Vintage Tiger fuel filter?

It could be fuel filter or air filter. You don't say what bike you've got?

My 2006 955i Tiger was misbehaving and it turned out to be the IACV (Idle Air Control Valve), gave it a clean with aerosol brake and clutch cleaner and now seems fine.

 

Without knowing the service history of your bike, it could be anything so it's important to have a methodical approach to the diagnosis.

Have you have any work done on the bike recently? When was the last time the spark plugs/airfilter were replaced? Have you ever had the tank off?

 

Check the inlet tract's, they might not be sealing properly, vacuum ports/hoses etc , as the symptoms you put out are an indication of running lean when throttle is shut . a good easy simple test is baby powder or similar fine powder (flour will do it too) sprinkle it on the joining points between cylinder head and inlets, start the bike run it for awhile. couple of minutes will do vary the throttle no need to over rev it, look for clear/missing powder it will get sucked in if there is a leak!!!