In an old advertisment for the Musicians Institute, Paul said..
"Alternate picking is one of my favorite things. It works well for playing at an even tempo, gets a good tone out of the string and is efficient enough to allow one to play very fast and clean.
Here is an eight note sequence that has allowed me to develop my alternate picking enormously.
E----------------------------------- R
B----------------------------------- E
G---9-------9----------------------- P
D------12------12--10---9--10--12--- E
A----------------------------------- A
E----------------------------------- T
u d u d u d u d picking
Played in the ninth position on the D and G strings. Notice that E is the only note played on the G string and that it is always an upstroke. Make sure to keep your hands synchronised and don't stop practicing the lick until it sounds like a popsicle stick caught in you bicycle spokes.
The first Paul Gilbert lick that I ever learned was this one from his Intense Rock instructional video. It's an alternate picking exercise and when you get going it sounds really cool. It has a triplet feel to it. Remember to concentrate on making the lick sound really even speed wise. Accentuate the notes to your hearts content, but keep the speed even..
E--------------12---------- R
B--12--13--15------15--13-- E
G-------------------------- P
D-------------------------- E
A-------------------------- A
E-------------------------- T
d u d u d u picking
This lick can be expanded on to give the exercise in Paul's MI ad, but 12th position, E & B strings...
E--------------12------12---------- R
B--12--13--15------15------15--13-- E
G---------------------------------- P
D---------------------------------- E
A---------------------------------- A
E---------------------------------- T
d u d u d u d u picking
But you want to make some beautiful music huh? Well, try mixing them up a bit and see what comes out. I always thought this one sounded cool, especially at a million and a half miles an hour..
E--------------12----------------------12------12---------- R
B--12--13--15------15--13--12--13--15------15------15--13-- E
G---------------------------------------------------------- P
D---------------------------------------------------------- E
A---------------------------------------------------------- A
E---------------------------------------------------------- T
d u d u d u d u d u d u d u picking
..and finally. Try adding the F# and G on the E string...
E--------------12--14--15--14--12---------- R
B--12--13--15----------------------15--13-- E
G------------------------------------------ P
D------------------------------------------ E
A------------------------------------------ A
E------------------------------------------ T
d u d u d u d u d u picking