Basic sequences p(n 2 2八3437 02 A sum of scaled,delayed impulses pln]asoln 3+aoln -1]+aoln -2]+aoln -7 ◆arbitrary x[m=∑[k6[n-k] sequence =-00 17 10/18/2022 Zhongguo Liu_Biomedical Engineering_Shandong Univ
17 10/18/2022 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Basic sequences [ ] [ ] [ ] k x n x k n k =− = − ◆arbitrary sequence 3 1 2 7 p n = a −3 n + + a1 n − + a2 n − + a7 n − A sum of scaled, delayed impulses
Basic sequences n≥0 ◆Unit step sequence o n<o Unit step Mm=∑ò[] 之1-we50 since k≠0 k=-00 1k=0 wm=δn+6[n-l刂+δ[n-2]+…=∑δ[n-k] k=0 δ[n]=u[n]-4[n-l] First backward difference 18 10/18/2022 Zhongguo Liu_Biomedical Engineering_Shandong Univ
18 10/18/2022 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Basic sequences ◆Unit step sequence = 0 0 1 0 [ ] n n u n [ ] n k u n k =− = 0 [ ] [ ] [ 1] [ 2] [ ] k u n n n n n k = = + − + − + = − [n] = u[n]−u[n −1] First backward difference 0, 0 , 1, 0 0 0 1 0 since n k when n k when n k k k =− = = =
Basic Sequences Exponential sequences xn=Aa A and a are real:x[n]is real A is positive and 0<a<1,x[n]is positive and decrease with increasing n -1<a<0,x[n]alternate in sign,but decrease in magnitude with increasing n a>1:x[n]grows in magnitude as n increases Real exponential 19 0 n Jniv
19 10/18/2022 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Basic Sequences ◆Exponential sequences n x[n] = A ◆A and α are real: x[n] is real ◆A is positive and 0<α<1, x[n] is positive and decrease with increasing n ◆-1<α<0, x[n] alternate in sign, but decrease in magnitude with increasing n ◆ 1 : x[n] grows in magnitude as n increases
EX.2.1(第二版)Combining Basic sequences If we want an exponential sequences that is zero for n <0,then Aa n≥0 Cumbersome n<0 x[n]=Ao”u[n] simpler 20 10/18/2022 Zhongguo Liu_Biomedical Engineering_Shandong Univ
20 10/18/2022 Zhongguo Liu_Biomedical Engineering_Shandong Univ. EX. 2.1(第二版) Combining Basic sequences = 0 0 0 [ ] n A n x n n ◆If we want an exponential sequences that is zero for n <0, then x[n] A u[n] n = Cumbersome simpler
Basic sequences ◆Sinusoidal sequence xIn]=Acos(win+d)for all n Sinusoidal n 21 10/18/2022 Zhongguo Liu_Biomedical Engineering_Shandong Univ
21 10/18/2022 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Basic sequences ◆Sinusoidal sequence x[n] = Acos(w0 n +) for all n