A new synthesis filter for filter bank systems with transmission delay

In this paper, a new synthesis filter is designed for filter bank systems with transmission delay by adapting random time delay or data-missing situations in the communication network. Firstly, we formulate a mathematical description of the data transmission delay and a measurement model. Secondly, the state model and the measurement model are adapted into new forms by expanding their dimensions. In this way, non-white noise can be converted to white noise, which can be dealt with using standard Kalman filtering. Thirdly, a dimensionality reduction method is proposed to overcome the complexity generated by expanding dimensions, and then a synthesis filter is designed with dimensions equal to those of the original system. Finally, a simulation is presented to demonstrate the effectiveness and the advantages of the proposed method.