Spectral analysis of multirate system and its application

The statistical properties of multirate systems are formulated in this work. Related to this is the issue of coding error. Multirate system is developed with the assumption of negligible quantization errors at the coding stage of the system, while in practice this is not the case. The behaviour of an ideal multirate filter system toward quantization error with an wide sense stationary input signal is formulated. A closed form expression of the quantization error of a multirate system for ARMA input signal is formulated. With such a description, generalized coding gain is formulated and is applicable for performance measure of both orthogonal and nonorthogonal system. Another issue is the multirate filter banks design problem. One of the problems in constructing multirate filter system having the minimal quantization error effects is the difficulty in formulating a general description of quantization error. With the application of the generalized coding gain, optimal multirate filter design problem can be formulated as an optimization problem. Noticeable achievement in the performance of the filter banks developed through optimizing the coding gain is obtained. In summary, two research directions are explored in this thesis. One is to formulate the statistical properties of multirate system. The other is to formulate the quantization error (coding error) effect of multirate system. Applications of the developed theories will also be discussed. These include the analysis of signal to noise ratio (SNR) of the synthesized signal when quantization is applied at the coding stage, optimization of the performance of multirate system, etc..