Causal LTI DSP System by LCCDE A general Nth-order Linear Constant-Coefficient Difference/ Differential Equation: M ∑a,[n-k]=∑b,xn-k] k=0 k=0 Recursive equation for LCCDE: avyIn-N]+av-1yIn-(N-1)]+..+ayIn-1]+aoy[n] =bwx[n-M]+bM-[n-(M-1)]+…+bx[n-1]+bx[n] Solution for LCCDE: xIn-k] Nonrecursive equation (N=0) k=0a0 系统函数h(n) M nl=∑b[n-k]-∑a[n-k] Recursive equation (N>=1) k=0 k= 2021/1/13 ASIC Design,by Yan Bo 12ASIC Design, by Yan Bo Causal LTI DSP System by LCCDE 2021/1/13 12   = = − = − M k k N k k a y n k b x n k 0 0 [ ] [ ] A general Nth-order Linear Constant-Coefficient Difference/ Differential Equation: [ ] [ ( 1) ] [ 1] [ ] [ ] [ ( 1) ] [ 1] [ ] 1 1 0 1 1 0 b x n M b x n M b x n b x n a y n N a y n N a y n a y n M M N N = − + − − + + − + − + − − + + − + − −   Recursive equation for LCCDE: Solution for LCCDE: = = − M k k x n k a b y n 0 0 [ ] [ ] Nonrecursive equation (N＝0)   = = = − − − N k k M k k y n b x n k a y n k 0 1 [ ] [ ] [ ] Recursive equation (N>=1) 系统函数h(n)