Does statute of limitations still apply after a person has been arrested but not tried?

The usual procedure is for the prosecuting attorney's office to file charges against the alledged perpetrator(s) of the crime and then a warrant to be issued for his or her arrest. That being the case, charges can be filed but the person charged will not be immediately taken into custody. The named person however, will eventually be arrested, booked and arraigned. There are no SOL's when a warrant has been issued and SOL's only apply to the length of time when the crime is committed to the time charges can be filed. Depending upon the state or Federal Laws pertaining to the crime committed an SOL may not be applicable.