A signal processor has an input terminal and an output terminal for use in a wireless transmitter, for generating a radio frequency signal suitable for transmission, either with or without further power amplification. The signal processor separates an input signal into first and second processing paths, the first processing path generating a pulse train signal which is a digitised envelope signal, and the second processing path comprising phase processing means operable to generate a constant envelope phase signal. An RF switch is operable to switch the phase signal by means of the pulse train signal.