1.2 Discrete-time signals ● Typical sequences We now consider several basic sequences that play important roles in the analysis and design of discrete-time systems. An arbitrary sequence can be expressed in terms of some of these basic sequences The most common basic sequences are the unit sample sequence, the unit step sequence, rectangle sequence, etc
1.2 Discrete-time signals ◆We now consider several basic sequences that play important roles in the analysis and design of discrete-time systems. An arbitrary sequence can be expressed in terms of some of these basic sequences. ◆The most common basic sequences are the unit sample sequence, the unit step sequence, rectangle sequence,etc. ⚫ Typical sequences
1.2 Discrete-time signals Unit sample sequence The simplest and one of the most useful sequences is the unit sample sequence, often called the discrete time impulse or the unit impulse. It is denoted by o[n] and defined by 1n=0 0n≠0 6(2)=10n≠k
1.2 Discrete-time signals ◆ Unit sample sequence ( ) 1 0 0 0 n n n = = ( ) 1 0 n k n k n k = − = The simplest and one of the most useful sequences is the unit sample sequence, often called the discretetime impulse or the unit impulse. It is denoted by δ[n] and defined by
1.2 Discrete-time signals Unit sample sequence Figure 2.13: (a) The unit sample sequence s(n)), and(b)the shifted unit sample sequence (8n-21
1.2 Discrete-time signals ◆ Unit sample sequence
1.2 Discrete-time signals ◆ Unit step sequence 1n≥0 k un 0n<0 u(n-k) o n<k Figure 2.14: (a)The unit step sequence fu[n]l, and the shifted unit step sequence (uin+2)
◆ Unit step sequence 1.2 Discrete-time signals ( ) 1 0 0 0 n u n n = ( ) 1 0 n k u n k n k − =
1.2 Discrete-time signals The unit sample and the unit step sequence are related as follows l小=∑[n-m=∑[k] {n}=]-un
1.2 Discrete-time signals ◼ The unit sample and the unit step sequence are related as follows 0 n m k u n n m k = =− = − = n u n u n = − − 1