Have the OBDII ran, take it to a advanced auto parts to see if there is a code you may be running rich, or a number of other problems my Audi had a minor misfire which didn't flag the check engine light but caused an occasional backfire because the fuel was being exhausted. If the engine shudders it could be a misfire. Or its possible that your intake filter is clogged.
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The 2002 Audi A4 has 20 valves.