The tracking performance of PLL-based is often expressed in terms of error variance. To take into account the effect of Loop bandwidth, another parameter, called loop SNR is used. Loop SNR for an analog implementation is expressed as shown below (Appendix C of Michael Rice's "Digital Communication: A discrete-time approach"). Here, the loop bandwidth is expressed in Hz. I was wondering how the loop SNR derivation in the digital domain where the frequency is expressed in radians/sample.

Thanks in advance.

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