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Chapter 2
Discrete-Time Signals and Systems
⚫ Representation of Discrete-Time Signals
⚫ Operations on Discrete-Time Signals and
block diagram
⚫ Typical DT signals
unit impulse and unit step sequences
⚫ Sampling: relation between the Discrete-
Time Signals and the continuous-time signals
Sect.2.1 Time- representation
➢ Representation of Discrete-time Signals
Ex. A-1
{x [n]} =x [n] ={, -0.2, 2.1, 1.1, 0.28, } (2.1)
›
i.e., … ,x [-1]= -0.2, x [0] = 2.1, x [1]=1.1, …
y [n] ={1+2j , 0, -1-0.5j , 2.1+0.2j , 1.1-3j , 0.28}
›
y [n] = {1, 0, -1,2.1, 1.1, 0.28} +{2j , 0, -0.5j , 0.2j , -3j , 0}
›
›
Eg. 1 n
x [n] =( ) u[n]
1
2
p
j n
x [n] =cos p n, -2 £n £3 x [n] =(-2) -n e 2
2
3
4
Sect. 2.1 Time- representation
Sect 2.1.1 Length of Discrete-time Signals
➢ Fini ength & infini ength sequence
➢ Length of fini ength sequences
Sect 2.1.2 Strength of a discrete-time signal (Energy)
¥
N
e= lim x [n] 2 = x [n] 2
x
N fi¥
n =-N n=-¥
Sect 2.3.3 Classification of sequence
➢ S
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