A Unified Perspective on Time-Domain and Frequency-Domain Kalman Filters for Acoustic System Identification

Time-domain and frequency-domain Kalman filters are applied as adaptive filters to many audio signal processing problems, especially to acoustic system identification. As the formal relationship between these two Kalman filters is not obvious, we connect them using a unified perspective. To this end, we show the equivalence of both filters as a special case and transfer concepts from one domain to the other. Specifically, the concept of considering multiple past observations is transferred to the frequency-domain Kalman filters, and the concept of block-based processing is transferred to the time-domain Kalman filters. Transferring these concepts yields new Kalman filter variants that allow for a different trade-off between convergence speed, steady-state performance and computational complexity.