唐斌-数字信号处理课件-chp4 第4讲（changed for next year）.pptVIP

4.7 Multirate signal prcessing 4.7 Multirate signal prcessing 4.7 Multirate signal prcessing 4.7.1 Interchange of filtering and downsampling/upsampling 4.7.1 Interchange of filtering and downsampling/upsampling 4.7.1 Interchange of filtering and downsampling/upsampling 4.7.2 Polyphase decomposition Polyphase decomposition of filter Polyphase decomposition of filter Another derivation of polyphase decomposition Polyphase realization structure of filter 4.7.3 Polyphase implementation of decimation filters Computation comparison 4.7.4 Polyphase implementation of interpolation filters Computation comparison Conclusions 对于抽取和内插，通过滤波器的多项分解以及滤波与增采样/减采样的交换，使得滤波在低采样率下完成，从而大大提高了计算效率。 Class Test Solution: Solution: Let , then L=100, M=101 Disadvantage: require large amounts of computation for each output sample Assume T=1.01T, The amount of computation can be greatly reduced by taking advantage of some basic techniques in the area of mulirate signal processing. Multirate techniques: utilizing upsampling, downsampling, compressors, and expanders in a variety of ways to increase the efficiency of signal-processing systems. Sampling rate conversion A/D and D/A systems that exploit oversampling and noise shaping. Filter banks Applications: Interchange of filtering and downsampling/upsampling Polyphase decomplosition Greatly improve the efficiency of sampling rate conversion Our focus: Interchange of filtering and downsampling 可见，两个系统等效。但滤波器放在抽取后，采样率降低了M倍，计算量相应降低M倍。 Interchange of filtering and upsampling 可见，两个系统等效。但滤波器放在插值前，采样率较低，计算量相应降低L倍。 decimation interpolation 利用上面两种等效关系，可改变抽取和内插中滤波器总是在高速率端的情况，降低计算量，更有利于实时处理。 The polyphase decomposition of a sequence is obtained by representing it as a superposition of M subsequences, each consisting of every Mth value of successively delayed version of the sequence. When this decomposition is applied to a filter impulse response, it can lead to efficient implementation structures for linear filters. + + = h[n] M=