A transmitter comprising a baseband modulator arranged to modulate a complex baseband signal and to output a complex modulated signal xin(n) with amplitude g and phase q, i.e. xin(n)=g(n)ejq(n), to the input port of a filter, the filter in turn having its output coupled to a transmit unit, said filter being arranged to output a filtered complex output signal xout(n) with amplitude g but phase m, i.e. xout(n)=g(n)ejm(n), so that the filter is arranged to affect the phase but not the amplitude of its input signal. The filter is arranged to have as its transfer function for the phase of its input signal the z-transform F(z)=1+wz−1, where w is a weighting function whose value is determined by means of the additive noise autocorrelation, the phase noise autocorrelation and the signal amplitude of xin.