2001 Buick LeSabre engine sputters

Hello to all of you, I have a problem with my 2001 Buick LeSabre Engine "3.8" V6.
I have 52K miles on it, the problem started about 3 months ago, while driving on the highway pushed on the gas to make a pass and the car jolted/hesitated to downshift and pick up speed, I though it was a coincidence, about 3 week ago while in traffic the engine started to sputter and vibrate harder then usual, after a while the problem went away on its own.
now the car idles fine but when I step on the gas no matter which gear I'm in the engine bugles, jolt/sputters. I did the following things to fix the problem: Checked air filter, its OK, replaced fuel filter and used fuel injectors cleaner solution, all these things haven fix the problem yet, does any one have any idea for this problem?
Thank you all

you need to check your fuel pressure on your fuel pump first. dose your check engine lite on? we had 3 of them counting my mom and dads cars what went wrong on mine it was the cps. and the tbs and module went before coil pack. but i bet your not getting enough gas so have fuel pump checked first it just may just a coil in coil pack. reson why i ask if check engine lite was on is so you could goto autozone or advanced and they'll hook it up for free.

Thank you ParK Avenue, I have the feeling that is fuel pressure related too. I aslo got your private message as well, I'm gonna take the car to a mechanic tomorrow, this problem has become more severe in the past 24 hours, now I hear clinking noise from the engine when this sputtering occours.
Engine light comes on bliking and then it resets its self so the mechanic hasn't been able get a code because the check engine light is off by the time I get to him.
Thank you.

Obd11 will have history codes when scanned.