Basic sequences 4-20134568 2 A sum of scaled delayed impulses ]=as{+3]+an-1]+a-2]+ap ◆ arbitrary 对m=∑xk]6[m-k sequence k 2/6/2021 Zhongguo Liu_Biomedical Engineering_shandong Univ
17 2/6/2021 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 1n≥0 ◆ Unit step sequence uln 0n<0 Unit step Skl= o, whennso hen n≥0 l-∑k since d 0k≠0 k=0 lm]=6n]+8[n-1]+n-2]+…=∑δn-k k=0 [n]=un]-uln-1 first backward difference 18 2/6/2021 Zhongguo Liu_Biomedical Engineering_shandong Univ
18 2/6/2021 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[] is real A is positive and o<a<l, xn is positive and decrease with increasing n -1<a<0, x[n] alternate in sign, but decrease n magnitude with increasing n oa>1: x[n] grows in magnitude as n increases Real exponential 19 0 n Niv
19 2/6/2021 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
EX21(第二版) Combining Basic sequences If we want an exponential sequences that is zero for n <0 then Aann≥0 x Cumbersome 0n<0 xn=Aaun simpler 20 2/6/2021 Zhongguo Liu_Biomedical Engineering_shandong Univ
20 2/6/2021 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 x[n]=Acos(won+) or all n Sinusoidal 21 2/6/2021 Zhongguo Liu_Biomedical Engineering_shandong Univ
21 2/6/2021 Zhongguo Liu_Biomedical Engineering_Shandong Univ. Basic sequences ◆Sinusoidal sequence x[n] = Acos(w0 n +) for all n