2001 Sable - rough Idling



Good morning! I wonder if you could help me solve two problems with my car. Here goes.

This Sable has traveled 163,000 miles and has performed admirably over its useful life but it is encountering the following problems:

Rough idle after warm-up, and at all traffic stops after RPM’s dip to below 500 and shoot-up to 700. They settle at 600.

Secondly, at RPM’s greater than 4000 the car misses and loses power.

Are these two problems related?

What is the likely cause(s) ?

I have changed the idle air control valve, the throttle control module and the ignition coil, all within the last month.

The transmission was replaced last year.

Thanks for your help!!

Kindest regards