

 

How many counts are we talking, what signal speed/frequency etc? How hard is it to distinguish your signal, i.e. how complex will the analog processing be?
I could imagine a two part system, where the first part is a CMOS counter or similar with some pulse shaping circuitry and possibly a micropower comparator, powered by your battery or super cap.
Second part would be powered by the RF field, so when the reader comes close some processor gets powered up, gathers the data from the counters and then sends over RFID. In this step you could also recharge the super cap that would power for the first part.

 

Hello friends. I want to develop an ultra-low power counting system as the figure shown below. Is there a possible circuit scheme to achieve this? Thanks.

There probably is but no one will find it without an awful lot more information such as:
Input signal amplitude and frequencies.
Power available.
Physical size constraints.
Portability,
Budget available.
Features of display.
Operator interface.
etc.

 

i would add to @KeithWalker's questions:

Why? What is the problem this is expected to solve?

 

I cannot ofer any concrete idea to the OP.

I got used to the concept years ago when Crosby (top brand of lifting tools) commenced to offer some of them fitted with data traceable via RFID and handheld terminals.