Optimal design of deconvolution filters for stochastic multirate signal systems

Abstract

Multirate digital signal processing techniques are widely applied to data compression and storage in communications, speech processing, video processing, etc. Signal reconstruction in conventional multirate signal processing systems is mainly based on the property of perfect reconstruction from the viewpoint of inverse filtering. Signal corruption due to quantization and channel noise is neglected in the conventional design of multirate systems. Therefore, the performance of conventional multirate systems is deteriorated by channel noise. The signal reconstruction problem in multirate systems with consideration of channel noise is discussed in this paper from a more practical viewpoint. This is a so-called deconvolution filtering problem in stochastic multirate signal processing. A multirate state-space model is first introduced to unify signals with different sampling rates into a signal system model. Channel noise is modeled as a measurement noise in this state-space form. The deconvolution problem turns out to be a problem of optimal state estimation. A multirate Kaiman deconvolution filter is then proposed to solve this problem. Three types of stochastic multirate systems including filter banks and transmultiplexers are discussed to illustrate the design procedure of multirate deconvolution filters. The proposed deconvolution filters are compared with conventional systems without consideration of channel noise. The performance of the proposed design is significantly better than the conventional design in the case of channel noise.