Linear system modeling and identification by basis functions selective in time and frequency

Often, a design of technical systems has to satisfy requirements simultaneously specified in the physical domain (e.g. time) and the transform (analysis) domain (e.g. frequency). An approach to the task is to use as design "atoms" objects with known and controllable characteristics in the both domains. Here, discrete-time basis functions (BF) selective in time and frequency are proposed for modeling of discrete-time linear systems. The systems are in general time-varying. The BF-based models are further used in identification of linear discrete-time systems and in adaptive filtering. System parameter estimates are affected by the output noise. The nose effects can vanish if the input signal and the system model satisfy some conditions. Basis functions selective in time and frequency can provide the selective sensitivity of parameter estimates to the narrow-band noise and/or impulse noise. This is illustrated by two examples: the identification of a echo path and the identification of a periodically time-varying system.