Why oversample if you already satisfy Nyquist rate?

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Oversampling beyond the Nyquist rate is recommended to capture phase information accurately in a signal. While the Nyquist rate prevents aliasing, oversampling provides additional data points that enhance signal fidelity and improve reconstruction. This practice helps mitigate issues like quantization noise and allows for better filtering and processing techniques. The discussion highlights the importance of understanding the trade-offs between sampling rates and signal integrity. Overall, oversampling is a valuable technique for achieving higher quality in signal processing.
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I am told that if I want to get phase information from a signal, I should oversample the signal well beyond the nyquist rate.

I am confused about why this is suggested, since I thought the nyquist rate was the minimum frequency needed to avoid aliasing. I understand building in some safety space, but why is it necessary to go well beyond this rate?
 
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