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Raised cosines represent more or less the de facto standard for baseband shaping in satellite communications. However, any pulse function satisfying the first Nyquist criterion could be used for this purpose. As reported in a recent paper, some of them exhibit considerably less self-noise jitter than raised cosines if they are employed for non-data-aided recovery of the symbol timing with Gardner detectors. With an extended version of the latter, it is shown analytically and by simulation results that the self-noise floor can be decreased significantly in the medium-to-low range of the excess bandwidth, if the corresponding synchronizer is applied to M-PSK signals shaped by a linear instead of a raised cosine pulse function.