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Crystal is a very high Q device. Ok, the non-sinusoidal noise, you talk about has a sinusoidal component to it. One of the components is at the resonant frequency of the crystal. See the model of the crystal, that should help see how it starts if you inject a small sinusoidal voltage across the crystal model. Don't forget the capacitors on the ends of the crystal.
Noise is generated within ckt elements such as resistors etc. The one generated in resistors is also known as shot noise. Now suppose you are using an RC oscillator as the feedback network and an opamp as a amplifying device, then by Barkhausens criteria the gain * feedback = 1 for sustained oscilations. Initially assuming that only the resistor noise is available at the input of the OPAMP, the OPAMP has sufficient gain to amplify this noise. i.e the o/p of opamp tries to move towards saturation ( just by the noise). Here the point is that the necessity os sinusoidal component is not important, and at any point of time a noise signal can be defined as a sinusoidal component by determining the fourier component of noise.
I got the point that how a non-sinusoidal noise can lead to a sinusoidal output,(the sinusoidal component of noise signal is picked up by the ckt if it is at the resonating frequency of the crystal).
when the noise is amplified by the op-amp , if the output increases beyond saturation limits then there exists a possibility that the output signal will be clipped off,but it never happens rather the amplitude of the output signal is so adjusted that it appears fully sinusoidal.Why?or Where is the fault in my understanding .