Abstract: A transmitter employing a sigma delta modulator having a noise transfer function adapted to shift quantization noise outside at least one frequency band of interest. A technique is presented to synthesize the controllers within a single-loop sigma delta modulator such that the noise transfer function can be chosen arbitrarily from a family of functions satisfying certain conditions. Using the novel modulator design technique, polar and Cartesian (i.e. quadrature) transmitter structures are supported. A transmitter employing polar transmit modulation is presented that shapes the spectral emissions of the digitally-controlled power amplifier such that they are significantly and sufficiently attenuated in one or more desired frequency bands. Similarly, a transmitter employing Cartesian transmit modulation is presented that shapes the spectral emissions of a hybrid power amplifier such that they are significantly and sufficiently attenuated in one or more desired frequency bands.