/986 10.2.2 Efficient single channel interleaving Problems with M-slow implementation: A sample rate M times slower than the clock rate, Inefficient utilization of processing elements. Look-ahead transformation overcomes these problems,in which the linear recursion is first iterated a few times to create additional concurrency. 2021年2月 6
2021年2月 6 10.2.2 Efficient single channel interleaving Problems with M-slow implementation: A sample rate M times slower than the clock rate, Inefficient utilization of processing elements. Look-ahead transformation overcomes these problems, in which the linear recursion is first iterated a few times to create additional concurrency
/966 y(n+1)=ay(n)+bu(n) y(n+2)=alay(n)+bu(n)]+bu(n+1) u(m+1) u(n) D y(n+1) T,=2(Tm+Ta)/2 No improvement. 2D●→ y(n+2) y(n+2)=a2y(n)+abu(n)+bu(n+1) u(n+1) u(n) D b ab T=(Tm+T)/2 →2D◆→ y() y(m+2) 7
7 y(n 2) a[ay(n) bu(n)] bu(n 1) ( 2) ( ) ( ) ( 1) 2 y n a y n abu n bu n T 2(Tm Ta )/ 2 T (Tm Ta )/ 2 No improvement. y(n 1) ay(n) bu(n)
/966 Applying (M-1)steps of look-ahead to the iteration.we can obtain an equivalent implementation. M-1 y(n+M)=a“y(n)+∑abu(n+M-1-i) i=0 u(+M-1) u(n+M-2) u(D) D I- ）T。=(Tm+Ta)/M y(n+M) Time (n) 0 2 3 4 5 6 7 8 9 10 State Y(-4) Y(-3) Y(-2) Y(-1) Y(0) Y(1) Y(2) Y(3) Y(4) Y(5) Y(6) 2021年2月 8
2021年2月 8 Applying (M-1) steps of look-ahead to the iteration. we can obtain an equivalent implementation. ( ) ( ) ( 1 ) 1 0 y n M a y n a bu n M i M i M i T (Tm Ta )/ M Time (n) State 0 1 2 3 4 5 6 7 8 9 10 Y(-4) Y(-3) Y(-2) Y(-1) Y(0) Y(1) Y(2) Y(3) Y(4) Y(5) Y(6)
/96 M-1 y(n+M=a“y(n)+∑abn+M-1-) i=0 the loop delay is Z-M instead of Z-1,which means that the loop computation must be completed in Mclock cycles (not 1 clock cycle). The iteration bound of this computation is (TM+TA)/M, which corresponds to a sample rate /times higher than that of the original filter. The terms aib,aM can be pre-computed. The second term in the right hand side is the look-ahead computation term (referred to as the /ook-ahead comp/exity);it is non-recursive and can be easily pipelined. 2021年2月 9
2021年2月 9 the loop delay is Z-M instead of Z-1 , which means that the loop computation must be completed in M clock cycles (not 1 clock cycle). The iteration bound of this computation is (TM+TA )/M, which corresponds to a sample rate M times higher than that of the original filter. The terms aib, aM can be pre-computed. The second term in the right hand side is the look-ahead computation term (referred to as the look-ahead complexity); it is non-recursive and can be easily pipelined. ( ) ( ) ( 1 ) 1 0 y n M a y n a bu n M i M i M i
/96 Look-ahead computation has allowed a single serial computation to be transformed into M independent concurrent computations,and to pipeline the feedback loop to achieve high speed filtering of a single time series while maintaining full hardware utilization. Assume the multiplier and the adder can be conveniently pipelined,the iteration bound can be achieved by retiming or cutset transformation 2021年2月 10
2021年2月 10 Look-ahead computation has allowed a single serial computation to be transformed into M independent concurrent computations, and to pipeline the feedback loop to achieve high speed filtering of a single time series while maintaining full hardware utilization. Assume the multiplier and the adder can be conveniently pipelined, the iteration bound can be achieved by retiming or cutset transformation