Digital Signal Processing Reference
In-Depth Information
channel. The reconstructed channels are played simultaneously to simulate the
effect of real audio.
Example 9.4
Consider a digital monochrome CCD camera that records an image
x
[
m
,
n
]
at a resolution of 800
1200 picture elements (pixels). In other words, each
image consists of 800
1200
=
0
.
96
10
6
pixels. Assuming that the human
visual system cannot distinguish between more than 200 different shades of
gray, determine how many bytes are required to store a single image. If the
CCD camera has 32 million bytes of memory space to store images, how many
images can be saved simultaneously in the camera?
Solution
An image pixel can have 200 different shades of gray. The number of bits
required to represent the intensity value of each pixel is given by
⌈
log
2
(200)
⌉
or
⌈
7
.
64
⌉
or 8 bits;
space required to save one image
=
0
.
96
10
6
pixels
8 bits/pixel
=
7
.
68
10
6
bits or 0
.
96
10
6
bytes.
Since the disc space for storing images is 32
10
6
bytes,
number of images that can be stored simultaneously
=
32
10
6
bytes
/
0
.
96
10
6
bytes
=
33.
9.5 Summary
In this chapter, we introduced the principle of sampling that is used to transform
a CT baseband signal into an equivalent DT sequence. Section 9.1 discussed
the ideal impulse-train sampling, where a periodic impulse train is multiplied
by a CT baseband signal, resulting in a sequence of equally spaced samples at
the location of the impulses (
t
=
kT
s
). In the frequency domain, the spectrum
of the sampled signal consists of several shifted replicas of the spectrum of the
original signal. We observe that the original CT signal is recoverable from its
DT version by ideal lowpass filtering if the sampling rate
f
s
=
1
/
T
s
is greater
than twice the highest frequency present in the baseband signal. This condition
is referred to as the sampling theorem. Violating the sampling theorem distorts
the spectrum of the original baseband signal; a phenomenon known as aliasing.
In practice, impulses are difficult to generate and are often approximated by
narrow rectangular pulses. This leads to a more practical approach to sampling,
covered in Section 9.2, in which a periodic rectangular pulse train is multiplied
by the CT baseband signal to produce the sampled signal. Compared with the
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