Use of allpass networks to tune the center frequency of sigma delta modulators

The standard sigma-delta modulator uses feedback around 1-bit quantizers to transform open loop integrator poles into closed loop transmission zeros of the noise transfer function. The DC transmission zeros permit high resolution quantization of data over a frequency band in their neighborhood. Closed loop zeros can be shifted to arbitrary spectral locations by doubling the number of integrators and then applying local feedback around integrator pairs thereby converting them to resonators. These spectrally shifted zeros support high resolution quantization at the selected (arbitrary) center frequency. In the paper the authors describe an alternate technique for shifting the open loop poles around the unit circle. In this method, rather than forming resonators, they use a spectral transformation on the baseband process performed by embedded all-pass filters