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cross over distortion is usually occur in push pull amplifier because of the biasing (biased at cut off). In this type two matched transistors are used 1 is pnp and the other is npn. npn is on for the positive half cycle and pnp is on for the negative half cycle. No transistor is on for the complete cycle because there is a delay to turn on the transistors. No signal appear at the output when the signal changes its polarity.
Please read class B amplifiers.
Cross over distortion happens in other circuits, not only those using PNP/NPN output transistors, it even happens in vacuum tube amplifiers. Basically it occurs whenever each half of the signal cycle is carried through different output devices but the change-over point is badly defined. In general, you see it when the devices are under-biased and the signal is so small it cannot overcome the threshold at which the device starts to conduct. The fix is normally to provide just enough static bias to hold the output stages at the point conduction just starts or in most cases, a little further beyond that point to avoid any non-linear characteristics in the devices low conduction region.
As others said, when the audio signal level is near zero (the time of crossing over the signal polarity) , (under + .7 and over -.7 volt) both transistors remain off because the base emitter voltage should be at least .7 volt for a BJT to turn on. during this time the output load gets no power... so output wave gets flatten during this time.. It's also called dead zone... so the output audio gets distorted.....