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# 03 digital mediafundamental

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### 03 digital mediafundamental

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19. 19. 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 sampFigure 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
20. 20. 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 sampFigure 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
21. 21. 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 quantizationHowever, 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 beingthe 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 Digitizationrepresentation of the original analogue signal? The only meaningful measure of accuracy must be continuous signal reduced to a sequence of equally spaced values; in thehow 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 everyset 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 thatdescription provides an exact specification of the theoretically best are normally carried out by special hardware devices, These processes way to generate the requiredsignal. In practice, we use methods that are simplercalled the theoretical optimum but (ADCs), whose internal workings than analogue to digital converters which caneasily 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 ofOne 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 samplingis used for the entire extent between it and the following sample. As generally assume that the levels to which a signal rate. Similarly, we willFigure 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 greatas a monitor or a loudspeaker – for display or playback, the lags stems from the fact that only certain signal values – analogue ones andimperfections inherent in the physical device will those at thediscon- cause these quantization levels – are valid. If a signal is transmittedtinuities to be smoothed out, and the result actually approximates the on some physical medium such as magnetic tape, over a wire or storedtheoretical 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 holdin the technology for the playback of sound and picture will stray magnetic fields, or simply because of the unavoidable quantization ence from demand reconstructionmatching 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 reconstructioninadequate, because there may be details in the analogue signal that, as it were, slipped betweensamples. Figure 2.5 shows an example: the values of the consecutive samples taken at si and si+1are identical, and there cannot possibly be any way of inferring the presence of the spike inbetween those two points from them – the signal could as easily have dipped down or stayed at
22. 22. Digitization24 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
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32. 32. CHAPTER 2 D I G I TA L DATAFigure 2.12. Posterizationbetween areas of those colours would be elided. The effect on black and white images can beseen clearly in Figure 2.11, which shows a gradient swatch using 256, 128, 64, 32, 16, 8, 4, and2 different grey levels. The original gradient varies linearly from pure white to pure black, andas we reduce the number of different greys, you can see how values band together as they are
33. 33. :16G=G"+!8"29, (Data Compression)
34. 34. 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 thewith directly, so storage schemes which make less than optimal use ofthe 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 toLossless and lossy compression arethe amount separate techniques. Mostrepresent it. If data has been compressed, an inverse reduce not entirely of storage required tolossy 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 totalcompression process. Generally,Software that performs compression and decompression is often called a codec (short for used. once insignificant information has been compressdiscarded, the resulting data is more amenable to lossless compression. context of video and audio. compressor/decompressor), especially in theThis is particularly true in the case of image compression, as we willexplain 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 propertyIdeally, lossy compression will data be applied atdecompresspossible original only the latest data that has been compressed and retrieve an exact copystage in the preparation of the media for delivery. Any processing that as indicated in Figure 2.13. Any compression algo- of the original data, decompressis required should be done on uncompressed or losslesslythat is not lossless is lossy, which means that some data has been rithm compresseddata whenever possible. There are two reasons for this. When data is compress discarded in the compression process and cannot be restored, so that thelossily compressed the lost information can never be retrieved, which decompressed data is only an approximation to the original, as shownmeans that if data is repeatedly compressed and decompressed in this in Figure 2.14. The discarded data will represent information that isway its quality will gradually deteriorate. Additionally, some processing decompress not significant, and lossy algorithms which are in common use do aoperations 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 datapressed 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 compressionThis ideal cannot always be achieved.Video data is usually compressed in some lossy compression will be used. However, forthe 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 severelywhen the pictures are being taken. It may be necessary for a photographer to allow the camera tocompress 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