Audio Coding and MP3 - folk.uio.nofolk.uio.no/inf5080/mkt04a-audio.pdf · Audio Coding and MP3 Wolfgang Leister ... Ideal sub-band coder ... nMicrosoft Windows Media Audio (WMA) nAC-3

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Norsk Regnesentral

Audio Coding and MP3

Wolfgang Leistercontributions by:

Torbjørn Ekman

26-Feb-03

Norsk RegnesentralWolfgang Leister

What is Sound?

n Sound waves: 20Hz - 20kHzn Speed: 331.3 m/s (air)n Wavelength: 165 cm - 1.65 cm

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Analogue audio

n frequencies: 20Hz - 20kHzn mono: x(t) scalarn stereo:

=

)(

)()(

tx

txtx

l

r

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Audio Compression

n small files, low data rate at transmissionn reconstruction must be (as much as

possible) equal to original signaln redundancy (lossless coding)n irrelevancy (do not code what you cannot hear)

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Data rates

Quality Sample Rate Bit/Sample Channels Data Rate kb/s FrequencyTelephone 8.000 8 Mono 64,00 200-3400MW 11.025 8 Mono 88,00UKW 22.050 16 Stereo 705,60CD 44.100 16 Stereo 1411,00 20-20000DAT 48.000 16 Stereo 1536,00 20-20000

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Dynamics compression

n A-Law

+⋅+

⋅

≤+⋅

⋅=

else ln1

))(ln(1)(

1for

ln1)(

)('

ASabsA

Ssign

Aabs(S)

ASabsA

SsignS

n µ-Law

255,)1ln(

))(1ln(1)(' =

+⋅++

⋅= µµ

µ SabsSsignS

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Masking

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Masking

n Threshold for human earn Threshold changes:

n neighbouring frequencies(Example 0.5, 1, 4, 8 kHz)

n in time

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Sampling

• When x(t) is bandwidth limited:

• then

• with

0)( =⇒> fxf ω

[ ]∑∞

−∞=

∆⋅−=n

tntgnxtx )()(

ω211

<=∆sf

t [ ] )( tnxnx ∆⋅= tttg

πωπω

2)2sin()( =

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Quantisation

n

n

n

n

)(xQx → tionsrepresenta2Lbits k=⇒k

iji yxQyxyx =⇒−≤− )(

{ }nyy ,,1 K

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PCM = Pulse Code Modulation

n Sampling:n Quantisation:n Coding:

n Play:

{ } [ ]{ }nxtx →)(

[ ]{ } [ ]( ){ }nxQnx →

[ ]{ }( ) { }innxQ →

( ) [ ]( ) ( )tntgnxQty ii ∆⋅−⋅= ∑

redundancy

irrelevancy

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Stereo CD Audio

n Data rate: 1-31044.1bit162 −⋅⋅⋅ s

sbit

102.1411 3⋅=

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MPEG compression factors

n MPEG 1 Audio: PCM 32, 44.1, 48 kHz, max 448 kBit/s

n MPEG 2 Audio: PCM 16, 22.05, 24, 32, 44.1, 48 kHz, max 384 KBit/s

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MPEG Audio Layer I,II,III

n Layer In Layer II ⇒ Digital TVn Layer III ⇒ MP3

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MP3 - MPEG 1 Audio Layer 3

n Sampling: 16 kHz - 48 kHzn Bit rate: 32 kb/s - 192 kb/s

(CD Audio: 44.1 kHz, 1411 kb/s)

n www.iis.fhg.de/amm/gallery/index.htmln Karlheinz Brandenburg: “MP3 and AAC

explained”http://www.exp-math.uni-essen.de/~dreibh/diplom/bra99.pdf

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perceptual encoding / decoding

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Filterbank

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Ideal sub-band coder

n impossible: ideal sub-band codern downsampling ⇒ aliasingn possible: “nearly perfect”

=∈

=else0

,,1,ffor 1)(

MmDf m

mHK

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Downsampling

n from back ton sub-bandwidth B, upper frequency is multiple of B

n can sample at (instead of )

Bfs 2=

sf

BMfs ⋅= 2

sfM ⋅

↓M

[ ] [ ]Mkxky mm ⋅=

[ ]nxm [ ]kym

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Filterbank in MPEG-1 audio layer 1-3

n Polyphase filterbankn 32 subbandsn 512 tap FIR-filtersn 80 + and * per output

n Equal widthn Not perfect reconstructionn Frequency overlap

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A closer look

n The subbands overlap at 3 dB to the adjacent bands.n The leakage to the other bands is small.n The total response almost adds up to one (0 dB).

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White noisen The white noise run

through the filterbank.n The samples from each

band are played in the order of the subbands.

n The subsampled filtered sequence.

n The samples from eachband are played in the order of the subbands.

n The reconstruction error is –84 dB.

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Nonideal filterbanks

n In a perfect filterbankthe first part is the only part.

n The second part consists of the aliasing terms.

n The filterbank is designed so that the aliasing is small.

+=

≈

−

=∑

4444 34444 211

1

0

)()(1

)()( ωωωω jAk

jM

k

Rk

jj eHeHM

eXeY

44444 344444 210

21

0

1

1

2

)()(1

)(

≈

−−

=

−

=

−

∑∑ Mn

jAk

jM

k

Rk

M

n

Mn

jeHeH

MeX

πω

ωπ

ω

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Tubthumper, a time domain view

The red line is the reconstruction error after splitting the signal in subbands, down sampling and applying the synthesisfilterbank. The reconstruction error is –84 dB and sounds like

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Tubthumper, frequency view

Subsampled 32 times

No subsampling

21.710.75.22.41.00.3Center frequency[kHz]

32168421Subband

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Filterbank MPEGpolyphase

filterbank

12 samples

band 1

band 2

band 31

...

12 samples 12 samples

Layer I frame

384 samples

Layer II/III frame

1152 samples

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Critical Bands

n Heinrich Barkhausen (1881-1956)n psycho-acousticn width measured in bark

⋅+

<=

elsef

fforfbark

)1000/log(49

500100/1

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MPEG - Sub bands

n Layer I: 32 bands, 625 Hz each, Fourier transform

n Layer II: 32 bands, three frames, time masking

n Layer III: Division according to critical bands

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MPEG masking

n Psycho-acoustic modeln masking of neighbouring bandsn signals are coded when above masking

thresholdn MUSICAM (Masking-pattern adapted

Universal Subband Integrated Coding and Multiplexing)

n Layer I: simplified, Layer II: entirely, Layer III: with other methods

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2035

Example: Masking MPEG Audio

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 8 12 10 6 2 10 60 15 2 3 5 3 1

bandlevel

?15? ? ? ? ? ? 12 x ? ? ? ? ? ?masking

?x? ? ? ? ? ? - x ? ? ? ? ? ?coding

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MPEG-1 Layer 3 encoder

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MP3

n Filter bank - sub bandsn Series MDCTn fine grain frequency resolutionn non-uniform quantisationn perception model n Huffman coding

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MP3 (vs. Layer I/II)

n modified DCT (Series MDCT vs. FFT)

n critical bandsn Huffman codingn entropy reductionn dynamics compressionn difference and sum of stereo signals

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MPEG Audio Layer I,II,III

n Layer I: 19 ms delay, FFT, 384 samples, frequency masking, equal bands

n Layer II: 35 ms delay, FFT, 1152 samples, frequency masking, time simulated, equal bands

n Layer III: 59 ms delay, DCT, 1152 samples, frequency and time masking, bands as in bark scale

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MPEG Layer I, II, III

subj. quality bandwidth compression 1 min audioAudio CD CD 1400 1:1 10.58 MBMPEG1 Layer I CD 384 3.6:1 2.88 MBMPEG1 Layer II CD 256 5.5:1 1.92 MBMPEG1 Layer III CD 128 11:1 962 kBMPEG2 Layer III Radio 64 22:1 481 kBMPEG2 Layer III Telephone 16 88:1 120 kBCS-ACELP Speech 5,30 264:1 40 kB

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MPEG-2 AAC

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Audio Formats

n PCM - Pulse Code ModulationITU G.711; speech data 4kHz bandwidth, 64 kb/s

data rate

n ADPCM (Adaptive Differential PCM)ITU G.726, G.727; 16, 24, 32, 40 kBit/s. Standard

for CCITT G.721

n SB-ADPCM (Sub-Band ADPCM)ISDN, G.722; 7 kHz bandwidth in 64 kBit/s streams

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Audio Formats

n AIFF - Audio Interchange File FormatApple (extension from IFF by Electronic Arts)

n Wave (by Microsoft and IBM)Part of RIFF (Resource Interchange File Format)

n NeXT/Sun Audio File Format! big endian

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Proprietary Audio Formats

n AT&T Proprietary Compression Algorithm

n EPAC (Bell Labs)n Microsoft Windows Media Audio (WMA)n AC-3 Audio Code No. 3 - Dolby Digital

Surround

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Speech compression formats

n GSM 06-10: 160 13-bit values in 260 Bit (33 Byte) are compressed; 8000 samples/s result in data rate of 1650 Byte/s

n CELP (Code Excited Linear Prediction): analytical model

n LD-CELP (Low Delay CELP): G.728n LPC-10E (Linear Prediction Coder

(Enhanced): military coder, analytical model, 2.4 kBit/s understandable, but low quality.

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End of Part

Thank you for your attention!

Documents

Audio Coding and MP3 - folk.uio.nofolk.uio.no/inf5080/mkt04a-audio.pdf · Audio Coding and MP3 Wolfgang Leister ... Ideal sub-band coder ... nMicrosoft Windows Media Audio (WMA) nAC-3