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Introduction to Digital
Recording Techniques
This paper was published in Canadian Acoustical Association Journal, 1989 Copyright 1989-2014, Digital Recordings. All Rights Reserved.
Introduction In the simplest case, the word digital refers to the representation of a quantity in numerical form and analog refers to a continuous physical quantity. To digitize means to convert an analog physical quantity into a numerical value. For example, if we represent the intensity of a sound by numbers proportionally related to the intensity, the analog value of the intensity has been represented digitally. The accuracy of the digital conversion depends upon the number of discrete numerical values that can be assigned and the rate at which these numerical measurements are made. For example, 4 numerical levels will represent changes in the amplitude of sound less accurately than 256 numerical levels and a rate of 8 conversion/sec will be less accurate than a rate of 10,000 conversions/sec. The process for digitally coding sound by computer was first developed in 1957 by Max Mathews of Bell Telephone Laboratories in Murray Hill (Mathews, 1963). Other advances in digital electronics and microchips led to the development of the first digital Pulse Code Modulation (PCM) audio recorder in 1967 at the NHK Technical Research Institute (Nakajima, 1983). This machine was a 12- bit companded scheme (using a compression/expansion of sound to improve dynamic range) with a 30 kHz sampling rate. Data were recorded on a one- track, two-head helical scan VTR (Video Tape Recorder). The first commercial PCM/digital recording session was performed by DENON in 1972 (Takeaki, 1989). Digital Recording Principles
During digital recording of the analog signal,
analog to digital (A/D) conversion takes place from
continuous time-amplitude coordinates to discrete
time-amplitude coordinates as illustrated in Figure 1.
The difference between the instantaneous analog
signal and de digital representation is digital error.
Figure 1: Use of an A/D (or D/A) converter to
convert a continuous function (time-amplitude) to a
discrete function (discrete time - discrete amplitude).
Conversion introduces a digital error in the signal -
digital noise.
We will separately consider the consequences
of discrete time and discrete amplitude coordinates
on the representation of the analog signal.
Discrete Time
Nyquist theorem
This is a remarkable result. The recovered signal will have all the frequencies in the range from 0 to fs/2 Hz. Discrete Amplitude The term bit stands for binary digit and is associated with a two-choice situation (0 and 1). Thus, any digital system with just two levels has a 1 bit resolution. Generally, the logarithm to the base 2 is used to convert the number of available quantization levels to number of bits. A device with two stable positions, such as a relay or a flip-flop, can store 1 bit of information. N such devices can store N bits of information, because the total number of possible states is 2N and amount of information is equal to log22N = N bits ( Shannon, 1949/1975). Thus, 4 levels is 2 bits, 8 is 3 bits, 16 is 4 bits, etc. For an N-bit A/D or D/A converter
When a voltage amplitude from 0 to Vmax is used (for example from 0 to 1 Volt), then one quantization step will be:
At an adequately high level and complexity of input
signal V(t), the digital error (difference between
analog signal and stored digital value) from sample
to sample will be statistically independent and
uniformly distributed in the range of [ - Thus, the maximum Signal-to-Noise Ratio (S/N) in decibels can be calculated to be (Nakajima, 1983; Mieszkowski, 1987):
Thus, converter resolutions of 8, 12,16, and 20 bits would allow a 48, 72, 96, and 120 dB S/N ratio respetively. A Digital Recording/Processing System
A block diagram of a digital
recording/processing system is shown in figure 2.
The processes at each of the numbered blocks 1 to 7
are described below:
Following Nakajima (1983), Mieszkowski (1989)
and Wannamaker, Lipshitz and Vanderkooy (1989),
analog dither must be added to the input signal in
order to
a) linearize the A/D converter
b) make possible improvement of S/N by averaging
process according to formula:
c) eliminate harmonic distortions (created when
digital noise ND(t) is coherent with signal
V(t)).
d) eliminate intermodulation distortion (created as
well when digital noise ND(t) is coherent with
signal V(t) ).
e) eliminate "digital deafness" (when the signal V(t)
falls below
f) eliminate noise modulation by the signal
Input low pass filter (antialiasing filter) should
eliminate all frequencies above fs / 2 , where fs
= sampling frequency, in order to avoid aliasing
distortion (Folding of frequencies into passband:
fnew = fs - foriginal where foriginal
A/D converter converts analog signal into a digital number (for example, 10110110
represents a binary coded 8-bit amplitude). Sampling speeds range from 2 kHz to 10
GHz and amplitude resolution ranges from 4 bits to 20 bits.
If DSP is performed on the signal, one must add digital dither N2(t) (box 5) to
avoid digital distortions and coherent noise ND (t) on the output of D/A converter.
Digital processing should also be performed using sufficiently precise real numbers to
avoid round-off errors.
Storage of digital data can be performed on
magnetic tape, optical disk, magnetic disk, or RAM
(Random Access Memory). Prior to storage, extra
code is generated to allow for error correction. This
error correction code allows detection and correction
of errors during playback of the audio signal.
Redundant information must be added to the original
signal in order to combat noise inherent in any
storage/communication system. The particular type
of code and error correction system depends on
storage medium, communication channel used and
immunity from errors (an arbitrarily small probability
of error can be obtained, Nakajima, 1983;
Shannon, 1949/1975).
Prior to D/A conversion, digital dither must be
added to numbers representing amplitude
of the signal if DSP has been performed. Optimal
digital dither has triangular probability density
function (PDF) (Wannamaker, et al. 1989).
D/A converter converts digital numbers into analog signal.
Available conversion speeds are 2 kHz to 200 MHz and available amplitude
resolution is 4 bits to 20 bits.
Output low pass filter should eliminate all
frequencies above fs /2 which are generated during D/A conversion.
Table I summarizes the author's comparison of
studio quality reel-to-reel analog tape recorder with 16
bit digital recorder. These data are derived from specifications
by various manufacturers of analog and
digital audio products. This table implies that the
digital recorder has many advantages over its analog
counterpart Performance of the analog recorder
depends very much on the calibration and tape used, as
well as on the environmental conditions such as temperature and humidity.
This is not the case for a digital
recorder, as long as errors generated are within the
limits of error correctability of the particular device.
Digital Formats Common coding systems Below is a short list of commonly used digital coding algorithms (using as an example a single channel digital recording system with swnpling frequency fs = 44,100 Hz and 16 bit A/D and D/A conversion). The data compression algorithms, which are more efficient than PCM (use less storage space), preserve the information content of the signal. Not mentioned here are data reduction/compression algorithms, which reduce information content of the original signal (arbitrarily or on the basis of psychoacoustics research results). PCM - PCM was invented by A.H. Reeves in 1939 (American Patents 2272070, 1942-2 see Nakajima, 1983) and was analyzed and developed as a modulation system from the point of view of communication theory by C.E. Shannon (1949). Using only two alternative pulse values (0 and 1), a 16- pulse train is generated which indicates the sampled value (for example, 1010 1111 0110 1101, a binary coded 16 bit number). During conversion, 16 bit amplitudes A1, A2, A3 ... are generated with a rate 44,100/sec. The demand on the storage device and speed of transmission channel is 88,200 Bytes/sec. This is a 'brute force' approach, which is not the most effective way of using the storage device and transmission channel. DPCM - Differential Pulse Code Modulation. During conversion only 4 bit (for example) differences between consecutive amplitudes are generated (A2-A1), (A3-A2), (A4-A3) ... at the rate of 44,100 /sec. Demand on the storage device and speed of transmission channel is 22,050 Bytes/sec. ADPCM - Adaptive Differential Pulse Code Modulation. Depending on the signal, the number of available bits to represent the difference between consecutive 16 bit samples is varied. For example, for the case of total quiet at the input (or small signal) the difference could be switched off totally or represented only by 1 bit. Demand on the storage device and the speed of transmission channel could vary between 0 Bytes/sec and 88,200 Bytes/sec depending on signal complexity. This is probably the most effective way of coding. Similar means of coding could be used for video signals because there is not much change from frame to frame most of the time.
Recording/Storage Systems Listed below are current common recording/storage systems for digital audio data.
PCM unit + VCR recorder
- 2 and 4 channels.
DASH
(Digital Audio Stationary Head Recorder)
R-DAT
(Rotating Head Digital Audio Tape Recoder)
Magnetic Hard Disk and RAM
(Random Access
Memory) based Recorders. Optical WMRM (Write Many Read Many), Erasable Optical Disk based Recorders. This format is becoming popular for audio applications because the removable optical cartridge can store about 600 MBytes of data and is more robust than magnetic media. Writing and reading is done by laser without physical contact with the disk. The NeXT computer has the first commercially available optical disk drive with 256 MBytes capacity ( Thmpson and Baran, 1988). Also, Nakamichi recently showed during the AES 7th International Conference a working prototype of an optical disk recorder, similar to a CD player (Mascenik, 1989). Applications
Digital techniques for storing and transmission
of audio signals are attractive because they offer
high quality signals, which do not deteriorate with
transmission distance, number of copies or time.
Digital information when properly stored and transmitted
maintains its 100% integrity in contrast to
analog information which deteriorates during each
transmission and storage cycle.
DSP Some of the functions which could be performed by the DSP devices are: filtering, equalization, compression/expansion of dynamic range, time compression/expansion, delay, reverberation, pitch change, generation of arbitrary signal or noise, music and voice synthesis, noise reduction, signal restoration, automatic pattern and voice recognition, time- reverse, noise gate, automatic gain control, mixing of signals, and FFT (Fast Fourier Transforms). In recent years DSP units have become relatively affordable. Also, there are many products available as plug-in cards for popular microcomputers, which contain DSP chips from such manufacturers as Motorola or Texas Instruments. DSP systems based on microcomputers are relatively fast (but not as fast as devoted hardware) and very flexible. Conclusions
The future of digital recording and DSP looks very
bright. Higher speeds of microprocessors and DSP
chips make real time applications of even complex
algorithms realistic. Falling prices of RAM chips and
storage devices like the erasable optical disk make
them affordable for many researchers and musicians.
In the author's opinion it is almost certain that the
majority of future recording and DSP equipment will
be based on microcomputers. Storage media of the
future will probably be erasable optical disks and RAM
cards. With falling prices of RAM chips and already
available 4 Mbit chips in a single package, one can
expect portable RAM based ADPCM recorders to
replace mechanically complex R-DAT machines in the
near future.
References
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