Introduction to Digital Signal and System Analysis - Tutorsindia

Introduction to Digital Signal and System Analysis
Basic Types of Digital Signals
In Figure 2.4, a shifted unit impulse [ n −1]
by number a is ax [n]
.
d is been scaled by -2 to -2 d [ n −1]
. For general cases, a signal x[n]
scaled
0
1
n
-2
Figure 2.4 A shifted unit impulse is being scaled by -2.
2.4 Periodic signals
A periodic signal satisfies the following relationship
x [ n ± kN]
= x[
n]
(2.7)
where k is an arbitrary integer and N the period. The above relationship indicates that a periodic signal can remain the
same shape if it shifts to left or right by any integer number of periods. Typical periodic signals are sine and cosine waves.
⎛ np ⎞
e.g. For the signal x [ n]
= sin⎜
⎟ , we can find the period by following steps:
⎝ 1 ⎠
We know that the sine function has a period of
2 p . Therefore,
⎛ np
⎞ ⎛ np
⎞ ⎛ ( n ± 2
sin⎜
⎟ = sin⎜
± 2p
⎟ = sin⎜
⎝ 1 ⎠ ⎝ 1 ⎠ ⎝ 1
) p ⎞
⎟
⎠
This means that on the n-axis, a new signal after being shifted to left or right by 22 samples is still identical to the original
signal. Therefore, N=22 (samples) is the period.
2.5 Examples of signal operations
For 6 signals in Figure 2.5, the expressions using basic signals, including the unit impulse, unit step and ramp, can be
found as
a) x[n]=-2 u[n] b) x[n]=-5 u[-n-4]
c) x[n]= u[n+3] - u[n-5] d) x[n]= 5 d[n-6]
e) x[n]= d[n-6]-u[-n] f) x[n]= 2 r[n+6] - 2 r[n+2]
21
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