Identification of a one-bit lowpass sigma-delta modulator using BIMBO

We show how the BIMBO identification method can be used for the online identification of the digital filter in a sigma-delta modulator´s loop. This parameter estimation method only requires the knowledge of the bit stream at the modulator output. This approach does not rely on an approximation of the comparator (such as additive white noise or describing function approximation). Moreover, it requires no amplitude measurement, as opposed to most other methods, and, thus, it involves no additional electronics: it is therefore very economical to implement it practically. The method is described from a theoretical point of view and an experimental validation is given.