Robust data equalization, fractional tap spacing and the Zak transform.

To counter intersymbol interference and noise, a data equalizer must be dimensioned in accordance with the characteristics of the transmission channel that it operates upon. Adaptive techniques can be a suitable means provided that the equalizer is sufficiently flexible. Prior knowledge about the ensemble of possible characteristics may be exploited to equip a non-adaptive equalizer with a sufficiently robust dimensioning to withstand all possible parameter variations. For the most commonly applied types of data equalizer, viz. the linear quantizer, its partial response variants and the decision feedback equalizer, this paper presents a unified derivation of their optimum adaptive and robust versions, using a mean-square measure of performance. The analysis is carried out by using the Zak transform, which is a linear time-frequency signal representation stemming from quantum mechanics.