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For symbol timing recovery with feedback loops, Mueller and Mueller (MM) detectors can be an attractive solution in comparison to other algorithms. This is mainly due to the fact that they are operated at baud rate, thus avoiding any performance degradation in form of the jitter floor as it is the case with zero-crossing or Gardner synchronizers as most prominent examples in this respect. However, in order to guarantee reliable results, MM trackers require the carrier phase to be established. Motivated by this background, a timing error detector for carrier-independent and non-data-aided (blind) synchronization of the symbol timing is analyzed and discussed, which needs only one sample per symbol. Assuming linearly modulated signals, the detector characteristic (S-curve) is computed exactly and verified by simulation results, with the slope in the stable equilibrium point given in closed form such that the tracking loop can be specified accordingly.