Tracking Theory of Adaptive Filters with Input-Output Sampling Rate Offset

Adaptive filter theory for supervised identification of linear time-invariant (LTI) systems is an established and fruitful discipline in digital signal processing. In certain applications, however, the input and output signals of an LTI system may be asynchronously sampled at slightly different sampling frequencies resulting in a small input-output sampling rate offset (IO-SRO). In this contribution, we argue that an LTI system with IO-SRO is seen as a linear time-variant system by the adaptive filter. By conducting a convergence-in-the-mean analysis, we propose a model to capture the influence of IO-SRO on the tracking properties of the adaptive filter. Eventually, we validate our model by reconstruction of the IO-SRO based on the proposed model and the observable adaptive filter behavior. The model-based IO-SRO reconstruction turns out to be highly precise and robust against noise and excitation bandwidth limitations when compared to a state-of-the-art method.