Abstract: Processing apparatus is provided that directly samples and quantizes a complex envelope of a bandlimited waveform centered at a predetermined carrier frequency. An oversampling delta-sigma modulator 1 samples and quantizes the input signal to a single bit data stream. A serial-to-parallel converter converts the single bit data stream into a parallel bit stream. A digital decimation filter digitally filters the parallel bit stream to produce an estimate of the baseband in-phase and quadrature components of the input signal. In-phase and quadrature video filters generate in-phase and quadrature samples that are output from the analog signal converter. A controller 26 and a plurality of digital-to-analog converters 25 are used to center noise shaping nulls of the delta-sigma modulator around the carrier frequency. The controller sets the spacing between nulls of the serial-to-parallel converter to maximize the signal-to-noise ratio of the analog signal.