This document discusses digitization and sampling of multimedia signals. It explains that digitization involves sampling a continuous analogue signal at discrete intervals and quantizing the signal values to a fixed set of levels. This reduces the continuous signal to a sequence of discrete samples. Some information is lost during this process. The document discusses how to reconstruct the original analogue signal from the digital samples and the problems that can occur from undersampling, such as distortions and artefacts. It notes that the sampling rate needs to be high enough to avoid losing important signal details between samples.

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19. Digitization
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20. Digitization
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21. 22 F U N DA M E N TA L S not usually distinguishing between time-varying and space-varying bit
of sig
analog
When we have a continuously varying sign measu
Figure 2.2. An analogue signal
In multimedia, we encounter values of several kinds that change continuously, either the value we measure,
in Figure 2.2, both because we re
Digitiz ation
they originate in physical phenomena or because they exist in some can measure it, can vary infinitesimally.
we analogue representation.
For example, the amplitude (volume) of a sound wave varies continuously over time, as does thewe would first s
convert it to a digital signal,
can b
have
amplitude of an electrical signal produced by a microphone in response to a sound wave. The contin
a set of discrete values that could be represen
quant
colour of the image formed inside a camera by its lens varies continuously across the digitization – the process o
image plane.
of bits. That is, one li
As you see, we may be measuring different quantities, and they mayanalogue to either over timeconsists of two
be varying digital form –
or over space (or perhaps, as in the case of moving pictures, both). For this general discussion, we discrete interva
measure the signal’s value at These
will follow tradition, and refer to the
Figure value we are measuring, whatever it may be, as a “signal”,
2.2. An analogue signal
:6JGA/:16 Analogue to Digital Converter (ADC)
we restrict the value to a fixed set of levels.
called
not usually distinguishing between time-varying and space-varying signals. carried out in either order; Figure
can be we w
first sampled and then quantized. In where the s
When we have a continuously varying signal, such as the one shown a sequence of e
continuous signal reduced to sampl
in Figure 2.2, both the value we measure, and the intervalssome of these values areS
quantization step, at which rate.
we can measure it, can vary infinitesimally. Inlies on one of the lines defining the qua
one contrast, if we were to
is
allo
convert it to a digital signal, we would have to restrict both of these to
One
a set of discrete values that could be represented in some fixed normally carried out b
These processes are number
analog
of bits. That is, digitization – the processcalled analogue atosignal from
of converting digital converters (ADCs
those
analogue to digital form – consists of two steps:not examine. We will only consider a
we will sampling, when we over
measure the signal’s value at discrete intervals, and quantization, whensuccessive inevit
where the interval between samp
Figure 2.2. An analogue signal Figure 2.3. Sampling and
we restrict the value to a fixed set of levels. Samplingaand quantization time or space
quantization
samples in fixed amount of ence
can be carried out in either order; Figure 2.3 shows we will generally assume that
rate. Similarly, a signal being
$+LL1M first sampled and then quantized. In theissampling step, you see the levels – are
sampling quantization
quantizedapisake@gmail.com.................
Ex Libris – the quantization
analogue continuous signal reduced to a sequence of equally spaced values; in the
quantization step, some of these values are chopped off so that every that digital
One of the great advantages
one lies on one of the lines defining the allowed levels. stems from the fact that on
analogue ones
those at the quantization levels – are valid

22. 22 F U N DA M E N TA L S not usually distinguishing between time-varying and space-varying bit
of sig
analog
When we have a continuously varying sign measu
Figure 2.2. An analogue signal
In multimedia, we encounter values of several kinds that change continuously, either the value we measure,
in Figure 2.2, both because
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Digitiz ation
they originate in physical phenomena or because they exist in some can measure it, can vary infinitesimally.
we analogue representation.
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For example, the amplitude (volume) of a sound wave varies continuously over time, as does thewe would first s
convert it to a digital signal,
can b
have
noise
amplitude of an electrical signal produced by a microphone in response to a sound wave. The contin
a set of discrete values that could be represen
quant
colour of the image formed inside a camera by its lens varies continuously across the digitization – the process o
image plane.
of bits. That is, one li
As you see, we may be measuring different quantities, and they mayanalogue to either over timeconsists of two
be varying digital form –
or over space (or perhaps, as in the case of moving pictures, both). For this general discussion, we discrete interva
measure the signal’s value at These
will follow tradition, and refer to the
Figure value we are measuring, whatever it may be, as a “signal”,
2.2. An analogue signal
:6JGA/:16 Analogue to Digital Converter (ADC)
we restrict the value to a fixed set of levels.
called
not usually distinguishing between time-varying and space-varying signals. carried out in either order; Figure
can be we w
first sampled and then quantized. In where the s
When we have a continuously varying signal, such as the one shown a sequence of e
continuous signal reduced to sampl
in Figure 2.2, both the value we measure, and the intervalssome of these values areS
quantization step, at which rate.
we can measure it, can vary infinitesimally. Inlies on one of the lines defining the qua
one contrast, if we were to
is
allo
convert it to a digital signal, we would have to restrict both of these to
One
a set of discrete values that could be represented in some fixed normally carried out b
These processes are number
analog
of bits. That is, digitization – the processcalled analogue atosignal from
of converting digital converters (ADCs
those
analogue to digital form – consists of two steps:not examine. We will only consider a
we will sampling, when we over
measure the signal’s value at discrete intervals, and quantization, whensuccessive inevit
where the interval between samp
Figure 2.2. An analogue signal Figure 2.3. Sampling and
we restrict the value to a fixed set of levels. Samplingaand quantization time or space
quantization
samples in fixed amount of ence
can be carried out in either order; Figure 2.3 shows we will generally assume that
rate. Similarly, a signal being
$+LL1M first sampled and then quantized. In theissampling step, you see the levels – are
sampling quantization
quantizedapisake@gmail.com.................
Ex Libris – the quantization
analogue continuous signal reduced to a sequence of equally spaced values; in the
quantization step, some of these values are chopped off so that every that digital
One of the great advantages
one lies on one of the lines defining the allowed levels. stems from the fact that on
analogue ones
those at the quantization levels – are valid

23. measure the signal’s value at discrete intervals, and quantization, when
Figure 2.2. An analogue signal
we restrict the value to a fixed set of levels. Sampling and quantization
However, looking at Figure 2.3, you can see that some information must have been lost during
can be carried out in either order; Figure 2.3 shows a signal being
the digitization process. How can we claim that the digitized result is in any sense an accurate
first sampled and then quantized. In the sampling step, you see the
Digitization
representation of the original analogue signal? The only meaningful measure of accuracy must be
continuous signal reduced to a sequence of equally spaced values; in the
how closely the original can be reconstructed. In order to reconstruct an analogue signal from a
quantization step, some of these values are chopped off so that every
set of samples, what we need to do, informally speaking, is decide what to put in the gaps between
one lies on one of the lines defining the allowed levels.
the samples. We can describe the reconstruction process precisely in mathematical terms, and that
description provides an exact specification of the theoretically best are normally carried out by special hardware devices,
These processes way to generate the required
signal. In practice, we use methods that are simplercalled the theoretical optimum but (ADCs), whose internal workings
than analogue to digital converters which can
easily be implemented in fast hardware.
information lost
we will not examine. We will only consider the (almost invariable) case
where the interval between successive samples is fixed; the number of
One possibility is to “sample and hold”: that is, the value of a sample
samples in a fixed amount of time or space is known as the sampling
is used for the entire extent between it and the following sample. As generally assume that the levels to which a signal
rate. Similarly, we will
Figure 2.4 shows, this produces a signal with abrupt transitions,–which
is quantized the quantization levels – are equally spaced.
is not really a very good approximation to the original (shown dotted).
However, when such a signal is passed to an output device – suchadvantages that digital representations have over
One of the great
as a monitor or a loudspeaker – for display or playback, the lags stems from the fact that only certain signal values –
analogue ones and
imperfections inherent in the physical device will those at thediscon-
cause these quantization levels – are valid. If a signal is transmitted
tinuities to be smoothed out, and the result actually approximates the on some physical medium such as magnetic tape,
over a wire or stored
theoretical optimum quite Sampling and
Figure 2.3. well. (However, in the future, improvements
inevitably some randomFigure is introduced, either because of interfer-
noise 2.4. Sample and hold
in the technology for the playback of sound and picture will stray magnetic fields, or simply because of the unavoidable
quantization ence from demand reconstruction
matching improvements in the signal.) sample &
Ex Libris quantization
hold © MacAvon Media
apisake@gmail.com......................................................
Clearly, though, if the original samples were too far apart, any reconstruction is going to be
reconstruction
inadequate, because there may be details in the analogue signal that, as it were, slipped between
samples. Figure 2.5 shows an example: the values of the consecutive samples taken at si and si+1
are identical, and there cannot possibly be any way of inferring the presence of the spike in
between those two points from them – the signal could as easily have dipped down or stayed at

24. Digitization
24 F U N DA M E N TA L S
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Figure 2.5. Undersampling
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Nyquist rate
of sound and image processing.
You are probably familiar with the idea that a musical note played on
an instrument consists of waveforms of several different frequencies

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28. analogue to digital form – consists of two steps: sampling, when we
measure the signal’s value at discrete intervals, and quantization, when
Figure 2.2. An analogue signal
we restrict the value to a fixed set of levels. Sampling and quantization
can be carried out in either order; Figure 2.3 shows a signal being
Digitiz ation first sampled and then quantized. In the sampling step, you see the
continuous signal reduced to a sequence of equally spaced values; in the
quantization step, some of these values are chopped off so that every
one lies on one of the lines defining the allowed levels.
These processes are normally carried out by special hardware devices,
called analogue to digital converters (ADCs), whose internal workings
we will not examine. We will only consider the (almost invariable) case
where the interval between successive samples is fixed; the number of
samples in a fixed amount of time or space is known as the sampling
rate. Similarly, we will generally assume that the levels to which a signal
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over a wire or stored on some physical medium such as magnetic tape,
Figure 2.3. Sampling and inevitably some random noise is introduced, either because of interfer-
quantization ence from stray magnetic fields, or simply because of the unavoidable
Ex Libris quantization
apisake@gmail.com...................................................... © MacAvon Media

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34. CHAPTER
2 D I G I TA L DATA
Figure 2.12. Posterization
between areas of those colours would be elided. The effect on black and white images can be
seen clearly in Figure 2.11, which shows a gradient swatch using 256, 128, 64, 32, 16, 8, 4, and
2 different grey levels. The original gradient varies linearly from pure white to pure black, and
as we reduce the number of different greys, you can see how values band together as they are

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36. 2
Compression
CHAPTER DIGITAL DATA 31
You will learn, as we examine the individual media types in detail, that a characteristic property
Compression of media data is that it occupies a lot of storage. This means, in turn, that it needs a lot of band-
width when it is transferred over networks. Storage and bandwidth are limited resources, so the
with directly, so storage schemes which make less than optimal use of
the available bits are usedhigh demands of instead. data can pose a problem. The common response to this problem is to
most of the time media
original data
apply some form of compression, which means any operation that can be performed on data to
Lossless and lossy compression arethe amount separate techniques. Mostrepresent it. If data has been compressed, an inverse
reduce not entirely of storage required to
lossy algorithms make use of some lossless technique as part required to restore it to a form in which it can be displayed or
decompression operation will be of the total
compression process. Generally,Software that performs compression and decompression is often called a codec (short for
used. once insignificant information has been compress
discarded, the resulting data is more amenable to lossless compression. context of video and audio.
compressor/decompressor), especially in the
This is particularly true in the case of image compression, as we will
explain in Chapter 4. Compression algorithms can be divided into two classes: lossless and
lossy. A lossless algorithm hascompressed datathat it is always possible to
the property
Ideally, lossy compression will data be applied atdecompresspossible
original only the latest data that has been compressed and retrieve an exact copy
stage in the preparation of the media for delivery. Any processing that as indicated in Figure 2.13. Any compression algo-
of the original data, decompress
is required should be done on uncompressed or losslesslythat is not lossless is lossy, which means that some data has been
rithm compressed
data whenever possible. There are two reasons for this. When data is
compress discarded in the compression process and cannot be restored, so that the
lossily compressed the lost information can never be retrieved, which
decompressed data is only an approximation to the original, as shown
means that if data is repeatedly compressed and decompressed in this
in Figure 2.14. The discarded data will represent information that is
way its quality will gradually deteriorate. Additionally, some processing
decompress
not significant, and lossy algorithms which are in common use do a
operations can exaggerate the loss of quality caused by some types of
remarkable uncom- preserving the qualitydata images, video and sound,
compression. For both these reasons, it is best to work with
job at decompressed of
compressed data
pressed data, and only compress it for final delivery. even though a considerable amount of data has been discarded. Lossless
Figure 2.13. Lossless compression algorithms are generally less effective than lossy ones, so for most multi-
media applications Figure 2.14. Lossy compression
This ideal cannot always be achieved.Video data is usually compressed in some lossy compression will be used. However, for
the camera, and although text the loss of even a produce uncompressed
digital still cameras that single bit of information would be significant, so there is no such thing as
lossy text compression.
images are increasingly common, many cheaper cameras will compress photographs fairly severely
when the pictures are being taken. It may be necessary for a photographer to allow the camera to
compress images, in order to fit thembe apparent that any sort of data these circumstances, data without loss. If no informa-
It may not onto the available storage. Under can be compressed at all