Digital Signal Processing Reference
In-Depth Information
1
Processing of Signals
Any sequence or set of numbers, either continuous or discrete, defines a signal in
the broad sense. Signals originate from various sources. They occur in data
processing or share markets, human heartbeats or telemetry signals, a space shuttle
or the golden voice of the Indian playback singer Lata Mangeshkar, the noise of a
turbine blade or submarine, a ship or instrumented signal inside a missile.
Processing of signals, whether analogue or digital, is a prerequisite to under-
standing and analysing them. Conventionally, any signal is associated with time.
Typically, a one-dimensional signal has the form x
ð
t
Þ
and a two-dimensional signal
has the form f
ð
x
t
Þ
. Understanding the origin of signals or their source is of
paramount importance. In strict mathematical form, a signal is a mapping function
from the real line to the real line, or in the case of discrete signals, it is a mapping
from the integer line to the real line;
1
and finally it is a mapping from the integer
line to the integer line.
Typically the measured signal
;
y
;
y
ð
t
Þ
is different from the emanated signal y
ð
t
Þ
.
This is due to corruption and can be represented as follows:
^
y
ð
t
Þ¼
y
ð
t
Þþð
t
Þ
in continuous form
;
ð
1
:
1
Þ
y
k
¼
y
k
þ
k
in discrete form
;
ð
1
:
2
Þ
where
is the unwanted signal, commonly referred to as noise and most of the time
statistical in nature. This is one of the reasons why processing is performed to
obtain
^
y
k
from y
k
.
1.1 Organisation of the Topic
Chapter 1 describes how analogue signals are converted into numbers and the
associated problems. It gives essential principles of converting the analogue signal
1
Time series.
