Digital Audio Compression
`
`By Davis Yen Pan
`
`Abstract
`
`Compared to most digital data types, with the
`exception of digital video, the data rates associ-
`ated with uncompressed digital audio are substan-
`tial. Digital audio compression enables more effi-
`cient storage and transmission of audio data. The
`many forms of audio compression techniques offer a
`range of encoder and decoder complexity, compressed
`audio quality, and differing amounts of data com-
`pression. The -law transformation and ADPCM
`coder are simple approaches with low-complexity,
`low-compression, and medium audio quality algo-
`rithms. The MPEG/audio standard is a high-
`complexity, high-compression, and high audio qual-
`ity algorithm. These techniques apply to general au-
`dio signals and are not specifically tuned for speech
`signals.
`
`Introduction
`
`Digital audio compression allows the efficient stor-
`age and transmission of audio data. The various au-
`dio compression techniques offer different levels of
`complexity, compressed audio quality, and amount
`of data compression.
`
`This paper is a survey of techniques used to com-
`press digital audio signals. Its intent is to provide
`useful information for readers of all levels of ex-
`perience with digital audio processing. The paper
`
`begins with a summary of the basic audio digitiza-
`tion process. The next two sections present detailed
`descriptions of two relatively simple approaches to
`audio compression: -law and adaptive differential
`pulse code modulation. In the following section, the
`paper gives an overview of a third, much more so-
`phisticated, compression audio algorithm from the
`Motion Picture Experts Group. The topics covered
`in this section are quite complex and are intended
`for the reader who is familiar with digital signal
`processing. The paper concludes with a discussion
`of software-only real-time implementations.
`
`Digital Audio Data
`
`The digital representation of audio data offers
`many advantages: high noise immunity, stability,
`and reproducibility. Audio in digital form also al-
`lows the efficient implementation of many audio
`processing functions (e.g., mixing, filtering, and
`equalization) through the digital computer.
`
`The conversion from the analog to the digital do-
`main begins by sampling the audio input in regular,
`discrete intervals of time and quantizing the sam-
`pled values into a discrete number of evenly spaced
`levels. The digital audio data consists of a sequence
`of binary values representing the number of quan-
`tizer levels for each audio sample. The method of
`representing each sample with an independent code
`word is called pulse code modulation (PCM). Figure
`1 shows the digital audio process.
`
`00110111000...
`
`11001100100...
`
`ANALOG
`AUDIO
`INPUT
`
`ANALOG-TO-DIGITAL
`CONVERSION
`
`PCM
`VALUES
`
`DIGITAL SIGNAL
`PROCESSING
`
`PCM
`VALUES
`
`DIGITAL-TO-ANALOG
`CONVERSION
`
`ANALOG
`AUDIO
`OUTPUT
`
`Figure 1 Digital Audio Process
`
`Digital Technical Journal Vol. 5No. 2,Spring1993 1
`
`IPR2016-01710
`UNIFIED EX1015
`
`

`
`Digital Audio Compression
`
`According to the Nyquist theory, a time-sampled
`signal can faithfully represent signals up to half the
`sampling rate.[1] Typical sampling rates range from
`8 kilohertz (kHz) to 48 kHz. The 8-kHz rate covers
`a frequency range up to 4 kHz and so covers most of
`the frequencies produced by the human voice. The
`48-kHz rate covers a frequency range up to 24 kHz
`and more than adequately covers the entire audi-
`ble frequency range, which for humans typically ex-
`tends to only 20 kHz.
`In practice, the frequency
`range is somewhat less than half the sampling rate
`because of the practical system limitations.
`
`The number of quantizer levels is typically a power
`of 2 to make full use of a fixed number of bits per au-
`dio sample to represent the quantized values. With
`uniform quantizer step spacing, each additional bit
`has the potential of increasing the signal-to-noise
`ratio, or equivalently the dynamic range, of the
`quantized amplitude by roughly 6 decibels (dB). The
`typical number of bits per sample used for digital
`audio ranges from 8 to 16. The dynamic range ca-
`pability of these representations thus ranges from
`48 to 96 dB, respectively. To put these ranges into
`perspective, if 0 dB represents the weakest audi-
`ble sound pressure level, then 25 dB is the mini-
`mum noise level in a typical recording studio, 35 dB
`is the noise level inside a quiet home, and 120 dB
`is the loudest level before discomfort begins.[2] In
`terms of audio perception, 1 dB is the minimum au-
`dible change in sound pressure level under the best
`conditions, and doubling the sound pressure level
`amounts to one perceptual step in loudness.
`
`Compared to most digital data types (digital video
`excluded), the data rates associated with uncom-
`pressed digital audio are substantial. For example,
`the audio data on a compact disc (2 channels of au-
`dio sampled at 44.1 kHz with 16 bits per sample) re-
`quires a data rate of about 1.4 megabits per second.
`There is a clear need for some form of compression
`to enable the more efficient storage and transmis-
`sion of this data.
`
`The many forms of audio compression techniques
`differ in the trade-offs between encoder and decoder
`complexity, the compressed audio quality, and the
`amount of data compression. The techniques pre-
`sented in the following sections of this paper cover
`the full range from the -law, a low-complexity,
`low-compression, and medium audio quality algo-
`rithm, to MPEG/audio, a high-complexity, high-
`compression, and high audio quality algorithm.
`These techniques apply to general audio signals and
`are not specifically tuned for speech signals. This
`paper does not cover audio compression algorithms
`designed specifically for speech signals. These al-
`gorithms are generally based on a modeling of the
`vocal tract and do not work well for nonspeech audio
`
`2 Digital Technical Journal Vol. 5No. 2,Spring1993
`
`signals.[3,4] The federal standards 1015 LPC (linear
`predictive coding) and 1016 CELP (coded excited lin-
`ear prediction) fall into this category of audio com-
`pression.
`
`-law Audio Compression
`
`The -law transformation is a basic audio compres-
`sion technique specified by the Comité Consultatif
`Internationale de Télégraphique et Téléphonique
`(CCITT) Recommendation G.711.[5] The transfor-
`mation is essentially logarithmic in nature and al-
`lows the 8 bits per sample output codes to cover
`a dynamic range equivalent to 14 bits of linearly
`quantized values. This transformation offers a com-
`pression ratio of (number of bits per source sample)
`/8 to 1. Unlike linear quantization, the logarithmic
`step spacings represent low-amplitude audio sam-
`ples with greater accuracy than higher-amplitude
`values. Thus the signal-to-noise ratio of the trans-
`formed output is more uniform over the range of
`amplitudes of the input signal. The -law transfor-
`mation is
`
`y = 255 127
`ln(1+)  ln(1 + jxj) f or x < 0
`
`ln(1+)  ln(1 + jxj) f or x  0
`127 127
`
`where m = 255, and x is the value of the input sig-
`nal normalized to have a maximum value of 1. The
`CCITT Recommendation G.711 also specifies a simi-
`lar A-law transformation. The -law transformation
`is in common use in North America and Japan for
`the Integrated Services Digital Network (ISDN) 8-
`kHz-sampled, voice-grade, digital telephony service,
`and the A-law transformation is used elsewhere for
`the ISDN telephony.
`
`Adaptive Differential Pulse Code
`Modulation
`
`Figure 2 shows a simplified block diagram of an
`adaptive differential pulse code modulation (AD-
`PCM) coder.[6] For the sake of clarity, the figure
`omits details such as bit-stream formatting, the pos-
`sible use of side information, and the adaptation
`blocks. The ADPCM coder takes advantage of the
`fact that neighboring audio samples are generally
`similar to each other. Instead of representing each
`audio sample independently as in PCM, an ADPCM
`encoder computes the difference between each au-
`dio sample and its predicted value and outputs the
`PCM value of the differential. Note that the AD-
`PCM encoder (Figure 2a) uses most of the compo-
`nents of the ADPCM decoder (Figure 2b) to compute
`the predicted values.
`
`

`
`X[n] +
`
`+
`
`–
`
`D[n]
`
`(ADAPTIVE)
`QUANTIZER
`
`C[n]
`
`Xp[n – 1]
`
`(ADAPTIVE)
`PREDICTOR
`
`(ADAPTIVE)
`DEQUANTIZER
`
`+
`
`Dq[n]
`
`Xp[n]
`
`+
`
`+
`
`(a) ADPCM Encoder
`
`C[n]
`
`(ADAPTIVE)
`DEQUANTIZER
`
`Dq[n] +
`
`+
`
`+
`
`Xp[n]
`
`Xp[n – 1]
`
`(ADAPTIVE)
`PREDICTOR
`
`(b) ADPCM Decoder
`
`Figure 2 ADPCM Compression and Decompression
`
`The quantizer output is generally only a (signed)
`representation of the number of quantizer levels.
`The requantizer reconstructs the value of the quan-
`tized sample by multiplying the number of quan-
`tizer levels by the quantizer step size and possibly
`adding an offset of half a step size. Depending on
`the quantizer implementation, this offset may be
`necessary to center the requantized value between
`the quantization thresholds.
`
`The ADPCM coder can adapt to the characteristics
`of the audio signal by changing the step size of ei-
`ther the quantizer or the predictor, or by changing
`both. The method of computing the predicted value
`and the way the predictor and the quantizer adapt
`to the audio signal vary among different ADPCM
`coding systems.
`
`Some ADPCM systems require the encoder to pro-
`vide side information with the differential PCM val-
`ues. This side information can serve two purposes.
`First, in some ADPCM schemes the decoder needs
`the additional information to determine either the
`predictor or the quantizer step size, or both. Second,
`the data can provide redundant contextual informa-
`tion to the decoder to enable recovery from errors in
`the bit stream or to allow random access entry into
`the coded bit stream.
`
`Digital Audio Compression
`
`The following section describes the ADPCM algo-
`rithm proposed by the Interactive Multimedia Asso-
`ciation (IMA). This algorithm offers a compression
`factor of (number of bits per source sample)/4 to 1.
`Other ADPCM audio compression schemes include
`the CCITT Recommendation G.721 (32 kilobits per
`second compressed data rate) and Recommendation
`G.723 (24 kilobits per second compressed data rate)
`standards and the compact disc interactive audio
`compression algorithm.[7,8]
`
`The IMA ADPCM Algorithm. The IMA is a consor-
`tium of computer hardware and software vendors
`cooperating to develop a de facto standard for com-
`puter multimedia data. The IMA’s goal for its audio
`compression proposal was to select a public-domain
`audio compression algorithm able to provide good
`compressed audio quality with good data compres-
`sion performance. In addition, the algorithm had to
`be simple enough to enable software-only, real-time
`decompression of stereo, 44.1-kHz-sampled, audio
`signals on a 20-megahertz (MHz) 386-class com-
`puter. The selected ADPCM algorithm not only
`meets these goals, but is also simple enough to en-
`able software-only, real-time encoding on the same
`computer.
`
`The simplicity of the IMA ADPCM proposal lies
`in the crudity of its predictor. The predicted value
`of the audio sample is simply the decoded value of
`the immediately previous audio sample. Thus the
`predictor block in Figure 2 is merely a time-delay
`element whose output is the input delayed by one
`audio sample interval. Since this predictor is not
`adaptive, side information is not necessary for the
`reconstruction of the predictor.
`
`Figure 3 shows a block diagram of the quantization
`process used by the IMA algorithm. The quantizer
`outputs four bits representing the signed magnitude
`of the number of quantizer levels for each input sam-
`ple.
`
`Digital Technical Journal Vol. 5No. 2,Spring1993 3
`
`

`
`Digital Audio Compression
`
`Adaptation to the audio signal takes place only in
`the quantizer block. The quantizer adapts the step
`size based on the current step size and the quan-
`tizer output of the immediately previous input. This
`adaptation can be done as a sequence of two table
`lookups. The three bits representing the number of
`quantizer levels serve as an index into the first table
`lookup whose output is an index adjustment for the
`second table lookup. This adjustment is added to a
`stored index value, and the range-limited result is
`used as the index to the second table lookup. The
`summed index value is stored for use in the next
`iteration of the step-size adaptation. The output of
`the second table lookup is the new quantizer step
`size. Note that given a starting value for the in-
`dex into the second table lookup, the data used for
`adaptation is completely deducible from the quan-
`tizer outputs; side information is not required for
`the quantizer adaptation. Figure 4 illustrates a
`block diagram of the step-size adaptation process,
`and Tables 1 and 2 provide the table lookup con-
`tents.
`
`Table 1
`First Table Lookup for the IMA
`ADPCM Quantizer Adaptation
`
`Three Bits Quantized
`Magnitude
`
`Index Adjustment
`
`000
`
`001
`
`010
`
`011
`
`100
`
`101
`
`110
`
`111
`
`-1
`
`-1
`
`-1
`
`-1
`
`2
`
`4
`
`6
`
`8
`
`START
`
`SAMPLE < 0
`?
`
`NO
`
`BIT 3 = 0
`
`YES
`
`BIT 3 = 1;
`SAMPLE = – SAMPLE
`
`>–
`SAMPLE
` STEP SIZE
` ?
`
`YES
`
`BIT 2 = 1;
`SAMPLE =
` SAMPLE – STEP SIZE
`
`NO
`
`BIT 2 = 0
`
`>–
` SAMPLE
`STEP SIZE/2
` ?
`
`YES
`
`BIT 1 = 1;
`SAMPLE =
` SAMPLE – STEP SIZE/2
`
`NO
`
`BIT 1 = 0
`
`>–
` SAMPLE
`STEP SIZE/4
` ?
`
`NO
`
`BIT 0 = 0
`
`YES
`
`BIT 0 = 1
`
`DONE
`
`Figure 3 IMA ADPCM Quantization
`
`4 Digital Technical Journal Vol. 5No. 2,Spring1993
`
`

`
`Digital Audio Compression
`
`LOWER THREE
`BITS OF
`QUANTIZER
`OUTPUT
`
`FIRST
`TABLE
`LOOKUP
`
`INDEX
`ADJUSTMENT
`+
`
`+
`
`+
`
`LIMIT VALUE
`BETWEEN
`0 AND 88
`
`STEP
`SIZE
`
`SECOND
`TABLE
`LOOKUP
`
`DELAY FOR NEXT
`ITERATION OF
`STEP-SIZE
`ADAPTATION
`
`Figure 4 IMA ADPCM Step-size Adaptation
`
`Table 2
`Second Table Lookup for the IMA ADPCM Quantizer Adaptation
`
`Index
`
`Step Size
`
`Index
`
`Step Size
`
`Index
`
`Step Size
`
`Index
`
`Step Size
`
`0
`
`1
`
`2
`
`3
`
`4
`
`5
`
`6
`
`7
`
`8
`
`9
`
`7
`
`8
`
`9
`
`10
`
`11
`
`12
`
`13
`
`14
`
`16
`
`17
`
`22
`
`23
`
`24
`
`25
`
`26
`
`27
`
`28
`
`29
`
`30
`
`31
`
`60
`
`66
`
`73
`
`80
`
`88
`
`97
`
`107
`
`118
`
`130
`
`143
`
`44
`
`45
`
`46
`
`47
`
`48
`
`49
`
`50
`
`51
`
`52
`
`53
`
`494
`
`544
`
`598
`
`658
`
`724
`
`796
`
`876
`
`963
`
`1,060
`
`1,166
`
`66
`
`67
`
`68
`
`69
`
`70
`
`71
`
`72
`
`73
`
`74
`
`75
`
`4,026
`
`4,428
`
`4,871
`
`5,358
`
`5,894
`
`6,484
`
`7,132
`
`7,845
`
`8,630
`
`9,493
`
`10
`
`11
`
`12
`
`13
`
`14
`
`15
`
`16
`
`17
`
`18
`
`19
`
`20
`
`21
`
`19
`
`21
`
`23
`
`25
`
`28
`
`31
`
`34
`
`37
`
`41
`
`45
`
`50
`
`55
`
`32
`
`33
`
`34
`
`35
`
`36
`
`37
`
`38
`
`39
`
`40
`
`41
`
`42
`
`43
`
`157
`
`173
`
`190
`
`209
`
`230
`
`253
`
`279
`
`307
`
`337
`
`371
`
`408
`
`449
`
`54
`
`55
`
`56
`
`57
`
`58
`
`59
`
`60
`
`61
`
`62
`
`63
`
`64
`
`65
`
`1,282
`
`1,411
`
`1,552
`
`1,707
`
`1,878
`
`2,066
`
`2,272
`
`2,499
`
`2,749
`
`3,024
`
`3,327
`
`3,660
`
`76
`
`77
`
`78
`
`79
`
`80
`
`81
`
`82
`
`83
`
`84
`
`85
`
`86
`
`87
`
`88
`
`10,442
`
`11,487
`
`12,635
`
`13,899
`
`15,289
`
`16,818
`
`18,500
`
`20,350
`
`22,358
`
`24,623
`
`27,086
`
`29,794
`
`32,767
`
`Digital Technical Journal Vol. 5No. 2,Spring1993 5
`
`

`
`of the output wave form is unchanged unless the
`index to the second step-size table lookup is range
`limited. Range limiting results in a partial or full
`correction to the value of the step size.
`
`The nature of the step-size adaptation limits the
`impact of an error in the step size. Note that an er-
`ror in step_size[m+1] caused by an error in a single
`code word can be at most a change of (1.1)9, or 7.45
`dB in the value of the step size. Note also that any
`sequence of 88 code words that all have magnitude
`3 or less (refer to Table 1) completely corrects the
`step size to its minimum value. Even at the lowest
`audio sampling rate typically used, 8 kHz, 88 sam-
`ples correspond to 11 milliseconds of audio. Thus
`random access entry or edit points exist whenever
`11 milliseconds of low-level signal occur in the audio
`stream.
`
`MPEG/Audio Compression
`
`The Motion Picture Experts Group (MPEG) audio
`compression algorithm is an International Organi-
`zation for Standardization (ISO) standard for high-
`fidelity audio compression. It is one part of a three-
`part compression standard. With the other two
`parts, video and systems, the composite standard
`addresses the compression of synchronized video
`and audio at a total bit rate of roughly 1.5 megabits
`per second.
`
`Like -law and ADPCM, the MPEG/audio com-
`pression is lossy; however, the MPEG algorithm can
`achieve transparent, perceptually lossless compres-
`sion. The MPEG/audio committee conducted exten-
`sive subjective listening tests during the develop-
`ment of the standard. The tests showed that even
`with a 6-to-1 compression ratio (stereo, 16-bit-per-
`sample audio sampled at 48 kHz compressed to 256
`kilobits per second) and under optimal listening con-
`ditions, expert listeners were unable to distinguish
`between coded and original audio clips with statisti-
`cal significance. Furthermore, these clips were spe-
`cially chosen because they are difficult to compress.
`Grewin and Ryden give the details of the setup, pro-
`cedures, and results of these tests.[9]
`
`The high performance of this compression algo-
`rithm is due to the exploitation of auditory mask-
`ing. This masking is a perceptual weakness of
`the ear that occurs whenever the presence of a
`strong audio signal makes a spectral neighborhood
`of weaker audio signals imperceptible. This noise-
`masking phenomenon has been observed and cor-
`roborated through a variety of psychoacoustic ex-
`periments.[10]
`
`Digital Audio Compression
`
`IMA ADPCM: Error Recovery. A fortunate side
`effect of the design of this ADPCM scheme is that
`decoder errors caused by isolated code word errors
`or edits, splices, or random access of the compressed
`bit stream generally do not have a disastrous impact
`on decoder output. This is usually not true for com-
`pression schemes that use prediction. Since predic-
`tion relies on the correct decoding of previous audio
`samples, errors in the decoder tend to propagate.
`The next section explains why the error propagation
`is generally limited and not disastrous for the IMA
`algorithm. The decoder reconstructs the audio sam-
`ple, Xp[n], by adding the previously decoded audio
`sample, Xp[n—1]to the result of a signed magnitude
`product of the code word, C[n], and the quantizer
`step size plus an offset of one-half step size:
`
`Xp[n] = Xp[n—1] + step_size[n]  C’ [n]
`
`where C’ [n] = one-half plus a suitable numeric con-
`version of C [n].
`
`An analysis of the second step-size table lookup
`reveals that each successive entry is about 1.1 times
`the previous entry. As long as range limiting of the
`second table index does not take place, the value
`for step_size[n] is approximately the product of the
`previous value, step_size[n—1], and a function of
`the code word, F(C[n—1]):
`
`step_size[n]= step_size[n—1]  F(C[n—1])
`
`The above two equations can be manipulated to
`express the decoded audio sample, Xp[n], as a func-
`tion of the step size and the decoded sample value
`at time, m, and the set of code words between time,
`m, and n
`
`Xp[n] = Xp[m]+ step_size [m]
`
`F (C[j ])gC 0[i]
`
`iQ
`
`j=m+1
`
`f
`
`nP
`
`i=m+1
`
`
`
`Note that the terms in the summation are only a
`function of the code words from time m+1 onward.
`An error in the code word, C[q], or a random access
`entry into the bit stream at time q can result in an
`error in the decoded output, Xp[q], and the quan-
`tizer step size, step_size[q+1]. The above equation
`shows that an error in Xp[m] amounts to a constant
`offset to future values of Xp[n]. This offset is in-
`audible unless the decoded output exceeds its per-
`missible range and is clipped. Clipping results in
`a momentary audible distortion but also serves to
`correct partially or fully the offset term. Further-
`more, digital high-pass filtering of the decoder out-
`put can remove this constant offset term. The above
`equation also shows that an error in step_size[m+1]
`amounts to an unwanted gain or attenuation of fu-
`ture values of the decoded output Xp[n]. The shape
`
`6 Digital Technical Journal Vol. 5No. 2,Spring1993
`
`

`
`Empirical results also show that the ear has a lim-
`ited frequency selectivity that varies in acuity from
`less than 100 Hz for the lowest audible frequencies
`to more than 4 kHz for the highest. Thus the audi-
`ble spectrum can be partitioned into critical bands
`that reflect the resolving power of the ear as a func-
`tion of frequency. Table 3 gives a listing of critical
`bandwidths.
`
`Because of the ear’s limited frequency resolving
`power, the threshold for noise masking at any given
`frequency is solely dependent on the signal activity
`within a critical band of that frequency. Figure 5 il-
`lustrates this property. For audio compression, this
`property can be capitalized by transforming the au-
`dio signal into the frequency domain, then dividing
`the resulting spectrum into subbands that approx-
`imate critical bands, and finally quantizing each
`subband according to the audibility of quantization
`noise within that band. For optimal compression,
`each band should be quantized with no more lev-
`els than necessary to make the quantization noise
`inaudible. The following sections present a more
`detailed description of the MPEG/audio algorithm.
`
`MPEG/Audio Encoding and Decoding
`
`Figure 6 shows block diagrams of the MPEG/audio
`encoder and decoder.[11,12] In this high-level rep-
`resentation, encoding closely parallels the process
`described above. The input audio stream passes
`through a filter bank that divides the input into
`multiple subbands. The input audio stream simul-
`taneously passes through a psychoacoustic model
`that determines the signal-to-mask ratio of each
`subband. The bit or noise allocation block uses the
`signal-to-mask ratios to decide how to apportion the
`total number of code bits available for the quanti-
`zation of the subband signals to minimize the au-
`dibility of the quantization noise. Finally, the last
`block takes the representation of the quantized au-
`dio samples and formats the data into a decodable
`bit stream. The decoder simply reverses the for-
`matting, then reconstructs the quantized subband
`values, and finally transforms the set of subband
`values into a time-domain audio signal. As speci-
`fied by the MPEG requirements, ancillary data not
`necessarily related to the audio stream can be fitted
`within the coded bit stream.
`
`The MPEG/audio standard has three distinct lay-
`ers for compression. Layer I forms the most basic
`algorithm, and Layers II and III are enhancements
`that use some elements found in Layer I. Each suc-
`cessive layer improves the compression performance
`but at the cost of greater encoder and decoder com-
`plexity.
`
`Digital Audio Compression
`
`Layer I. The Layer I algorithm uses the basic filter
`bank found in all layers. This filter bank divides
`the audio signal into 32 constant-width frequency
`bands. The filters are relatively simple and pro-
`vide good time resolution with reasonable frequency
`resolution relative to the perceptual properties of
`the human ear. The design is a compromise with
`three notable concessions. First, the 32 constant-
`width bands do not accurately reflect the ear’s crit-
`ical bands. Figure 7 illustrates this discrepancy.
`The bandwidth is too wide for the lower frequencies
`so the number of quantizer bits cannot be specifi-
`cally tuned for the noise sensitivity within each crit-
`ical band. Instead, the included critical band with
`the greatest noise sensitivity dictates the number of
`quantization bits required for the entire filter band.
`Second, the filter bank and its inverse are not loss-
`less transformations. Even without quantization,
`the inverse transformation would not perfectly re-
`cover the original input signal. Fortunately, the er-
`ror introduced by the filter bank is small and inaudi-
`ble. Finally, adjacent filter bands have a significant
`frequency overlap. A signal at a single frequency
`can affect two adjacent filter bank outputs.
`
`Table 3
`Approximate Critical Band Boundaries
`
`Band Number
`
`Frequency
`(Hz)1
`
`Band Number
`
`Frequency
`(Hz)1
`
`0
`
`1
`
`2
`
`3
`
`4
`
`5
`
`6
`
`7
`
`8
`
`9
`
`10
`
`11
`
`12
`
`13
`
`50
`
`95
`
`140
`
`235
`
`330
`
`420
`
`560
`
`660
`
`800
`
`940
`
`1,125
`
`1,265
`
`1,500
`
`1,735
`
`14
`
`15
`
`16
`
`17
`
`18
`
`19
`
`20
`
`21
`
`22
`
`23
`
`24
`
`25
`
`26
`
`1Frequencies are at the upper end of the band.
`
`1,970
`
`2,340
`
`2,720
`
`3,280
`
`3,840
`
`4,690
`
`5,440
`
`6,375
`
`7,690
`
`9,375
`
`11,625
`
`15,375
`
`20,250
`
`Digital Technical Journal Vol. 5No. 2,Spring1993 7
`
`

`
`Digital Audio Compression
`
`STRONG TONAL SIGNAL
`
`(cid:0)
`
`REGION WHERE WEAKER
`SIGNALS ARE MASKED
`
`
`
`(cid:0)(cid:0)
`
`AMPLITUDE
`
`(cid:0)
`(cid:0)
`(cid:0)
`
`FREQUENCY
`
`Figure 5 Audio Noise Masking
`
`PCM AUDIO
`INPUT
`
`TIME-TO-FREQUENCY
`MAPPING FILTER
`BANK
`
`BIT/NOISE
`ALLOCATION,
`QUANTIZER, AND
`CODING
`
`BIT-STREAM
`FORMATTING
`
`ENCODED
`BIT STREAM
`
`PSYCHOACOUSTIC
`MODEL
`
`ANCILLARY DATA
`(OPTIONAL)
`
`(a) MPEG/Audio Encoder
`
`ENCODED
`BIT STREAM
`
`BIT-STREAM
`UNPACKING
`
`FREQUENCY
`SAMPLE
`RECONSTRUCTION
`
`FREQUENCY-TO-TIME
`MAPPING
`
`DECODED
`PCM AUDIO
`
`ANCILLARY DATA
`(IF ENCODED)
`
`(b) MPEG/Audio Decoder
`
`Figure 6 MPEG/Audio Compression and Decompression
`
`8 Digital Technical Journal Vol. 5No. 2,Spring1993
`
`

`
`Digital Audio Compression
`
`MPEG/AUDIO FILTER BANK BANDS
`
`0
`
`1
`
`2
`
`3
`
`4
`
`5
`
`6
`
`7
`
`8
`
`9
`
`10
`
`11
`
`12
`
`13
`
`14
`
`15
`
`16
`
`17
`
`18
`
`19
`
`20
`
`21
`
`22
`
`23
`
`24
`
`25
`
`26
`
`27
`
`28
`
`29
`
`30
`
`31
`
`17
`
`18
`
`19
`
`20
`
`21
`
`22
`
`23
`
`24
`
`25
`
`26
`
`CRITICAL BAND BOUNDARIES
`
`Figure 7 MPEG/Audio Filter Bandwidths versus Critical Bandwidths
`
`The filter bank provides 32 frequency samples, one
`sample per band, for every 32 input audio samples.
`The Layer I algorithm groups together 12 samples
`from each of the 32 bands. Each group of 12 sam-
`ples receives a bit allocation and, if the bit alloca-
`tion is not zero, a scale factor. Coding for stereo
`redundancy compression is slightly different and is
`discussed later in this paper. The bit allocation de-
`termines the number of bits used to represent each
`sample. The scale factor is a multiplier that sizes
`the samples to maximize the resolution of the quan-
`tizer. The Layer I encoder formats the 32 groups of
`12 samples (i.e., 384 samples) into a frame. Besides
`the audio data, each frame contains a header, an
`optional cyclic redundancy code (CRC) check word,
`and possibly ancillary data.
`
`Layer II. The Layer II algorithm is a simple en-
`hancement of Layer I. It improves compression per-
`formance by coding data in larger groups. The Layer
`II encoder forms frames of 3 by 12 by 32 = 1,152
`samples per audio channel. Whereas Layer I codes
`data in single groups of 12 samples for each sub-
`band, Layer II codes data in 3 groups of 12 samples
`for each subband. Again discounting stereo redun-
`dancy coding, there is one bit allocation and up to
`three scale factors for each trio of 12 samples. The
`encoder encodes with a unique scale factor for each
`group of 12 samples only if necessary to avoid audi-
`ble distortion. The encoder shares scale factor val-
`ues between two or all three groups in two other
`cases: (1) when the values of the scale factors are
`sufficiently close and (2) when the encoder antici-
`pates that temporal noise masking by the ear will
`hide the consequent distortion. The Layer II algo-
`rithm also improves performance over Layer I by
`representing the bit allocation, the scale factor val-
`ues, and the quantized samples with a more efficient
`code.
`
`Layer III. The Layer III algorithm is a much
`more refined approach.[13,14] Although based on
`the same filter bank found in Layers I and II, Layer
`III compensates for some filter bank deficiencies by
`processing the filter outputs with a modified discrete
`cosine transform (MDCT). Figure 8 shows a block
`diagram of the process.
`
`The MDCTs further subdivide the filter bank out-
`puts in frequency to provide better spectral resolu-
`tion. Because of the inevitable trade-off between
`time and frequency resolution, Layer III specifies
`two different MDCT block lengths: a long block of
`36 samples or a short block of 12. The short block
`length improves the time resolution to cope with
`transients. Note that the short block length is one-
`third that of a long block; when used, three short
`blocks replace a single long block. The switch be-
`tween long and short blocks is not instantaneous. A
`long block with a specialized long-to-short or short-
`to-long data window provides the transition mech-
`anism from a long to a short block. Layer III has
`three blocking modes: two modes where the outputs
`of the 32 filter banks can all pass through MDCTs
`with the same block length and a mixed block mode
`where the 2 lower-frequency bands use long blocks
`and the 30 upper bands use short blocks.
`
`Digital Technical Journal Vol. 5No. 2,Spring1993 9
`
`

`
`Digital Audio Compression
`
`PCM
`AUDIO
`INPUT
`
`LAYER I
`AND
`LAYER II
`FILTER
`BANK
`
`SUBBAND 0 MDCT
`WINDOW
`
`SUBBAND 1 MDCT
`WINDOW
`
`SUBBAND 31 MDCT
`WINDOW
`
`MDCT
`
`MDCT
`
`MDCT
`
`ALIAS
`REDUCTION
`(ONLY FOR
`LONG
`BLOCKS)
`
`LONG, LONG-TO-SHORT
`SHORT, SHORT-TO-LONG
`WINDOW SELECT
`
`LONG OR SHORT BLOCK
`CONTROL (FROM
`PSYCHOACOUSTIC MODEL)
`
`Figure 8 MPEG/Audio Layer III Filter Bank Processing, Encoder Side
`
`Other major enhancements over the Layer I and
`Layer II algorithms include:
`
`is actually calculated and specifically allocated to
`each subband.
`
`• Alias reduction — Layer III specifies a method
`of processing the MDCT values to remove some
`redundancy caused by the overlapping bands of
`the Layer I and Layer II filter bank.
`
`• Nonuniform quantization — The Layer III quan-
`tizer raises its input to the 3/4 power before quan-
`tization to provide a more consistent signal-to-
`noise ratio over the range of quantizer values.
`The requantizer in the MPEG/audio decoder re-
`linearizes the values by raising its output to the
`4/3 power.
`
`• Entropy coding of data values — Layer III uses
`Huffman codes to encode the quantized samples
`for better data compression.[15]
`
`• Use of a bit reservoir — The design of the Layer
`III bit stream better fits the variable length na-
`ture of the compressed data. As with Layer II,
`Layer III processes the audio data in frames of
`1,152 samples. Unlike Layer II, the coded data
`representing these samples does not necessar-
`ily fit into a fixed-length frame in the code bit
`stream. The encoder can donate bits to or bor-
`row bits from the reservoir when appropriate.
`
`• Noise allocation instead of bit allocation — The
`bit allocation process used by Layers I and II
`only approximates the amount of noise caused
`by quantization to a given number of bits. The
`Layer III encoder uses a noise allocation iteration
`loop. In this loop, the quantizers are varied in an
`orderly way, and the resulting quantization noise
`
`The Psychoacoustic Model
`
`The psychoacoustic model is the key component
`of the MPEG encoder that enables its high perfor-
`mance.[16,17,18,19] The job of the psychoacoustic
`model is to analyze the input audio signal and de-
`termine where in the spectrum quantization noise
`will be masked and to what extent. The encoder
`uses this information to decide how best to repre-
`sent the input audio signal with its limited number
`of code bits. The MPEG/audio standard provides
`two example implementations of the psychoacoustic
`model. Below is a general outline of the basic steps
`involved in the psychoacoustic calculations for ei-
`ther model.
`
`• Time align audio data — The psychoacoustic
`model must account for both the delay of the au-
`dio data through the filter bank and a data off-
`set so that the relevant data is centered within
`its analysis window. For example, when using
`psychoacoustic model two for Layer I, the de-
`lay through the filter bank is 256 samples, and
`the offset required to center the 384 samples of
`a Layer I frame in the 512-point psychoacoustic
`analysis window is (512 — 384)/2 = 64 points.
`The net offset is 320 points to time align the psy-
`choacoustic model data with the filter bank out-
`puts.
`
`• Convert audio to spectral domain — The psy-
`choacoustic model uses a time-to-frequency map-
`ping such as a 512- or 1,024-point Fourier trans-
`
`10 Digital Technical Journal Vol. 5No. 2,Spring1993
`
`

`
`form. A standard Hann weighting, applied to
`audio data before Fourier transformation, condi-
`tions the data to reduce the edge effects of the
`transform window. The model uses this sepa-
`rate and independent mapping instead of the fil-
`ter bank outputs because it needs finer frequency
`resolution to calculate the masking thresholds.
`• Partition spectral values into critical bands —
`To simplify the psychoacoustic calculations, the
`model groups the frequency values into percep-
`tual quanta.
`• Incorporate threshold in quiet — The model in-
`cludes an empirically determined absolute mask-
`ing threshold. This threshold is the lower bound
`for noise masking and is determined in the ab-
`sence of masking signals.
`• Separate into tonal and nontonal components —
`The model must identify and separate the tonal
`and noiselike components of the audio signal be-
`cause the noise-masking characteristics of the
`two types of signal are different.
`• Apply spreading function — The model deter-
`mines the noise-masking thresholds by applying
`an empirically determined masking or spreading
`function to the signal components.
`• Find the minimum masking threshold for each
`subband — The psychoacoustic model calculates
`the masking thresholds with a higher-frequency
`resolution than provided by the filter banks.
`Where the filter band is wide relative to the crit-
`