One bit digital filtering

Many analogue-to-digital (A/D) and digital-to-analogue (D/A) converters use an intermediate sigma-delta modulating stage to convert signal inputs and outputs into a simple digital form for high quality conversion. In the case of A/D converters, a multibit representation of the signal is achieved with a decimating filter and, similarly, D/A converters employ interpolators to increase the sampling rate and to remove images of the baseband audio signal that are created by oversampling. The well-documented sigma-delta modulating technique, employing Nth order noise shaping, is then used to create a highly quantised two level signal. This one bit signal is a perfectly valid representation because it contains all of the audio band information. Processing the one bit signal directly offers an alternative approach to signal processing and removes the decimating or interpolating requirements in an analogue interface. It also allows a simpler system structure because the interconnections are naturally serial with no implied framing. Also, because the signal is heavily oversampled, the system characteristics can approach those of high quality analogue processors in terms of phase response and distortion effects, while retaining the advantages of digital processing techniques. This paper describes filter structures which operate on one-bit signals and develops an efficient structure for realising efficient IIR filters with no multipliers.