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ia Systems
520251: Multimed




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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   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
                                                                                            $+LL1M'()(*+,)J              we re


          Digitiz ation
           they originate in physical phenomena or because they exist in some can measure it, can vary infinitesimally.
                                                                                we analogue representation.
                                                                                            G66;*1<VLF1;6%&"#
           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
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
Digitization

24    F U N DA M E N TA L S
                                              :16 undersampl
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                              the reconstructed signal will be QF8;:('<VLF what the signal
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                                                                                     1itQ/time-varying
                                                                                           :16
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                              or space-varying. We will describe specific 1M*=&)J>$'# it to
                                                                                                  O
                              say, for now, that they are manifested as distortions and artefacts which
                              are always undesirable.

          si      si+1        It is easy enough to see that if the sampling rate is too low some detail
                              will be lost in the sampling. It is less easy to see whether there is ever
 Figure 2.5. Undersampling
                                                            "# output )J
                              any rate at which we can be sure that the samples are close enough
                                              J:+/C4MK1-!
                              together to allow the signal to be accurately reconstructed, and if
                                      ;-%&"<6
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                              there is, how close is close enough. To get a better understanding of
                                        D8"#Q
                              these matters, we need to consider an alternative way of representing
                                                         SU&#;*I1:+G 2f                      h
                              a signal. Later, this will also help us to understand some related aspects
                                           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
D+A"5I1#;$=5#*=& sampling
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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
                                                          Q/:6M=*=&;612=CI16J
                                        is quantized – the quantization levels – are equally spaced.
                                                                                            '+GQ/:16*7
                                                      quadvantagesathatodigital =&D
                                                           antiz ti n * representations have over
                                        One of the great                               &7)J;<P/D8/;FD4QF8
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                                        analogue ones stems from the fact that only certain signal values –
                                                                                            E!" transmittedt
                                        those at the quantization levels – are valid. If a signal#is out
                                                                                                         pu
                                        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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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
:16G=G"+'!8"29,
  (Data Compression)
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
03 digital mediafundamental
03 digital mediafundamental
03 digital mediafundamental
03 digital mediafundamental

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03 digital mediafundamental

  • 1. ia Systems 520251: Multimed -%./01/ !"# $%&"'()(*+, 20 2(34/15/ 2554
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  • 17. :16'()(?*SE!8"29, (DIGITIZATION)
  • 18. :16?'82 1!"# digital media QT8@<6>:62 C"2-(A;D"6E$681#!U./ @'5D6# ;TI/ ;61QT8@<6>:62 Paint Q/: 16A1'69<*=&;<P/'()(*+, *7:16><,#CI1;T(#:15K1- F6%"CI1 analogue QF8;<P/CI1 digital ;6=5: : 662A(B=/=.AI1 digitization
  • 19. Digitization K1-3I15
  • 20. Digitization G+/*U:;$=5#
  • 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 $+LL1M'()(*+,)J we re Digitiz ation they originate in physical phenomena or because they exist in some can measure it, can vary infinitesimally. we analogue representation. G66;*1<VLF1;6%&"# 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 :16 undersampl ingon!the #>Fin which the same level. The effects of such undersampling " way ,I# :7;/(' :I" perceived depend on the reconstructed signal will be QF8;:('<VLF what the signal r– construct $+L represents esound, image, and so on – and whether is 1itQ/time-varying :16 L instances later. Suffice , or space-varying. We will describe specific 1M*=&)J>$'# it to O say, for now, that they are manifested as distortions and artefacts which are always undesirable. si si+1 It is easy enough to see that if the sampling rate is too low some detail will be lost in the sampling. It is less easy to see whether there is ever Figure 2.5. Undersampling "# output )J any rate at which we can be sure that the samples are close enough J:+/C4MK1-! together to allow the signal to be accurately reconstructed, and if ;-%&"<6 undersampling T8"+D61:16 sa mpling '8A5 there is, how close is close enough. To get a better understanding of D8"#Q these matters, we need to consider an alternative way of representing SU&#;*I1:+G 2f h a signal. Later, this will also help us to understand some related aspects 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
  • 25. D+A"5I1#;$=5#*=& sampling '8A5" +D61*=&;F21J$2
  • 27. Q/;6%&"#K1- :16 undersampling *7QF 8;:('!"GF5+: F6%";:(' Moiré pattern
  • 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 Q/:6M=*=&;612=CI16J is quantized – the quantization levels – are equally spaced. '+GQ/:16*7 quadvantagesathatodigital =&D antiz ti n * representations have over One of the great &7)J;<P/D8/;FD4QF8 ;:('CA12?2I$2G96M analogue ones stems from the fact that only certain signal values – E!" transmittedt those at the quantization levels – are valid. If a signal#is out pu 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
  • 29. 381;612=CI16J'+GQ/: 16*7 quantization DI1 #W:+/ ;61)J ?'8C4MK1-!"#K1- *=&DI1#:+/
  • 30. 381;612=CI16J'+GQ/: 16*7 quantization DI1 #W:+/ ;61)J ?'8C4MK1-!"#K1- *=&DI1#:+/
  • 31. 381;612=CI16J'+GQ/: 16*7 quantization DI1 #W:+/ ;61)J ?'8C4MK1-!"#K1- *=&DI1#:+/
  • 32. 381;612=CI16J'+GQ/: 16*7 quantization DI1 #W:+/ ;61)J ?'8C4MK1-!"#K1- *=&DI1#:+/
  • 33. 381;612=CI16J'+GQ/: 16*7 quantization DI1 #W:+/ ;61)J ?'8C4MK1-!"#K1- *=&DI1#:+/
  • 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
  • 35. :16G=G"+'!8"29, (Data Compression)
  • 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