2.5 What is a Digital Signal?

It is a characteristic of analog systems that degradations cannot be separated from the original signal, so nothing can be done about them. At the end of a system a signal carries the sum of all degradations introduced at each stage through which it passed. This sets a limit to the number of stages through which a signal can be passed before it is useless. Alternatively, if many stages are envisaged, each piece of equipment must be far better than necessary so that the signal is still acceptable at the end. The equipment will naturally be more expensive.

One of the vital concepts to grasp is that digital audio and video are simply alternative means of carrying the same information. An ideal digital recorder has the same characteristics as an ideal analog recorder: both of them are totally transparent and reproduce the original applied waveform without error. One need only compare high quality analog and digital equipment side by side with the same signals to realize how transparent modern equipment can be. Needless to say, in the real world, ideal conditions seldom prevail, so analog and digital equipment both fall short of the ideal. Digital equipment simply falls short of the ideal to a smaller extent than does analog and at lower cost, or, if the designer chooses, can have the same performance as analog at much lower cost.

Although there are a number of ways in which audio and video waveform can be represented digitally, there is one system, known as pulse code modulation (PCM), that is in virtually universal use. Figure 2.3 shows how PCM works. Instead of being continuous, the time axis is represented in a discrete, or stepwise, manner. The waveform is not carried by continuous representation, but by measurement at regular intervals. This process is called sampling and the frequency with which samples are taken is called the sampling rate or sampling frequency F _s . The sampling rate is generally fixed and is not necessarily a function of any frequency in the signal, although in video it may be for convenience. If every effort is made to rid the sampling clock of jitter, or time instability, every sample will be made at an exactly even time step. Clearly if there is any subsequent timebase error, the instants at which samples arrive will be changed and the effect can be detected . If samples arrive at some destination with an irregular timebase, the effect can be eliminated by storing the samples temporarily in a memory and reading them out using a stable, locally generated clock. This process is called timebase correction and all properly engineered digital systems must use it. Clearly timebase error is not simply reduced; it can be totally eliminated. As a result there is little point measuring the wow and flutter or timebase error of a digital recorder; it doesn't have any. What happens is that the crystal clock in the timebase corrector measures stability of the measuring equipment. It should be stressed that sampling is an analog process. Each sample still varies infinitely as the original waveform did.

Figure 2.3: The major process in PCM conversion. A/D conversion (top) and D/A conversion (bottom). Note that the quantizing step can be omitted to examine sampling and reconstruction independently of quantizing ( dotted arrow).

Those who are not familiar with digital processes often worry that sampling takes away something from a signal because it is not taking notice of what happened between the samples. This would be true in a system having infinite bandwidth, but no analog signal can have infinite bandwidth. All analog signal sources from microphones, tape decks, cameras and so on have a frequency response limit, as indeed do our ears and eyes. When a signal has finite bandwidth, the rate at which it can change is limited, and the way in which it changes becomes predictable. When a waveform can only change between samples in one way, it is then only necessary to carry the samples and the original waveform can be reconstructed from them.

Figure 2.3 also shows that each sample is also discrete, or represented in a stepwise manner. The length of the sample, which will be proportional to the voltage of the waveform, is represented by a whole number. This process is known as quantizing and results in an approximation , but the size of the error can be controlled until it is negligible. If, for example, we were to measure the height of humans to the nearest metre, virtually all adults would register 2 metres high and obvious difficulties would result. These are generally overcome by measuring height to the nearest centimetre. Clearly there is no advantage in going further and expressing our height in a whole number of millimetres or even micrometres. The point is that an appropriate resolution can be found just as readily for audio or video, and greater accuracy is not beneficial. The link between quality and sample resolution is explored later in this chapter. The advantage of using whole numbers is that they are not prone to drift . If a whole number can be carried from one place to another without numerical error, it has not changed at all. By describing waveforms numerically , the original information has been expressed in a way that is better able to resist unwanted changes.

Essentially, digital systems carry the original waveform numerically. The number of the sample is an analog of time, and the magnitude of the sample is an analog of the signal voltage. As both axes of the waveform are discrete, the waveform can be accurately restored from numbers as if it were being drawn on graph paper. If we require greater accuracy, we simply choose paper with smaller squares. Clearly more numbers are required and each one could change over a larger range.

In simple terms, the waveform is conveyed in a digital recorder as if the voltage had been measured at regular intervals with a digital meter and the readings had been written down on a roll of paper. The rate at which the measurements were taken and the accuracy of the meter are the only factors which determine the quality, because once a parameter is expressed as a discrete number, a series of such numbers can be conveyed unchanged. Clearly in this example the handwriting used and the grade of paper have no effect on the information. The quality is determined only by the accuracy of conversion and is independent of the quality of the signal path .

In practical systems, binary numbers are used, as was explained in Chapter 1 in which it was also shown that there are two ways in which binary signals can be used to carry samples. When each digit of the binary number is carried on a separate wire this is called parallel transmission. The states of the signals change at the sampling rate. This approach is used in the parallel video interfaces, as video needs a relatively short word length: eight or ten bits. Using multiple wires is cumbersome where a long word length is in use, and a single wire can be used where successive digits from each sample are sent serially . This is the definition of pulse code modulation. Clearly the clock frequency must now be higher than the sampling rate. Whilst the transmission of audio by such a scheme is advantageous in that noise and timebase error have been eliminated, there is a penalty that a single high quality audio channel requires around one million bits per second. Digital audio could only come into use when such a data rate could be handled economically.

As a digital video channel requires of the order of two hundred million bits per second it is not surprising that digital audio equipment became common somewhat before digital video.