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I often read that one of the benefits of FSE vs a symbol rate equalizer, besides avoiding any aliasing in the roll off region, is that it is less sensitive to the timing phase. What does that really mean? Does it mean that if at the output of the matched filter instead of taking one sample (assuming it is not exactly at the center of the eye diagram) , two samples are chosen, then the performance in terms of SNR will improve? How? by interpolation? I don't really understand the relation between the equalizer and what is called the timing phase ( not sure what that expression means either)

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The more samples you have per symbol the less timing error you have since delay in samples is converted to delay in time by dividing by the sampling rate. I beleive the far more dominant reason for a fractionally spaced equalizer is the aliasing you mention as can be seen in the frequency response of the equalizer. For example, 2 samples per symbol can capture all the phase and amplitude distortion represented over the channel bandwidth uniquely as depicted in the graphic below. (This is assuming the signal was sufficiently filtered prior to being decimated to the fractional rate used).

Baud vs Fractional

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