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12 SIGNALS AND SYSTEMS [CHAP. 1
1.4 BASIC DISCRETE-TIME SIGNALS
A. The Unit Step Sequence:
The unit step sequence u[n] is defined as
which is shown in Fig. 1-10(a). Note that the value of u[n] at n = 0 is defined [unlike the
continuous-time step function u(f) at t = 01 and equals unity. Similarly, the shifted unit step
sequence ii[n - k] is defined as
which is shown in Fig. 1-lO(b).
(a) (b)
Fig. 1-10 (a) Unit step sequence; (b) shifted unit step sequence.
B. The Unit Impulse Sequence:
The unit impulse (or unit sample) sequence 6[n] is defined as
which is shown in Fig. 1-ll(a). Similarly, the shifted unit impulse (or sample) sequence
6[n - k] is defined as
which is shown in Fig. 1-1 l(b).
(a) (b)
Fig. 1-11 (a) Unit impulse (sample) sequence; (6) shifted unit impulse sequence.
