A method and apparatus for generating digitally modulated signals in which a serial data stream of digital signals to be modulated (70) is provided, the serial data stream being converted into real and imaginary components (74) which are then converted into a complex polar signal (80) representing the serial data stream. A carrier of appropriate frequency is generated by an infinite impulse response filter (84,86) and the polar signal is mixed with the output of the infinite impulse response filter to provide a representation of the complex polar signal modulated at the frequency generated by the infinite impulse response filter (88). Subsequently the imaginary component of the resulting representation is stripped from the signal (90) and the real component of the resulting representation is applied to a digital to analog converter (92) to produce an analog version of the serial data stream.