Steps of Reflection and Shift Method (1)Graph both x[k]and h[n-k]as a function of k. (2)Begin with n large and negative. (3)Write the mathematical representation for the product signal wn[k]. (4)Increase the shift n until wn[k]changes.The value of n at which the change occurs defines the end of the current interval and the beginning of a new interval
Steps of Reflection and Shift Method (1) Graph both x[k] and h[n-k] as a function of k. (2) Begin with n large and negative. (3) Write the mathematical representation for the product signal wn[k]. (4) Increase the shift n until wn[k] changes. The value of n at which the change occurs defines the end of the current interval and the beginning of a new interval
Steps of Reflection and Shift Method (5)Let n be in the new interval.Repeat steps 3 and 4 until all intervals of n and the corresponding wn[k]are identified. (6)For each interval of n,sum all the values of the corresponding wn[k]to obtain y[n]on that interval
Steps of Reflection and Shift Method (5) Let n be in the new interval. Repeat steps 3 and 4 until all intervals of n and the corresponding wn[k] are identified. (6) For each interval of n, sum all the values of the corresponding wn[k] to obtain y[n] on that interval
Reflection and Shift y[n]=[n*n]=∑w,[k] k=一00 w2[k] w[k] x[] 9-9-9 k 012 0 0 hn-k] k w:[k] n-2n-1 n w,[k] w,[k] k 无 0 2
Reflection and Shift
Method 4:Direct Form yIn]x[n]*hn]=>x[k]hin-k] k=-00 h1≤k≤n2 n1≤k≤n2 n3≤n-k≤n4 n-n4≤k≤n-n3 n+n3≤n≤n2+n4 max{n,n-n4}≤k≤min{n2,n-n3}
Method 4: Direct Form max{ , } min{ , } [ ] [ ] [ ] [ ] [ ] 1 4 2 3 1 3 2 4 4 3 1 2 3 4 1 2 n n n k n n n n n n n n n n k n n n k n n n k n n k n y n x n h n x k h n k k