Imagine the pulse coil is a switch - when the crankshaft reaches the correct position the switch closes and sends a signal to the igniter and, depending on a number of variables, the igniter will, at the right time, then supply a momentary return path for one of the coils which will cause a spark.
You said you changed the coils - did they come with new leads and caps? Have you cleaned the carbs - the choke plungers on the carbs can stick and cause rough running.
There was a case when the pick up coil affected 1 cylinder:
http://forums.sv650.org/showthread.php?t=133901
but it's unusual.
If you use google to search this site it works better than the site's own search function. As an example, type everything between the quotation marks into the address bar on your browser.
"site: sv650.org pick up coil"