Introduction to systems - Continuous and Discrete Time Signals and Systems - page 72

the values of the b k 's. Such a DT system that accumulates the values of the
input is referred to as an accumulator. It may be noted that the receiver of a
DM system is a linear system as it can be modeled by a constant-coefficient
difference equation.

2.1.8 Digital filter

Digital images are made up of tiny “dots” obtained by sampling a two-
dimensional (2D) analog image. Each dot is referred to as a picture element, or
a pixel. A digital image, therefore, can be modeled with a 2D array, x [ m , n ],
where the index ( m , n ) refers to the spatial coordinate of a pixel with m being
the number of the row and n being the number of the column. In a monochrome
image, the value x [ m , n ] of a pixel indicates its intensity value. When the pixels
are placed close to each other and illuminated according to their intensity values
on the computer monitor, a continuous image is perceived by the human eye.
In digital image processing, spatial averaging is frequently used for smooth-
ing noise, lowpass filtering, and subsampling of images. In spatial averaging,
the intensity of each pixel is replaced by a weighted average of the intensities
of the pixels in the neighborhood of the reference pixel. Using a unidirectional
fourth-order neighborhood, the reference pixel x [ m , n ] is replaced by the spa-
tially averaged value:
y [ m , n ] = 1

4 ( x [ m , n ] + x [ m , n − 1] + x [ m − 1 , n ] + x [ m − 1 , n − 1]) ,
(2.27)
where y [ m , n ] represents the 2D output image of the spatial averaging system.
Equation (2.27) is an example of a 2D finite-difference equation and it models
a 2D DT system with input x [ m , n ] and output y [ m , n ].
In this section, we have considered some interesting applications of signal
processing in CT and DT systems. Our goal has been to motivate the reader
to learn about the techniques and basic concepts required to investigate one
or more of these application areas. Each of the discussed areas is a subject
of considerable study. Nevertheless, certain fundamentals are central to most
applications, and many of these basic concepts will be discussed in the chapters
that follow.

2.2 Classification o f systems

In the analysis or design of a system, it is desirable to classify the system
according to some generic properties that the system satisfies. In this segment
we introduce a set of basic properties that may be used to categorize a system.
For a system to possess a given property, the property must hold true for all
possible input signals that can be applied to the system. If a property holds for
some input signals but not for others, the system does not satisfy that property.