The problem started to appear gradually, increasing over time. The popping became very annoying especially on steep descents when using engine braking in low gears. In general this problem is caused by a lean air/fuel mixture (poor in gasoline). The wrong ratio causes some misfires, the unburned gasoline then explodes in the exhaust due to the high temperature.
I solved it with a thorough cleaning of the carburetors, paying particular attention to the air cut-off valve circuit and the idle jets; see this article: Honda NTV650 Revere - Carburetor.
After a long period of non-use (16 years), I restarted an NTV650. I had already cleaned the carburetor from the sludge that had formed following the evaporation of the petrol.
The bike starts easily and holds the minimum speed well, but when you increase the gas, around 3000 - 4000 rpm, it begins to splutter noticeably. After a few minutes of operation it seems that the front cylinder does not work because it is practically cold, unlike the rear which has reached the temperature. After checking the ignition coil by measuring the resistance of the primary and secondary windings and verifying that there was a spark at the spark plug, I decided that I had to disassemble the carburetors again.
It turned out that the idle circuit had been cleaned correctly, in fact the bike worked perfectly at idle. But the main jet duct still contained some dirt: opening the throttle the air/fuel mix were too lean, to the point that the engine ran on only one cylinder. The uncobusted petrol sometimes was detonating, thus the sputtering.