Introduction to Digital Signal and System Analysis - Tutorsindia

Introduction to Digital Signal and System Analysis
Basic Types of Digital Signals
∞
k=
0
u [ n]
= δ [ n]
+ δ[
n −1]
+ δ[
n −2]
+ ... = δ[
n −k]
= δ[
m]
n
m=−∞
(2.8)
And, the unit impulse can be represented by the unit steps as
u[
n]
−u[
n −1]
=
n
m=
−∞
n−1
n−1
n−1
δ [ m]
− δ[
m]
= δ[
n]
+ δ[
m]
− δ[
m]
= δ[
n]
m=−∞
m=−∞
m=−∞
i.e. the impulse response is the difference of two unit steps.
d[ n]
= u[
n]
− u[
n −1]
. (2.9)
Problems
Q2.1 Sketch and label the following digital signals
a) − u[ n +1]
b) u[ −n +1]
c) u[ n + 2] + 2d
[ n − 3]
d) 3u[
n + 4] − 3u[
n − 5]
e) r[ n + 1] − 2r[
n − 2]
Q2.2 Sketch and label the digital signal
a)
1 p n
x[
n]
= u[
n]sin
n 2
b) x[ n]
= u[
n + 2] − u[
n − 3] + r[
n − 3] − r[
n − 6] + 2d
[ n]
where d [ n],
u[
n]
and r[
n]
are the unit impulse, unit step and ramp functions, respectively.
Q2.3 Let d [ n],
u[
n]
and r[
n]
be the unit impulse, unit step and ramp functions, respectively. Given
x [ n]
= u[
n]
− u[
n − 6]
1
x [ n]
= r[
n]
+ d[
n]
+ d[
n − 2] −d[
n − 4] − r[
n − 5]
2
Sketch and label the digital signals n]
x [ ]
x + and x n]
⋅ x [ ] .
1[ 2
n
1[ 2
n
23
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