dsp2纯课件数字信号处理第4讲changed for next year

1、4.7 Multirate signal prcessingLet ,then L=100, M=101Disadvantage: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.4.7 Multirate signal prc

2、essingMultirate techniques: utilizing upsampling, downsampling, compressors, and expanders in a variety of ways to increase the efficiency of signal-processing systems.Sampling rate conversionA/D and D/A systems that exploit oversampling and noise shaping.Filter banksApplications:4.7 Multirate signa

3、l prcessingInterchange of filtering and downsampling/upsamplingPolyphase plositionGreatly improve the efficiency of sampling rate conversionOur focus:4.7.1 Interchange of filtering and downsampling/upsampling 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。4.7.1 Inter

4、change of filtering and downsampling/upsampling 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。4.7.1 Interchange of filtering and downsampling/upsampling 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。4.7.2 Polyphase positionThe polyphase positio

5、n 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 position is applied to a filter impulse response, it can lead to efficient implementation structures for linear filters.+=

6、 hnM=3Polyphase position of filterMMMleft shift 1right shift 0right shift 1right shift 2left shift 2Polyphase position of filterpolyphase components of hnPolyphase position of filterH(z) is expressed as a sum of delayed polyphase component filtersright shift k, sumAnother derivation of polyphase pos

7、ition polyphase components of hnLet Then ZT= Polyphase realization structure of filter4.7.3 Polyphase implementation of decimation filterspolyphase positioninterchange of filtering and downsamplingComputation comparisonvkn: 1/M sample/s, Ek(z): N/M-point Direct structure Polyphase structureH(z): N-p

8、oint FIR filterxn: 1 sample/sAssume: N-1 N multiplication: addition: multiplication: addition: each filter Ek(z)the entire system:multiplication: addition: 4.7.4 Polyphase implementation of interpolation filterspolyphase positioninterchange of filtering and upsamplingComputation comparison Direct st

9、ructure Polyphase structureH(z): N-point FIR filterxn: 1 sample/sAssume: wn: L sample/sEk(z): N/L-pointLN LN-1 multiplication: addition: multiplication: addition: each filter Ek(z)the entire system:multiplication: addition: 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。在内插和抽取

10、混合使用实现非整数倍采样率变化的系统中，当需要高的中间采样率时，这种计算效率上的提高会非常显著。Class TestDetermine the required multiplication per unit time if implemented using the direct structure.2) Determine the most efficient polyphase structure.H(z): N-point FIR filterxn: 1 sample/sAssume: Solution:1) Direct structure:multiplications 2) Polyphase structure 1:multiplication:计算效率提高M倍Solution:3) Polyphase structure 2:multiplication:计算效