Introduction to Digital Signal and System Analysis - Tutorsindia

Introduction to Digital Signal and System Analysis
Digital Signals and Sampling
..., x[
−1],
x[0],
x[1],
x[2],
...
where -1, 0, 1, 2 etc are the sample numbers, x[0], x[1], x[2], etc are samples. The square brackets represent the digital
form. The signal can be represented as a compact form
x [ n]
− ∞ <
n < ∞
(1.1)
In the signal, x[-1], x[1], x[100], etc, are the samples, n is the sample number. The values of a digital signal are only being
defined at the sample number variable n , which indicates the occurrence order of samples and may be given a specific
unit of time, such as second, hour, year or even century, in specific applications.
We can have many digital signal examples:
--
Midday temperature at Brighton city, measured on successive days,
--
Daily share price,
--
Monthly cost in telephone bills,
--
Student number enrolled on a course,
--
Numbers of vehicles passing a bridge, etc.
Examples of digital signal processing can be given in the following:
Example 1.1 To obtain a past 7 day’s average temperature sequence. The averaged temperature sequence for past 7 days is
1
y [ n]
= ( x[
n]
+ x[
n −1]
+ x[
n − 2]... + x[
n − 6] )
7
.
For example, if n=0 represents today, the past 7 days average is
1
y[ 0] = x −
7
( x[0]
+ x[
−1]
+ x[
−2]...
+ [ 6] )
where x [ 0], x[
−1],
x[
−2],
... represent the temperatures of today, yesterday, the day before yesterday, …; y [0]
represents the average of past 7 days temperature from today and including today. On the other hand,
1
y[ 1] = x −
7
( x[1]
+ x[0]
+ x[
−1]
+ ... + [ 5] )
represents the average of past 7 days temperature observed from tomorrow and including tomorrow, and so on. In a
shorter form, the new sequence of averaged temperature can be written as
9
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