A transmission system for transmitting data signals in a modulation band comprising a transversal smearing filter at the transmitter end and a transversal desmearing filter at the receiver end. In order to obtain an optimum smearing efficiency, the sequence of real individual coefficients of the multiplying factors of the transversal desmearing filter satisfy the requirement that for a given upper limit for the intersymbol interference produced by the cascade arrangement formed by the smearing filter, and the desmearing filter a substantially maximum value is derived for a merit factor indicating by what factor the maximum value of a disturbance is decreased by including a smearing filter and a desmearing filter in the transmission system.