Digital Signal Processing Reference
In-Depth Information
Introduction
The subject of this topic could be summarized by a simple scheme as that
depicted in
Figure 1.1
.
We have an original set of data of our interest that we want, for instance,
to transmit, store, extract any kind of useful information from; such data
are represented by a quantity
s
. However, we do not have direct access to
s
but have access only to a modified version of it, which we represent by
the quantity
x
. So, we can state that there is a data mapping
H(
·
)
so that the
observed data
x
are obtained by
x
=
H(
s
)
(1.1)
to
be applied in the available data so that we could, based on a certain perfor-
mance criterion, recover suitable information about the original set of data.
We represent this step by another mapping that provides, from
x
, what we
could name an estimate of
s
, represented by
Then our problem consists in finding a kind of inverse mapping
W
ˆ
=
W(
)
s
x
(1.2)
The above description is generalized on purpose so that a number of dif-
ferent concrete problems could fit it, with also a great variety of approaches
to tackle with them. According to the area of knowledge, the aforementioned
problem can be considerably relevant in signal processing, telecommunica-
tions, identification and control, pattern recognition, Bayesian analysis, and
other fields. The scope of this topic is clearly
signal processing oriented
,witha
focus on two major problems:
channel equalization
and
source separation
.Even
thus, such character of the work does not restrict the wide field of application
of the theory and tools it presents.
1.1 Channel Equalization
In general terms, an equalization filter or, simply, equalizer, is a device
that compensates the distortion due to an inadequate response of a given
system. In communication systems, it is well known that any physical
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