Is there a specific car you wanted to detect or should any nearby car trigger the garage door?
If it's any car then a metal detector loop or an optical tripwire or a mechanical strip switch would be a better solution. An electric car might not produce enough noise to detect at a reasonable distance.
If it's a specific car then putting something on the car (IR beacon, Ultrasonic beacon, radio beacon) would be a much simpler solution than trying to discriminate the noise of one car from all other cars.