电子科技大学：《DSP算法实现技术与架构 VLSI Digital Signal Processing Systems Design and Implementation》课程教学资源（课件讲稿）Chapter 09 算法强度缩减 Algorithmic strength reduction in filters and transforms

/96 This 2-parallel filter requires 2L-1=3 distinct sub-filters of length N/2 and 4 pre/post- processing additions. It requires 3N/2=1.5N multiplications and 3(N/2-1)+4=1.5N+1 additions. While the traditional 2-parallel filter requires 2N multiplications and 2(N-1)additions. 2021年2月 16

2021年2月 16  This 2-parallel filter requires 2L-1=3 distinct sub-filters of length N/2 and 4 pre/post￾processing additions.  It requires 3N/2=1.5N multiplications and 3(N/2-1)+4=1.5N+1 additions.  While the traditional 2-parallel filter requires 2N multiplications and 2(N-1) additions

/96 Example-1: when N=8 and H=tho,h1,h2,h3,h4,hs,h6,h},the 3 sub-filters are H。={h,h2,h4,hs} H1={h,h,h,h,} H+H1={h。+h,h2+h,h+h,h。+h,} 2021年2月 17

2021年2月 17  Example-1:  when N=8 and H={h0 , h1 , h2 , h3 , h4 , h5 , h6 , h7 }, the 3 sub-filters are

/966 Y=9H,·PX P2 is a pre-processing matrix which determines the manner in which the inputs should be combined. H,are the sub-filters required in this parallel FIR filter. Q2 is a post-processing matrix which determines the manner in which the filter outputs are combined to correctly produce the parallel outputs; 2021年2月 18

2021年2月 18  P2 is a pre-processing matrix which determines the manner in which the inputs should be combined.  H2 are the sub-filters required in this parallel FIR filter.  Q2 is a post-processing matrix which determines the manner in which the filter outputs are combined to correctly produce the parallel outputs;

9.2.2.1 Three-parallel FFAs /986 The 3-parallel FIR filter is constructed using 6 sub-filters of length N/3, ■ With 3 pre-processing and 7 post-processing additions,this filter requires 2N multiplications and 2N+4 additions which is 33%less than a traditional 3-parallel filter. 。=H,X。-z3HX2+z3[(H,+H2X+X2)-HX] y=[H+HX。+X)-HX]-H,X。-zH,X2 ,=[(H。+H,+H2XX。+X+X2】 -[H。+HXX。+X)-H,X -[(H,+H2X+X2)-HX 2021年2月 19

2021年2月 19  The 3-parallel FIR filter is constructed using 6 sub-filters of length N/3,  With 3 pre-processing and 7 post-processing additions, this filter requires 2N multiplications and 2N+4 additions which is 33% less than a traditional 3-parallel filter. 9.2.2.1 Three-parallel FFAs

女 /966 Y=QH3P·X3 10-z3 000 1 0 100 Y,= 9= - 1 011 ）1 Ho 1 0 0 H2 0 0 1 x H =diag H。+H, P= X3= 1 1 0 H1+H2 X2 0 1 1 H。+H1+H2」 1 1 1 2021年2月 20

2021年2月 20