Chapter 6. The compact disc and digital audio

234



The Compact Disc and Digital Audio



Unfortunately, each time a successive analogue tape copy is made, some

degradation of the original signal will occur, in respect of bandwidth and

signal-to-noise ratio, and as a result of minor tape malfunctions and

'dropouts'. So by the time the recording has been converted into a cassette

tape, or an undulating groove on the surface of a vinyl disc, a lot of the

immediacy and transparency of the original recording will have been lost.

By comparison with this, a 'digital' recording- in which the analogue

signal has been converted into a 'digitally encoded' electronic equivalent

where the continuously variable voltage levels of the original signal are

represented by a repetitively sampled sequence of alternating '0's and 'l's,

which signify clearly defined, constant and distinct electrical voltage levels

- is, at least in principle, capable of being copied over and over again,

without any degradation at all. Any minor errors in the received '0' or '1'

levels can be automatically corrected, and freed from any spurious noisea process which is obviously impracticable with any signal in analogue

form.

In addition, the incoming signal, once converted into its digital form,

need no longer exist in any specific time domain. After all, it is now just a

collection of data, divided into a sequence of blocks. This allows the data

to be divided, stored and manipulated, and reassembled in any way

necessary for the purposes of recording or handling. It also means that,

once the signal is converted into digital form, it is intrinsically free from

any added 'rumble', 'wow' or 'flutter' or other intrusions due to the speed

irregularities of the subsequent recording or replay systems. However,

there are also snags.



PROBLEMS WITH DIGITAL ENCODING

Quantisation noise

Although a number of ways exist by which an analogue signal can be

converted into its digital equivalent, the most popular, and the technique

used in the CD, is the one known as 'pulse code modulation', usually

referred to as 'PCM'. In this, the incoming signal is sampled at a

sufficiently high repetition rate to permit the desired audio bandwidth to

be achieved. In practice this demands a sampling frequency somewhat

greater than twice the required maximum audio frequency. The measured

signal voltage level, at the instant of sampling, is then represented

numerically as its nearest equivalent value in binary coded form (a process

which is known as 'quantisation').

This has the effect of converting the original analogue signal, after

encoding and subsequent decoding, into a voltage 'staircase' of the kind

shown in Fig. 6.1. Obviously, the larger the number of voltage steps in



235



The Compact Disc and Digital Audio

I-- Input waveform



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Digitally encoded~decoded waveform.



which the analogue signal can be stored in digital form (that shown in the

figure is encoded at '4-bit' - 24 or 16 possible voltage levels), the smaller

each of these steps will be, and the more closely the digitally encoded

waveform will approach the smooth curve of the incoming signal.

The difference between the staircase shape of the digital version and the

original analogue waveform causes a defect of the kind shown in Fig. 6.2,

known as 'quantisation error', and since this error voltage is not directly

related in frequency or amplitude to the input signal it has many of the

characteristics of noise, and is therefore also known as 'quantisation noise'.

This error increases in size as the number of encoding levels is reduced. It

will be audible if large enough, and is the first problem with digitally

encoded signals. I will consider this defect, and the ways by which it can be

minimised, later in this chapter.



t

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r



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tu

Fig. 6.2



Time



Quantisation error.



236



The Compact Disc and Digital Audio



Bandwidth



The second practical problem is that of the bandwidth which is necessary to

store or transmit such a digitally encoded signal. In the case of the CD, the

specified audio bandwidth is 20 I-Iz to 20 kHz, which requires a sampling

frequency somewhat greater than 40 kI-Iz. In practice, a sampling

frequency of 44.1 kHz is used. In order to reduce the extent of the staircase

waveform quantisation error, a 16-bit sampling resolution is used in the

recording of the CD, equivalent to 216 or 65 536 possible voltage steps. If

16 bits are to be transmitted in each sampling interval, then, for a stereo

signal, the required bandwidth will be 2 x 16 x 44100 I-Iz, or 1.4112 mHz,

which is already seventy times greater than the audio bandwidth of the

incoming signal. However, in practice, additional digital 'bits' will be

added to this signal for error correction and other purposes, which will

extend the required bandwidth even further.

Translation non-linearity



The conversion of an analogue signal both into and from its binary coded

digital equivalent carries with it the problem of ensuring that the

magnitudes of the binary voltage steps are defined with adequate

precision. If, for example, '16-bit' encoding is used, the size of the 'most

significant bit' (MSB) will be 32 768 times the size of the 'least significant

bit' (LSB). If it is required that the error in defining the LSB shall be not

worse than +0.5%, then the accuracy demanded of the MSB must be at

least within +0.0000152% if the overall linearity of the system is not to be

degraded.

The design of any switched resistor network, for encoding or decoding

purposes, which demanded such a high degree of component precision

would be prohibitively expensive, and would suffer from great problems as

a result of component ageing or thermal drift. Fortunately, techniques are

available which lessen the difficulty in achieving the required accuracy in

the quantisation steps. The latest technique, known as 'low bit' or

'bit-stream' decoding, side-steps the problem entirely by effectively using a

time-division method, since it is easier to achieve the required precision in

time, rather than in voltage or current, intervals.

Detection and correction of transmission errors



The very high bandwidths which are needed to handle or record PCM

encoded signals means that the recorded data representing the signal must

be very densely packed. This leads to the problem that any small blemish

on the surface of the CD, such as a speck of dust, or a scratch, or a thumb



The Compact Disc and Digital Audio



237



print could blot out, or corrupt, a significant part of the information

needed to reconstruct the original signal. Because of this, the real-life

practicability of all digital record/replay systems will depend on the

effectiveness of electronic techniques for the detection, correction or, if the

worst comes to the worst, masking of the resultant errors. Some very

sophisticated systems have been devised, which will also be examined

later.



Filtering for bandwidth limitation and signal recovery

When an analogue signal is sampled, and converted into its PCM encoded

digital equivalent, a spectrum of additional signals is created, of the kind

shown in Fig. 6.3(a), where f~ is the sampling frequency and fm is the upper

modulation frequency. Because of the way in which the sampling process

operates, it is not possible to distinguish between a signal having a

frequency which is somewhat lower than half the sampling frequency and

one which is the same distance above it; a problem which is called

'aliasing'. In order to avoid this, it is essential to limit the bandwidth of the

incoming signal to ensure that it contains no components above fs/2.

If, as is the case with the CD, the sampling frequency is 44.1 kHz, and

the required audio bandwidth is 20 Hz to 20 kHz, +0/ 1 dB, an input

'anti-aliasing' filter must be employed to avoid this problem. This filter

must allow a signal magnitude which is close to 100% at 20 kHz, but nearly

zero (in practice, usually - 6 0 dB) at frequencies above 22.05 kHz. It is

possible to design a steep-cut, low-pass filter which approximates closely to

this characteristic using standard linear circuit techniques, but the phase

shift, and group delay (the extent to which signals falling within the

affected band will be delayed in respect of lower frequency signals)

introduced by this filter would be too large for good audio quality or stereo

image presentation.

This difficulty is illustrated by the graph of Fig. 6.4, which shows the

relative group delay and phase shift introduced by a conventional low-pass

analogue filter circuit of the kind shown in Fig. 6.5. The circuit shown gives

only a modest - 9 0 dB/octave attenuation rate, while the actual slope

necessary for the required anti-aliasing characteristics (say, 0 dB at 20 kHz

and - 6 0 dB at 22.05 kHz) would be - 4 2 6 dB/octave. If a group of filters of

the kind shown in Fig. 6.5 were connected in series to increase the

attenuation rate from - 9 0 dB to - 4 2 6 dB/octave, this would cause a group

delay, at 20 kHz, of about I ms with respect to I kHz, and a relative phase

shift of some 3000~, which would be clearly audible.*

*In the recording equipment it is possible to employ steep-cut filter systems in which the

phase and group delay characteristics are more carefully controlled than would be practicable

in a mass-produced CD replay system where both size and cost must be considered.



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Fig. 6.3 PCM frequency spectrum (a) when sampled at 44.1 kHz and (b) when four times oversampled.



The Compact Disc and Digital Audio



239



Similarly, since the frequency spectrum produced by a PCM encoded

20 kHz bandwidth audio signal will look like that shown in Fig. 6.3(a), it is

necessary, on replay, to introduce yet another equally steep-cut low-pass

filter to prevent the generation of spurious audio signals which would result

from the heterodyning of signals equally disposed on either side of fs/2.

An improved performance in respect both of relative phase error and of

group delay in such 'brick wall' filters can be obtained using so-called

'digital' filters, particularly when combined with pre-filtering phase

correction. However, this problem was only fully solved, and then only on

replay (because of the limitations imposed by the original Philips CD

patents), by the use of 'over-sampling' techniques, in which, for example,

the sampling frequency is increased to 176.4 kHz ('four times oversampling'), which moves the aliasing frequency from 22.05 kHz up to

154.35 kHz, giving the spectral distribution shown in Fig. 6.3(b). It is then

a relatively easy matter to design a filter, such as that shown in Fig. 6.14,

having good phase and group delay characteristics, which has a

transmission near to 100% at all frequencies up to 20 kHz, but near zero at

154.35 kHz.



THE RECORD-REPLAY SYSTEM



The recording system layout

How the signal is handled, on its way from the microphone or other signal

source to the final CD, is shown in the block diagram of Fig. 6.6. Assuming

the signal has by now been reduced to a basic L - R stereo pair, this is

amplitude limited to ensure that no signals greater than the possible

encoding amplitude limit are passed on to the analogue-to-digital converter

(ADC) stage. These input limiter stages are normally crosslinked in

operation to avoid disturbance of the stereo image position if the maximum

permitted signal level is exceeded, and the channel gain reduced in

consequence of this, in only a single channel.

The signal is then passed to a very steep-cut 20 kHz anti-aliasing filter

(often called a 'brick wall filter') to limit the bandwidth offered for

encoding. This bandwidth limitation is a specific requirement of the digital

encoding/decoding process, for the reasons already considered. It is

necessary to carry out this filtering process after the amplitude limiting

stage, because it is possible that the action of peak clipping may generate

additional high frequency signal components. This would occur because

'squaring-off' the peaks of waveforms will generate a Fourier series of

higher frequency harmonic components.

The audio signal, which is still, at this stage, in analogue form, is then

passed to two parallel operating 16-bit ADCs, and, having now been

converted into a digital data stream, is fed into a temporary data-storage



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The Compact Disc and Digital Audio



243



device - usually a 'shift register' - from which the output data stream is

drawn as a sequence of 8-bit blocks, with the 'L' and 'R' channel data now

arranged in a consecutive but interlaced time sequence.

From the point in the chain at which the signal is converted into digitally

encoded blocks of data, at a precisely controlled 'clock' frequency, to the

final transformation of the encoded data back into analogue form, the

signal is immune to frequency or pitch errors as a result of motor speed

variations in the disc recording or replay process.

The next stage in the process is the addition of data for error correction

purposes. Because of the very high packing density of the digital data on

the disc, it is very likely that the recovered data will have been corrupted to

some extent by impulse noise or blemishes, such as dust, scratches, or

thumb prints on the surface of the disc, and it is necessary to include

additional information in the data code to allow any erroneous data to be

corrected. A number of techniques have been evolved for this purpose, but

the one used in the CD is known as the 'Cross-interleave Reed-Solomon

code' or CIRC. This is a very powerful error correction method, and allows

complete correction of faulty data arising from quite large disc surface

blemishes.

Because all possible '0' or '1' combinations may occur in the 8-bit

encoded words, and some of these would offer bit sequences which were

rich in consecutive 'O's or 'l's, which could embarrass the disc speed or spot

and track location servo-mechanisms, or, by inconvenient juxtaposition,

make it more difficult to read the pit sequence recorded on the disc

surface, a bit-pattern transformation stage known as the 'eight to fourteen

modulation' (EFM) converter is interposed between the output of the

error correction (CIRC) block and the final recording. This expands the

recorded bit sequence into the form shown in Fig. 6.7, to facilitate the

operation of the recording and replay process. I shall explain the functions

and method of operation of all these various stages in more detail later in

this chapter.

Disc recording

This follows a process similar to that used in the manufacture of vinyl EP

and LP records, except that the recording head is caused to generate a

spiral pattern of pits in an optically flat glass plate, rather than a spiral

groove in a metal one, and that the width of the spiral track is very much

smaller (about 1/60th) than that of the vinyl groove. (Detail of the CD

groove pattern is, for example, too fine to be resolved by a standard optical

microscope.) When the master disc is made, 'mother' and 'daughter' discs

are then made preparatory to the production of the stampers which are

used to press out the track pattern on a thin (1.4 mm) plastics sheet, prior

to the metallisation of the pit pattern for optical read-out in the final disc.



8114 bit ROM



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Disc indentations (with EFM)



Fig. 6.7



The EFM process.



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