Digital Signal Processing Reference
In-Depth Information
6
Digital Filte
r Design II: Applications
6.1
Introduction to Digital Filtering Applications
In the previous chapter, we covered the basic techniques of digital filtering,
which included analytical and CAD methods for FIR/IIR digital filters. This
chapter will focus on practical applications of digital filtering, involving the
use of software tools that were discussed in the previous chapter. Typical
applications of filters, which were explained briefly in the previous chapter,
include frequency selection, signal demodulation, filtering of noisy audio
and video signals, and time/frequency analysis of widely used signals such
as the EKG (heart) and EEG (brain)
.
In order to effectively carry out the
video filtering exercise in this chapter, a brief overview of digital video
processing will be presented.
1
6.1.1
Brief Introduction to Digital Video Processing
A one-dimensional signal
x
(
t
) is a function of one independent variable,
t
,
or time, as in a speech signal. A two-dimensional signal
f
(
x,y
) is a function of
two independent variables,
x
and
y
, which are usually the coordinates of space
and are called
spatial variables
. Examples of two-dimensional spatial signals
are images (photographic, infrared, or ultrasound), as shown in
Figure 6.1
.
The function
f
).
For example, in the black-and-white image of Figure 6.1, the range of the
function
f
(
x,y
) represents the intensity of the image at the point (
x,y
(
x,y
) would vary from 0 (black) to 1 (white) in a normalized inten-
sity scale.
Two-dimensional discrete signals
two-dimensional
continuous signals. A general point in the sampling grid is (
n
Two-dimensional discrete signals are obtained by
sampling
∆
x, n
∆
y
), and
1
2
the sampled signal is
f
(
n
∆
x, n
∆
y
)
,
or simply
f
(
n
1
, n
) in the range
0
≤
n
≤
1
2
2
1
N
1
-
1
; 0
≤
n
N
2
-
1. The sampled signal can be represented by the matrix
2
≤
function:
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