My prelude wiil not accelerate past 30 to 40 miles per hour, starts fine, idles fine run fine beloww about 30 or 40 mikles per hour, does not really miss but will not accelerat past 30 or 40

may be a faulty tps (throttle position sensor)

would check the idle speed sensor at the same time

if no better
solenoids on the transmission

it is in limp mode
run the fault codes to find the problem, fix the problem then reset the ECM using a scan tool

they are correct change the fuel filters

fuel filter might be clogged

does the engine run badly while idling at 5 miles an hour?

no thats about right

DIRTY INJECTORS OR SPARK PLUGS FOULED OUT.

Idle is rough because not a right Air/ Gas mixture.
The ideal air /gas ratio is 14.6:1. If less than that it has rich mixture. If it more then that it has a lean mixture.
Back fire happens when accelerated because of of rich mixture pumped out at exhaust cycle is burning.
At speed above 40 miles/hour, temperature and fast compression cycle make the problem is less obvious.
Cheap first shot is to replace the air filter to correct this ratio. If it doesn't help, need Fuel distributor service. ( However people like to make easy money from you first, they will convince you for a turn up) Good Luck. I'll check back to see how the progress going.

these jeeps did have a small problem with the tp sensor. i would also have the back pressure of the exhaust checked to see if you have a catalytic converter choked up.

no not muffler problem could be bad gas or TPS sensor how many miles you have on it?