STAFF TRAINING INSITUTE(TECH.)-~LL INDIA RADIO & DOORDARSHAN

KING SWAY DELHI-110009

DIGIT AL RECORDING AND PLAY BACK

EQUIPMENT

SESSION NO 1932

17-06-2002 TO 21-06-2002

CONTENTS

TOPICSS.NO Page No

-I\nalog to Digital Conversion 1

2 7Introduction to Computer

Computer Hard Ware 20

4 Computer Networks 31

495 Understanding Audio Compression

Sound Card 646

667 Hard Disc Based Recording System

Compact Disc & Players 738.

Course Co-ordinator

Sanjeev Chawla

Dy. Dir. Engg.

ANALOG TO DIGITAL CONVERSION

2.1 INTRODUCTION

The aim of this unit is to explain the conversion of audio signals to the digitaldomain, and back to the arlalogue domain, without the aid of mathematics.The conversion of an analogue signal, such as the signal from a micropho:"'t;,to a form in which it may be digitally stored or manipulated requires tV/Odistinct processes -those of sampling and quantisation. Sampling and oversampling are concerned with the capture of an analogue quantity at a certaininstant in time; quantisation, dither and noise-shaping are concerned with therepresentation of this quantity by a digital word of finite length.

2.2 SAMPLING

Sampling can be defined as the capture of a continuously varying quantity ata precisely defined instant in time. Most usually, signals are sampled at a setof sample-points spaced at regular interval of time. Note that this sectionsays nothing about the digital word format used to represent this sample -

that is considered later in the section on quantisation. The Nyquist theorem(sampling theorem) states that in order to faithfully sample all of theinformation in a signal of one-sided bandwidth 8, it must be sampled at a rategreater than 28. The frequency 28 that is the minimum sample rate to retainall of the signal information is called the Nyquist frequency.

Mathematically this can be expressed as

If the highest frequency contained in an analog signal xa(t) is F max= 8 &.. jthe signal is sampled at a rate Fs=2Fmax = 28 then the signal xa(t) can be

recovered from its sample .

2.3 Aliasing

If we wish to sample at a rate of 28 then we must pre-filter the signal to a one-sided bandwidth of 8, otherwise it will not be possible to accuratelyreconstruct the original signal from the samples. The spectrum of the sampledsignal is the same as the spectrum of the continuous signal except that copies(known as aliases) of the original now appear centred on all integers multiplesof the sample rates. As a example, if a signal of 20kHz bandwidth is sampledat 50 kHz then alias spectra appear from 30- 70 kHz, 80- 120 kHz, and soon. It is because the alias spectra must not overlap that a sample rate ofgreater than 28 is required. In digital audio we are concerned with the base-band -that is to say the signal components which extend from 0 to 8.

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8aieb3rodThe figure above explains the sampling and aliasing in AID converter .Figure on the top is for time domain signals and at the bottom it is representedin frequency domain. Figure 'a' shows adequate samples per cycle. Figure 'b'shows inadequate sampling resulting in aliasing.

2.4 Anti-aliasing Filters

Therefore, to sample at the standard digital audio rate of 44.1 kHzrequires the input signal to be band-Iimited to the range 0 Hz to 22.05 kHz ifthe aliasing is to be avoided. Strictly speaking the input signal must be band-limited to less than 22.05kHz.

2.5 Sampling methods

The obvious, old and hard way of sampling an analogue voltage at 44.1 kHzis to do just that -feed the voltage into a conventional track and hold samplerrunning at a 44.1 kHz sample rate. As shown above, this requires that theinput signal be band-Iimited to half the sample and information will be lost.

For a practical implementation this may require an analogue filter of order 8 or10 to be inserted upstream of the sampler to provide an audio bandwidth of20kHz and also the 80 dB or so of attenuation above about 24 kHz that isrequired for high-fidelity sound reproduction. It is possible to design such afilter, but it would require a number of closely toleranced components and

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would suffer from all of the usual ailments associated with analogueelectronics.

2.6 Over sampling -Analogue to Digital Converters

The less obvious, but easier and cheaper way ( at least with the advent ofcheap VLSI multipliers) is to sample the input at a higher frequency, therebyrelaxing the constraints on the analogue input signal spectrum, and then low-pass filtering and decimating (reducing the sampling rate) in the digitaldomain. To do this the input is sampled at a higher frequency such as 4 x44.1 kHz. As before, this requires the signal to contain no significantcomponents above half the Nyquist frequency, but because of the increasedsampling rate the Nyquist frequency is now 176.4 kHz. Since the analoguefilter can still start to roll off at 20 kHz or so, but it does not need to be 80 dBdown until the first alias spectrum starts at 156 kHz it can be of lower order.

Now we have a digital data stream representing an analogue signal withcomponents from dc to 88.2 kHz. This data is passed through a digital filterwith a sharp cut-off at 22 kHz, which is relatively easy to implement, and canbe made to have a precisely linear phase response. The filter output is adigital data stream representing the original analogue waveform, but witr ~IIthe components above 22 kHz severely attenuated. Now we discard th~.f:eout of every four of the samples to get our stream of samples at a rate of 44.1kHz.

The scheme just outlined is conceptually fine. In a practical implementationthe digital filter would be designed so that, rather than discarding theunwanted output samples, they do not have to be calculated in the first place.This represents a significant saving of computational effort.

2.7 Over sampling Digital to Analogue Converters

Again the aim is to reduce the complexity of an analogue filter, this time theinterpolation filter after the DAC, whose purpose is to remove the alias spectrafrom the converter output. F or an audio signal of 20 kHz bandwidth thereconstruction filter has (ideally) to have a gain of one from dc to 20 kHz anda gain of zero from 24 kHz upwards. As in the case of the sampler this wouldrequire a complicated analogue filter.

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If, however, we increase the sample rqte by creating some new samplesdigitally then the first few alias spectra can be removed by a digital filter,relaxing the performance requirements of the analogue filter. For example afour times over sampling audio DAC runs at 176.4 kHz, so the first aliasspectrum starts at around 156 kHz, and the analogue reconstruction filter canbe of lower order since its transition-band is now 120 kHz wide.

The first step in this process is to insert three new samples in between eachof the original ones. The value is unimportant but zero is often used as itenables an efficient hardware implementation. If zeros are used then thespectrum of the sampled signal at this point is unchanged, although thesample rate has been quadrupled.

Next, this faster sample stream is passed through a digital filter whose actionis to make the new samples a smooth interpolation of the original data. Theoutput of this filter is a sample stream at 176.4 kHz whose base-bandspectrum (i.e. the music) is the same as the original, but the first three aliasspectra of the original sampled signal have now been removed.

Finally, the analogue signal is reconstructed with a DAC running at the four-time rate, and a low-order analogue filter, which removes the alias spectracentred around 176.4 kHz and multiples thereof.

2.8 Jitter

Jitter is defined as the timing error at the transition of a digital signal. Takingthe ADC as an example, the effect of timing errors on the sample clock is tosample the input signal at slightly the wrong time instant, so although theaverage sample rate may be very accurately 44.1 kHz the samples are notnecessarily taken exactly every1/44100th of a second, but perhaps a littleearly or a little late. Since the input is constantly changing, a timing error onthe sample clock translates to an erroneous sample level being captured.

The effects of sample clock jitter become more pronounced for high amplitudeand high frequency input signals. The level and nature of jitter required for itseffects to be audible is a current topic of research, debate and religious wars.

2.9 QUANTISA TION

At some point the sampled analogue quantity has to be converted to a finite-length digital word; this process is called quantisation. In other wards "theProcess of converting a discreet -time continuous amplitude signal intoa digital signal by expressing each sample value as a finite number ofdigits is called quantisation". This will generally be done immediately afterthe sampler so that the subsequent data manipulation may be done digitally,but this is not necessarily the case, for example if a switched-capacitor pre-filter is used.

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2.10 Quantisation error

The error introduced in representing the continuous valued signalby a finite set of discreet value levels is called quantisation error.

In a standard ADC (the "old, hard way", described above) the quantiserresolution and the output resolution are the same (since the digital out~utcomes directly from the quantiser). Assuming a random input signal th,Jerrors associated with this quantisation process are white and un-correlated,and yield a best-case signal to noise ratio of around 6.02n, +1. 76dB, where nis the number of bits in the output word. That is for 16 bit (216=65536 levels)

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2.11 DITHERMuch of the preceding text on quantisation and re-quantisation noiseassumes the signal to be random. For many signals this is not the C2se.When signal amplitude is constant and falls within two succes~~i\'equantisation levels the quantisation noise will be disturbing. This noise ratt .erthan being white, is found to be highly correlated with the signal. Thismanifests itself as very nasty-sounding level-dependent distortions whichbecome more prominent as the signal is decreased in amplitude.

To avoid this problem a small amount of noise is added to the signal beforequantisation, this process being known as dithering. The dither values areoften drawn from a triangular distribution, and it is desirable that they be un-correlated. The dither power is chosen such that the quantiser transferfunction is just linearised, without adding excess noise to the quanti sed signal.This has the effect of decorrelating the quantisation noise from the signal, andavoiding quantisation-related distortion.

2.12 CONCLUSION

Various aspects of analogue to digital conversion have been discussed. It wasseen that A to D conversion is performed as two distinct processes -

sampling and quantisation.

CAN YOU RECAPITULATE?

.What is sampling?

.What is Nyquist rate?

.What happens if the signal frequency more than half of sampling

frequency reach the sampler?.What is quarltisation? And what is quantisation error?

.Dither, Why it happens?

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