唐斌-数字信号处理课件-chp4 第4讲.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 realization structure of filter Relationship between and h[n] Relationship between and h[n] 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. —— polyphase compo