ISO/IEC 14496-3:2005/Amd 9:2008
(Amendment)Information technology - Coding of audio-visual objects - Part 3: Audio - Amendment 9: Enhanced low delay AAC
Information technology - Coding of audio-visual objects - Part 3: Audio - Amendment 9: Enhanced low delay AAC
Technologies de l'information — Codage des objets audiovisuels — Partie 3: Codage audio — Amendement 9: Retard faible amélioré AAC
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Frequently Asked Questions
ISO/IEC 14496-3:2005/Amd 9:2008 is a standard published by the International Organization for Standardization (ISO). Its full title is "Information technology - Coding of audio-visual objects - Part 3: Audio - Amendment 9: Enhanced low delay AAC". This standard covers: Information technology - Coding of audio-visual objects - Part 3: Audio - Amendment 9: Enhanced low delay AAC
Information technology - Coding of audio-visual objects - Part 3: Audio - Amendment 9: Enhanced low delay AAC
ISO/IEC 14496-3:2005/Amd 9:2008 is classified under the following ICS (International Classification for Standards) categories: 35.040 - Information coding; 35.040.40 - Coding of audio, video, multimedia and hypermedia information. The ICS classification helps identify the subject area and facilitates finding related standards.
ISO/IEC 14496-3:2005/Amd 9:2008 has the following relationships with other standards: It is inter standard links to ISO/IEC 14496-3:2005, ISO/IEC 14496-3:2009; is excused to ISO/IEC 14496-3:2005. Understanding these relationships helps ensure you are using the most current and applicable version of the standard.
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Standards Content (Sample)
INTERNATIONAL ISO/IEC
STANDARD 14496-3
Third edition
2005-12-01
AMENDMENT 9
2008-07-01
Information technology — Coding of
audio-visual objects
Part 3:
Audio
AMENDMENT 9: Enhanced low delay AAC
Technologies de l'information — Codage des objets audiovisuels
Partie 3: Codage audio
AMENDEMENT 9: Retard faible amélioré AAC
Reference number
ISO/IEC 14496-3:2005/Amd.9:2008(E)
©
ISO/IEC 2008
ISO/IEC 14496-3:2005/Amd.9:2008(E)
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ii © ISO/IEC 2008 – All rights reserved
ISO/IEC 14496-3:2005/Amd.9:2008(E)
Foreword
ISO (the International Organization for Standardization) and IEC (the International Electrotechnical
Commission) form the specialized system for worldwide standardization. National bodies that are members of
ISO or IEC participate in the development of International Standards through technical committees
established by the respective organization to deal with particular fields of technical activity. ISO and IEC
technical committees collaborate in fields of mutual interest. Other international organizations, governmental
and non-governmental, in liaison with ISO and IEC, also take part in the work. In the field of information
technology, ISO and IEC have established a joint technical committee, ISO/IEC JTC 1.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of the joint technical committee is to prepare International Standards. Draft International
Standards adopted by the joint technical committee are circulated to national bodies for voting. Publication as
an International Standard requires approval by at least 75 % of the national bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO and IEC shall not be held responsible for identifying any or all such patent rights.
Amendment 9 to ISO/IEC 14496-3:2005 was prepared by Joint Technical Committee ISO/IEC JTC 1,
Information technology, Subcommittee SC 29, Coding of audio, picture, multimedia and hypermedia
information.
© ISO/IEC 2008 – All rights reserved iii
ISO/IEC 14496-3:2005/Amd.9:2008(E)
Information technology — Coding of audio-visual objects
Part 3:
Audio
AMENDMENT 9: Enhanced low delay AAC
In the following, changes in existing text and tables are highlighted by grey background.
In 1.5.1.1, extend Table 1.1 with the following entries:
Table 1.1 — Audio Object Type definition based on Tools/Modules
Audio
Object
Type
…
ER AAC
39 X X X X X X X X X X X
ELD
40- (reserv-
95 ed)
Before 1.5.2, add 1.5.1.2.37:
1.5.1.2.37 Error Resilient (ER) AAC ELD object type
The enhanced low delay AAC object type (ER AAC ELD) is identical to the ER AAC LD object type, plus the
utilization of a Low Delay Filterbank (LDFB) and an enhanced low delay window. It also permits combinations
with the PNS tool as well as the Low Delay SBR tool. The ER AAC ELD object type provides the ability to
extend the usage of generic low bitrate audio coding to applications requiring a very low delay of the encoding
/ decoding chain (e.g. full-duplex real-time communications).”
In 1.5.2.4, insert the following new entries for the Baseline MPEG Surround Profile into Table 1.12
audioProfileLevelIndication and adapt the “reserved for ISO use” range accordingly (changes are highlighted
in gray):
© ISO/IEC 2008 – All rights reserved 1
Object Type ID
gain control
block switching
window shapes - standard
window shapes – AAC LD
Low Delay Window
filterbank - standard
filterbank - SSR
TNS
LTP
intensity
coupling
frequency deomain prediction
PNS
MS
SIAQ
FSS
upsampling filter tool
quantisation&coding - AAC
quantisation&coding – TwinVQ
quantisation&coding - BSAC
AAC ER Tools
ER payload syntax
EP Tool 1)
CELP
Silence Compression
HVXC
HVXC 4kbit/s VR
SA tools
SASBF
MIDI
HILN
TTSI
SBR
Layer-1
Layer-2
Layer-3
SSC (Transient, Sinusoid, Noise)
Parametric stereo
Low Delay SBR
Remark
ISO/IEC 14496-3:2005/Amd.9:2008(E)
Value Profile Level
… … …
0x33 High Efficiency AAC v2 Profile L5
0x34 Low Delay AAC Profile L1
0x35 Baseline MPEG Surround Profile (see ISO/IEC 23003-1) L1
0x36 Baseline MPEG Surround Profile (see ISO/IEC 23003-1) L2
0x37 Baseline MPEG Surround Profile (see ISO/IEC 23003-1) L3
0x38 Baseline MPEG Surround Profile (see ISO/IEC 23003-1) L4
0x39 Baseline MPEG Surround Profile (see ISO/IEC 23003-1) L5
0x3A Baseline MPEG Surround Profile (see ISO/IEC 23003-1) L6
0x3B - 0x7F reserved for ISO use -
0x80 - 0xFD user private -
0xFE no audio profile specified -
0xFF no audio capability required -
NOTE — Usage of the value 0xFE indicates that the content described by this
InitialObjectDescriptor does not comply to any audio profile specified in ISO/IEC 14496-3.
Usage of the value 0xFF indicates that none of the audio profile capabilities are required for
this content.
In 1.6.2.1, extend Table 1.13 “AudioSpecificConfig()” as follows:
Table 1.13 — Syntax of AudioSpecificConfig()
Syntax No. of bits Mnemonic
AudioSpecificConfig ()
{
audioObjectType = GetAudioObjectType();
samplingFrequencyIndex; 4 bslbf
if ( samplingFrequencyIndex == 0xf ) {
samplingFrequency; 24 uimsbf
}
channelConfiguration; 4 bslbf
sbrPresentFlag = -1;
psPresentFlag = -1;
if ( audioObjectType == 5 ||
audioObjectType == 29 ) {
extensionAudioObjectType = audioObjectType;
sbrPresentFlag = 1;
if ( audioObjectType == 29 ) {
psPresentFlag = 1;
}
extensionSamplingFrequencyIndex; 4 uimsbf
if ( extensionSamplingFrequencyIndex == 0xf )
extensionSamplingFrequency; 24 uimsbf
audioObjectType = GetAudioObjectType();
}
else {
extensionAudioObjectType = 0;
}
switch (audioObjectType) {
2 © ISO/IEC 2008 – All rights reserved
ISO/IEC 14496-3:2005/Amd.9:2008(E)
case 1:
case 2:
case 3:
case 4:
case 6:
case 7:
case 17:
case 19:
case 20:
case 21:
case 22:
case 23:
GASpecificConfig();
break:
case 8:
CelpSpecificConfig();
break;
case 9:
HvxcSpecificConfig();
break:
case 12:
TTSSpecificConfig();
break;
case 13:
case 14:
case 15:
case 16:
StructuredAudioSpecificConfig();
break;
case 24:
ErrorResilientCelpSpecificConfig();
break;
case 25:
ErrorResilientHvxcSpecificConfig();
break;
case 26:
case 27:
ParametricSpecificConfig();
break;
case 28:
SSCSpecificConfig();
break;
case 32:
case 33:
case 34:
MPEG_1_2_SpecificConfig();
break;
case 35:
DSTSpecificConfig();
break;
case 36:
fillBits; 5 bslbf
ALSSpecificConfig();
break;
case 37:
case 38:
SLSSpecificConfig();
break;
case 39:
© ISO/IEC 2008 – All rights reserved 3
ISO/IEC 14496-3:2005/Amd.9:2008(E)
ELDSpecificConfig(channelConfiguration);
break;
default:
/* reserved */
}
switch (audioObjectType) {
case 17:
case 19:
case 20:
case 21:
case 22:
case 23:
case 24:
case 25:
case 26:
case 27:
case 39:
epConfig; 2 bslbf
if ( epConfig == 2 || epConfig == 3 ) {
ErrorProtectionSpecificConfig();
}
if ( epConfig == 3 )
directMapping; 1 bslbf
if ( ! directMapping ) {
/* tbd */
}
}
}
if ( extensionAudioObjectType != 5 && bits_to_decode() >= 16 ) {
syncExtensionType; 11 bslbf
if (syncExtensionType == 0x2b7) {
extensionAudioObjectType = GetAudioObjectType();
if ( extensionAudioObjectType == 5 ) {
sbrPresentFlag; 1 uimsbf
if (sbrPresentFlag == 1) {
extensionSamplingFrequencyIndex; 4 uimsbf
if ( extensionSamplingFrequencyIndex == 0xf ) {
extensionSamplingFrequency; 24 uimsbf
}
if ( bits_to_decode() >= 12 ) {
syncExtensionType; 11 bslbf
if (syncExtensionType == 0x548) {
psPresentFlag; 1 uimsbf
}
}
}
}
}
}
4 © ISO/IEC 2008 – All rights reserved
ISO/IEC 14496-3:2005/Amd.9:2008(E)
In 1.6.2.2.1, extend Table 1.15 “Audio Object Types” as follows:
Table 1.15 — Audio Object Types
Object Audio Object definition of elementary stream Mapping of audio payloads to access
Type ID Type payloads and detailed syntax units and elementary streams
… … … …
39 ER AAC ELD ISO/IEC 14496-3 subpart 4 see subclause 1.6.2.2.2.4
Add 1.6.2.2.4 with the title "ER AAC ELD":
1.6.2.2.2 .4 ER AAC ELD
The top level payload for ER AAC ELD is defined in er_raw_data_block_eld(). All definitions mentioned in
subclause 1.6.2.2.2.3 are also valid for this AOT.
At the end of 1.6.5.1, add a sentence:
“NOTE: None of these signaling methods described in this subclause is allowed for AAC ELD in order to
signal the low delay sbr tool. For this case the ldSbrPresentFlag in the ELDSpecificConfig is to be used”
Before 4.5, insert Tables AMD9.2 to AMD9.8:
Table AMD9.2 — Syntax of top level payload for audio object types ER AAC ELD
(er_raw_data_block_eld())
Syntax No. of bits Mnemonic
er_raw_data_block_eld(channelConfiguration)
{
switch(channelConfiguration) {
case 1:
single_channel_element_eld();
break;
case 2:
channel_pair_element_eld ();
break;
case 3:
single_channel_element_eld ();
channel_pair_element_eld ();
break;
case 4:
single_channel_element_eld ();
channel_pair_element_eld ();
single_channel_element_eld ();
break;
© ISO/IEC 2008 – All rights reserved 5
ISO/IEC 14496-3:2005/Amd.9:2008(E)
case 5:
single_channel_element_eld ();
channel_pair_element_eld ();
channel_pair_element_eld ();
break;
case 6:
single_channel_element_eld ();
channel_pair_element_eld ();
channel_pair_element_eld ();
lfe_channel_element_eld ();
break;
case 7:
single_channel_element_eld ();
channel_pair_element_eld ();
channel_pair_element_eld ();
channel_pair_element_eld ();
lfe_channel_element_eld ();
break;
default:
/* reserved */
break;
}
if (ldSbrPresentFlag) {
er_low_delay_sbr_block(channelConfiguration);
}
cnt = bits_to_decode() / 8;
while ( cnt >= 1 ) {
cnt -= extension_payload(cnt);
}
byte_alignment();
}
Table AMD9.3 — Syntax of single_channel_element_eld()
Syntax No. of bits Mnemonic
single_channel_element_eld()
{
individual_channel_stream_eld (0);
}
Table AMD9.4 — Syntax of lfe_channel_element_eld()
Syntax No. of bits Mnemonic
lfe_channel_element_eld()
{
individual_channel_stream_eld (0);
}
6 © ISO/IEC 2008 – All rights reserved
ISO/IEC 14496-3:2005/Amd.9:2008(E)
Table AMD9.5 — Syntax of channel_pair_element_eld()
Syntax No. of bits Mnemonic
channel_pair_element_eld()
{
common_window = 1;
max_sfb; 6 uimsbf
ms_mask_present; 2 uimsbf
if ( ms_mask_present == 1 ) {
for (sfb = 0; sfb < max_sfb; sfb++) {
ms_used[0][sfb]; 1 uimsbf
}
}
individual_channel_stream_eld (common_window);
individual_channel_stream_eld (common_window);
}
Table AMD9.6 — Syntax of individual_channel_stream_eld()
Syntax No. of bits Mnemonic
individual_channel_stream_eld (common_window)
{
global_gain; 8 uimsbf
if (! common_window) {
max_sfb; 6 uimsbf
}
section_data ();
scale_factor_data ();
tns_data_present; 1 uimsbf
if (tns_data_present) {
tns_data ();
}
if (! aacSpectralDataResilienceFlag) {
spectral_data ();
}
else {
length_of_reordered_spectral_data; 14 uimsbf
length_of_longest_codeword; 6 uimsbf
reordered_spectral_data ();
}
}
© ISO/IEC 2008 – All rights reserved 7
ISO/IEC 14496-3:2005/Amd.9:2008(E)
Table AMD9.7 — Syntax of er_low_delay_sbr_block
Syntax No. of bits Mnemonic
er_low_delay_sbr_block(channelConfiguration)
{
switch (channelConfiguration) {
case 1:
low_delay_sbr_data(ID_SCE, ldSbrCrcFlag, bs_amp_res);
break;
case 2:
low_delay_sbr_data(ID_CPE, ldSbrCrcFlag, bs_amp_res);
break;
case 3:
low_delay_sbr_data(ID_SCE, ldSbrCrcFlag, bs_amp_res);
low_delay_sbr_data(ID_CPE, ldSbrCrcFlag, bs_amp_res);
break;
case 4:
low_delay_sbr_data(ID_SCE, ldSbrCrcFlag, bs_amp_res);
low_delay_sbr_data(ID_CPE, ldSbrCrcFlag, bs_amp_res);
low_delay_sbr_data(ID_SCE, ldSbrCrcFlag, bs_amp_res);
break;
case 5:
low_delay_sbr_data(ID_SCE, ldSbrCrcFlag, bs_amp_res);
low_delay_sbr_data(ID_CPE, ldSbrCrcFlag, bs_amp_res);
low_delay_sbr_data(ID_CPE, ldSbrCrcFlag, bs_amp_res);
break;
case 6:
low_delay_sbr_data(ID_SCE, ldSbrCrcFlag, bs_amp_res);
low_delay_sbr_data(ID_CPE, ldSbrCrcFlag, bs_amp_res);
low_delay_sbr_data(ID_CPE, ldSbrCrcFlag, bs_amp_res);
break;
case 7:
low_delay_sbr_data(ID_SCE, ldSbrCrcFlag, bs_amp_res);
low_delay_sbr_data(ID_CPE, ldSbrCrcFlag, bs_amp_res);
low_delay_sbr_data(ID_CPE, ldSbrCrcFlag, bs_amp_res);
low_delay_sbr_data(ID_CPE, ldSbrCrcFlag, bs_amp_res);
break;
default:
/* reserved */
break;
}
}
8 © ISO/IEC 2008 – All rights reserved
ISO/IEC 14496-3:2005/Amd.9:2008(E)
Table AMD9.8 — Syntax of low_delay_sbr_data()
Syntax No. of bits Mnemonic
low_delay_sbr_data(id_aac, ldSbrCrcFlag, bs_amp_res)
{
if (ldSbrCrcFlag) {
bs_sbr_crc_bits; 10 uimsbf
}
if (bs_header_flag) { 1
sbr_header();
}
If (id_aac==ID_SCE) {
sbr_single_channel_element(bs_amp_res);
} else if (id_aac==ID_CPE) {
sbr_channel_pair_element(bs_amp_res);
}
}
Note 1: bs_amp_res is in general transmitted inside sbr_header() function enclosed in the
ELDSpecificConfig(). But the parameter can be updated by the sbr_header() function here.
Extend Table 4.142 as followings:
Table 4.142 — AAC error sensitivity category assignment for extended payload and low delay sbr
payload
6 - drc_band_top dynamic_range_info()
6 - drc_bands_incr dynamic_range_info()
6 - drc_bands_present dynamic_range_info()
6 - drc_bands_reserved_bits dynamic_range_info()
6 - drc_tag_reserved_bits dynamic_range_info()
6 - dyn_rng_ct dynamic_range_info()
6 - dyn_rng_sgn dynamic_range_info()
6 - excluded_chns_present dynamic_range_info()
6 - pce_instance_tag dynamic_range_info()
6 - pce_tag_present dynamic_range_info()
6 - prog_ref_level dynamic_range_info()
6 - prog_ref_level_present dynamic_range_info()
6 - prog_ref_level_reserved_bits dynamic_range_info()
6 - additional_excluded_chns excluded_channels()
6 - exclude_mask excluded_channels()
5 - extension_type Extension_payload()
5 - data_element_version Extension_payload()
7 - fill_byte Extension_payload()
7 - fill_nibble Extension_payload()
7 - other_bits Extension_payload()
8 - dataElementLengthPart Extension_payload()
8 - data_element_byte extension_payload()
© ISO/IEC 2008 – All rights reserved 9
extension_payload
low delay sbr payload
data_element
Function
ISO/IEC 14496-3:2005/Amd.9:2008(E)
9 - bs_sbr_crc_bits sbr_extension_data()
9 - bs_header_flag sbr_extension_data()
9 - bs_fill_bits sbr_extension_data()
9 9 bs_amp_res sbr_header()
9 9 bs_start_freq sbr_header()
9 9 bs_stop_freq sbr_header()
9 9 bs_xover_band sbr_header()
9 9 bs_reserved sbr_header()
9 9 bs_header_extra_1 sbr_header()
9 9 bs_header_extra_2 sbr_header()
9 9 bs_freq_scale sbr_header()
9 9 bs_alter_scale sbr_header()
9 9 bs_noise_bands sbr_header()
9 9 bs_limiter_bands sbr_header()
9 9 bs_limiter_gains sbr_header()
9 9 bs_interpol_freq sbr_header()
9 9 bs_smoothing_mode sbr_header()
9 9 bs_data_extra sbr_single_channel_element()
9 9 bs_reserved sbr_single_channel_element()
9 10 bs_add_harmonic_flag sbr_single_channel_element()
9 10 bs_extended_data sbr_single_channel_element()
9 10 bs_extension_size sbr_single_channel_element()
9 10 bs_esc_count sbr_single_channel_element()
9 10 bs_extension_id sbr_single_channel_element()
9 9 bs_data_extra sbr_channel_pair_element()
9 9 bs_reserved sbr_channel_pair_element()
9 9 bs_coupling sbr_channel_pair_element()
9 10 bs_add_harmonic_flag sbr_channel_pair_element()
9 10 bs_extended_data sbr_channel_pair_element()
9 10 bs_extension_size sbr_channel_pair_element()
9 10 bs_esc_count sbr_channel_pair_element()
9 10 bs_extension_id sbr_channel_pair_element()
9 - bs_frame_class sbr_grid()
9 - tmp sbr_grid()
9 - bs_freq_res sbr_grid()
9 - bs_pointer sbr_grid()
9 - bs_var_bord_0 sbr_grid()
9 - bs_var_bord_1 sbr_grid()
9 - bs_num_rel_0 sbr_grid()
9 - bs_num_rel_1 sbr_grid()
9 9 bs_df_env sbr_dtdf()
9 9 bs_df_noise sbr_dtdf()
9 10 bs_invf_mode sbr_invf()
9 10 bs_env_start_value_balance sbr_envelope()
9 10 bs_env_start_value_level sbr_envelope()
9 10 bs_codeword sbr_envelope()
9 10 bs_noise_start_value_balanc sbr_noise()
e
9 10 bs_noise_start_value_level sbr_noise()
9 10 bs_codeword sbr_noise()
9 10 bs_add_harmonic sbr_sinusoidal_coding()
- 9 bs_frame_class sbr_ld_grid()
- 9 tmp sbr_ld_grid()
- 9 bs_freq_res sbr_ld_grid()
- 9 bs_transient_position sbr_ld_grid()
- 9 bs_sbr_crc_bits low_delay_sbr_data()
- 9 bs_header_flag low_delay_sbr_data()
10 © ISO/IEC 2008 – All rights reserved
ISO/IEC 14496-3:2005/Amd.9:2008(E)
At the end of 4.5.5, add the following new Figure:
SCE CPE CPE LFE SBR SBR SBR
ext. payloads
(SCE) (CPE) (CPE)
Anc Data bit
L R L R
stuffing
4a 4b 4c 4d 4e 4f
3f
3a 3b 3c 3d 3e
2a 2b 2c 2d 2e 2f 10a 10b 10c 8a 7a
1a 1b 1c 1d 1e 1f 9a 9b 9c 5a 5b
0a 0b
Figure AMD9.1 — Dependency structure in case of ER multichannel AAC ELD syntax
(channelConfigurati == 6)
After 4.6.18, add a new subclause with the title "Low Delay SBR":
4.6.19 Low Delay SBR
4.6.19.1 Introduction
Low Delay SBR is derived from the standard SBR tool in order to be utilized as a bandwidth extension coder
in communication scenarios. Thus, the algorithmic delay of this tool is minimized to achieve an overall delay
low enough for bi-directional communication applications.
Summary of modifications:
• Frame length adopted to a core codec with 512 or 480 samples per frame
• Frame-locked time/frequency grid
• Minimization of delay in QMF buffer
• Utilizing a Complex Low Delay Filterbank
The low delay SBR tool is defined by the following modifications with respect to the standard algorithm (i.e.
SBR audio object type). All clauses/subclauses can be found in the brackets after each headline.
4.6.19.2 Definitions, Constants and Variables
4.6.19.2.1 Definitions (changes to 4.6.18.2.1.20)
• time slot: finest resolution in time for SBR envelopes and noise floors. One time slot equals one
subsample in the QMF domain.
© ISO/IEC 2008 – All rights reserved 11
ISO/IEC 14496-3:2005/Amd.9:2008(E)
4.6.19.2.2 Constants (changes to 4.6.18.2.5)
• RATE: For core codec AAC ELD the constant RATE= 1 should be used instead of RATE= 2 .
4.6.19.2.3 Variables (changes to 4.6.18.2.6)
• numTimeSlots: The number of time slots for core codec AAC ELD is numTimeSlots= 16 , for 512
AAC frame and numTimeSlots= 15 , for 480 AAC frame.
• t : Due to the removed additional delay the offset of the HF-generation module is set to
HFGen
t = 2. The following Figure Figure AMD9.2 explains the offsets for core codec AAC ELD
HFGen
correctly.
numTimeSlots⋅RATE−+12
numTimeSlots⋅RATE−+12
Figure AMD9.2 — Synchronization for low delay SBR
4.6.19.2.4 Inverse Filtering (changes to 4.6.18.6.2)
Due to the modified buffer management the calculation of the covariance matrix has to be changed as follows:
The upper limit of n is to be changed from numTimeSlots⋅RATE+ 6−1 to numTimeSlots⋅RATE−1.
4.6.19.3 Time-Locked frequency grid
The time/frequency grid for the Low Delay SBR is specified in the following subclauses.
4.6.19.3.1 FrameClasses
Low Delay SBR uses a reduced set of frame classes which are listed in the Table below:
Table AMD9.9 — bs_frame_class
bs_frame_class Meaning
0 FIXFIX
1 LD_TRAN
4.6.19.3.2 sbr_ld_grid()
Low Delay SBR uses a different syntax to signal the grid data. The standard sbr_grid() syntax is replaced by
sbr_ld_grid(), as defined in the following:
12 © ISO/IEC 2008 – All rights reserved
ISO/IEC 14496-3:2005/Amd.9:2008(E)
Table AMD9.10 — Syntax of sbr_ld_grid
Syntax No. of bits Mnemonic
sbr_ld_grid(ch)
{
switch (bs_frame_class) { 1 uimsbf
case FIXFIX:
bs_num_env[ch] = 2^ tmp; 2 uimsbf,
Note 1
if (bs_num_env[ch] == 1)
bs_amp_res; 1 uimsbf
bs_freq_res[ch][0]; 1
for (env = 1; env < bs_num_env[ch]; env++)
bs_freq_res[ch][env] = bs_freq_res[ch][0];
break;
case LD_TRAN:
bs_transient_position 4 uimsbf
bs_num_env[ch] = Note 3
LD_Envelope_Table[bs_transient_position][num_envelopes];
for (env = 0; env < bs_num_env[ch]; env++)
bs_freq_res[ch][env]; 1
break;
if (bs_num_env[ch] > 1)
bs_num_noise[ch] = 2;
Else
bs_num_noise[ch] = 1;
}
Note 1: bs_num_env is restricted according to subclause 4.6.18.3.
Note 2: the Table LD_Envelope_Table is given in Table AMD9.11
4.6.19.3.3 Calculation of t (l) (changes to 4.6.18.3.3)
E
in case bs_frame_class = LD_TRAN:
t (0)= 0
E
t (L )=numberTimeSlots
E E
t (l)= LD _EnvelopeTable[bs _transient _ position][l+1]for0
E E
4.6.19.3.4 Calculation of l (changes to 4.6.18.7.2)
A
in case bs_frame_class = LD_TRAN:
l = LD _EnvelopeTable[bs _transient _ position][4]
A
© ISO/IEC 2008 – All rights reserved 13
ISO/IEC 14496-3:2005/Amd.9:2008(E)
4.6.19.3.5 Envelope Lookup Table
Table AMD9.11 — Lookup Table for LD_Envelope_Table (bs_transient_position)
bs_transient_position num_envelopes border[1] border[2] transientIdx
0 2 4 - 0
1 2 5 - 0
2 3 2 6 1
3 3 3 7 1
4 3 4 8 1
5 3 5 9 1
6 3 6 10 1
7 3 7 11 1
8 3 8 12 1
9 3 9 13 1
10* 3/2 10 14/- 1
11 2 11 - 1
12 2 12 - 1
13 2 13 - 1
14 2 14 - 1
15 2 15 - 1
* in case of AAC frame = 480 use second Table entry
4.6.19.4 Low Delay SBR Filterbank (changes to 4.6.18.4)
Instead of subclause 4.6.18.4, use the description below for filterbank processing. Note, that basically the
processing descibed in the flowcharts Figure 4.41, 4.42, 4.43, 4.50, 4.51, 4.52 is similar to the processing of
the low-delay filterbank. Only the windowing and the modulation differ.
4.6.19.4.1 Analysis filterbank
• Shift the samples in the array x by 32 positions. The oldest 32 samples are discarded and 32 new
samples are stored in positions 0 to 31.
• Multiply the samples of array x by the coefficient of window ci. The window coefficients ci are obtained by
linear interpolation of the coefficients c, i.e. through the equation
ci(i)=[]c(2i+1)+c(2i) , 0≤i< 320
The window coefficients of c can be found in Table AMD9.17.
• Sum the samples according to the formula in the flowchart in Figure 4.41 to create the 64-element array
u.
14 © ISO/IEC 2008 – All rights reserved
ISO/IEC 14496-3:2005/Amd.9:2008(E)
Calculate 32 new subband samples by the matrix operation Mu, where
0≤ k< 32
i⋅π⋅ (k+ 0.5)⋅ (2⋅n− 95) ⎧
⎛ ⎞
Μ(k,n)= 2⋅ exp ,
⎜ ⎟ ⎨
64 0≤ n< 64
⎝ ⎠
⎩
In the equation, exp() denotes the complex exponential function and i is the imaginary unit.
4.6.19.4.2 Synthesis filterbank
• Shift the samples in the array v by 128 positions. The oldest 128 samples are discarded.
The 64 new complex-valued subband samples are multiplied by the matrix N, where
0≤ k< 64
1 i⋅π⋅ (k+ 0.5)⋅ (2⋅n− 63) ⎧
⎛ ⎞
Ν(k,n)= ⋅ exp ,
⎜ ⎟
⎨
64 128 0≤ n< 128
⎝ ⎠
⎩
In the equation, exp() denotes the complex exponential function and i is the imaginary unit. The real part
of the output from this operation is stored in the positions 0 to 127 of array v.
• Extract samples from v according to the flowchart in Figure 4.42 to create the 640-element array g.
• Multiply the samples of array g by window c to produce array w. The window coefficients of c can be
found in Table AMD9.17.
• Calculate 64 new output samples by summation of samples from array w according to the last step in the
flowchart of in Figure 4.42
4.6.19.4.3 Downsampled synthesis filterbank
• Shift the samples in the array v by 64 positions. The oldest 64 samples are discarded.
The 32 new complex-valued subband samples are multiplied by the matrix N, where
0≤ k< 32
1 i⋅π⋅ (k+ 0.5)⋅ (2⋅n− 31) ⎧
⎛ ⎞
Ν(k,n)= ⋅ exp ,
⎜ ⎟
⎨
64 64 0≤ n< 64
⎝ ⎠
⎩
In the equation, exp() denotes the complex exponential function and i is the imaginary unit. The real part
of the output from this operation is stored in the positions 0 to 63 of array v.
• Extract samples from v according to the flowchart in Figure 4.43 to create the 320-element array g.
• Multiply the samples of array g by the coefficient of window ci to produce array w. The window
coefficients ci are obtained by linear interpolation of the coefficients c, i.e. through the equation
ci(i)=[]c(2i+1)+c(2i) , 0≤i< 320
The window coefficients of c can be found in Table AMD9.17.
• Calculate 32 new output samples by summation of samples from array w according to the last step in the
flowchart of Figure 4.43
© ISO/IEC 2008 – All rights reserved 15
ISO/IEC 14496-3:2005/Amd.9:2008(E)
4.6.19.5 Low Power SBR Filterbank (4.6.18.8.2)
4.6.19.5.1 Real-valued analysis filterbank
• Shift the samples in the array x by 32 positions. The oldest 32 samples are discarded and 32 new
samples are stored in positions 0 to 31.
• Multiply the samples of array x by the coefficient of window ci. The window coefficients ci are obtained by
linear interpolation of the coefficients c, i.e. through the equation
ci(i)=[]c(2i+1)+c(2i) , 0≤i< 320
The window coefficients of c can be found in Table Table AMD9.17.
• Sum the samples according to the formula in the flowchart to create the 64-element array u.
• Calculate new 32 subband samples by the matrix operation M u, where
r
0≤ k< 32
⎧
⎛π⋅ (k+ 0.5)⋅ (2⋅n− 95)⎞
Μ (k,n)= 2⋅ cos ,
⎜ ⎟
⎨
r
64 0≤ n< 64
⎝ ⎠
⎩
4.6.19.5.2 Real-valued synthesis filterbank
• Shift the samples in the array v by 128 positions. The oldest 128 samples are discarded.
The 64 new subband samples are multiplied by the matrix N , where
r
⎧0≤ k< 64
1 π⋅ (k+ 0.5)⋅ (2⋅n− 63)
⎛ ⎞
Ν (k,n)= ⋅ cos ,
⎜ ⎟
⎨
r
32 128 0≤ n< 128
⎝ ⎠
⎩
The output from this operation is stored in the positions 0 to 127 of array v.
• Extract samples from v according to the flowchart in Figure 4.50 to create the 640-element array g.
• Multiply the samples of array g by window c to produce array w. The window coefficients of c can be
found in Table Table AMD9.17.
• Calculate 64 new output samples by summation of samples from array w according to the formula in the
flowchart of Figure 4.50.
4.6.19.5.3 Downsampled real-valued synthesis filterbank
• Shift the samples in the array v by 64 positions. The oldest 64 samples are discarded.
The 32 new subband samples are multiplied by the matrix N , where
r
0≤ k< 32
⎧
1 ⎛π⋅ (k+ 0.5)⋅ (2⋅n− 31)⎞
Ν (k,n)= ⋅ cos ,
⎜ ⎟
⎨
r
32 64 0≤ n< 64
⎝ ⎠
⎩
The output from this operation is stored in the positions 0 to 61 of array v.
• Extract samples from v according to the flowchart in Figure 4.51 to create the 320-element array g.
16 © ISO/IEC 2008 – All rights reserved
ISO/IEC 14496-3:2005/Amd.9:2008(E)
• Multiply the samples of array g by the coefficient of window ci to produce array w. The window
coefficients ci are obtained by linear interpolation of the coefficients c, i.e. through the equation
ci(i)=[]c(2i+1)+c(2i) , 0≤i< 320
The window coefficients of c can be found in Table Table AMD9.17.
• Calculate 32 new output samples by summation of samples from array w according to the formula in the
flowchart of Figure 4.51.
After 4.6.19, add a new subclause with the title "Enhanced Low Delay codec":
4.6.20 Enhanced Low Delay Codec
4.6.20.1 Introduction
The Enhanced Low Delay (AAC-ELD) coding scheme provides an extension of the low delay coding
functionalities described in 4.6.17. The lowest algorithmic delay for this codec is 15ms. This codec allows the
usage of the Low Delay SBR tool in order to achieve a low bitrate and low delay coding scheme for
communication applications.
The ER AAC ELD codec is derived from the ER AAC LD codec, described in subclause 4.6.17 (ER AAC LD).
In order to achieve a sufficiently low delay, especially in combination with low delay SBR, some modifications
are necessary, e.g. Low Delay Window, as defined in the following:
4.6.20.2 Low Delay Window
The synthesis filterbank is modified in order to adopt a low-delay filterbank. The core IMDCT algorithm is
mostly unchanged, but with a longer window, such that n is now running up to 2N-1 (rather than up to N-1),
see 4.6.11.3.1, 4.6.17.2.1 and 4.6.17.2.2.
N
−1
2 ⎛ 2π 1 ⎞
⎛ ⎞
x =− spec[i][k]cos⎜()n+n k+ ⎟ for 0≤ n< 2N
⎜ ⎟
∑
i,n 0
⎜ ⎟
N N 2
k=0 ⎝ ⎝ ⎠⎠
where:
n = sample index
i = window index
k = spectral coefficient index
N = window length
n = (-N / 2 + 1) / 2
with N = 960 or 1024.
The windowing and overlap-add is modified, compared to 4.6.11.3.2, 4.6.11.3.3, 4.6.17.2.3, in the following
way:
The length N window is replaced by a length 2N window with more overlap in the past, and less overlap to the
future (N/8 values are actually zero).
Windowing for the Low Delay Window:
z = w (n)⋅x
i,n LD i,n
© ISO/IEC 2008 – All rights reserved 17
ISO/IEC 14496-3:2005/Amd.9:2008(E)
Where the window now has a length of 2N, hence n=0,…,2N-1, with coefficients listed in Table AMD9.15 for
N=1024 and Table AMD9.16 for N=960.
Overlap and add:
out = z + z + z + z
i,n i,n N i−2,n+N N
i−1,n+ i−3,n+N+
2 2
for 0<=n
4.6.20.3 ELDSpecificConfig
Table AMD9.12 — Syntax of ELDSpecificConfig ()
Syntax No. of bits Mnemonic
ELDSpecificConfig (channelConfiguration)
{
frameLengthFlag; 1 bslbf
aacSectionDataResilienceFlag; 1 bslbf
aacScalefactorDataResilienceFlag; 1 bslbf
aacSpectralDataResilienceFlag; 1 bslbf
ldSbrPresentFlag; 1 bslbf
If (ldSbrPresentFlag) {
ldSbrSamplingRate; 1 bslbf
ldSbrCrcFlag; 1 bslbf
ld_sbr_header(channelConfiguration);
}
while (eldExtType != ELDEXT_TERM) { 4 bslbf
eldExtLen; 4 uimsbf
len = eldExtLen;
if (eldExtLen == 15) {
eldExtLenAdd; 8 uimsbf
len += eldExtLenAdd;
}
if (eldExtLenAdd == 255) {
eldExtLenAddAdd; 16 uimsbf
len += eldExtLenAddAdd;
}
switch (eldExtType) {
default:
for(cnt=0; cnt
other_byte; 8 uimsbf
}
break;
/* add future eld extension configs here */
}
}
}
18 © ISO/IEC 2008 – All rights reserved
ISO/IEC 14496-3:2005/Amd.9:2008(E)
Table AMD9.13 — Syntax of ld_sbr_header ()
Syntax No. of bits Mnemonic
ld_sbr_header(channelConfiguration)
{
switch ( channelConfiguration ) {
case 1:
case 2:
numSbrHeader = 1;
break;
case 3:
numSbrHeader = 2;
break;
case 4:
case 5:
case 6:
numSbrHeader = 3;
break;
case 7:
numSbrHeader = 4;
break;
default:
numSbrHeader = 0;
break;
}
for (el=0; el
sbr_header();
}
}
4.6.20.4 Decoding of ELDSpecificConfig
The sematic of the syntax elements of the ELDSpecificConfig is described below.
frameLengthFlag see GASpecificConfig() (subclause 4.5.1.1)
aacSectionDataResilienceFlag see GASpecificConfig() (subclause 4.5.1.1)
aacScalefactorDataResilienceFlag see GASpecificConfig() (subclause 4.5.1.1)
aacSpectralDataResilienceFlag see GASpecificConfig() (subclause 4.5.1.1)
ldSbrPresentFlag The ldSbrPresentFlag corresponds to the variable sbrPresentFlag
used for non low delay SBR. The decoder has the same behaviour
with respect to this flag.
ldSbrCrcFlag The variable ldSbrCrcFlag signals the CRC syntax for low delay
SBR. The CRC calculation only includes the payload without any
byte alignment bits.
ldSbrSamplingRate The ldSbrSamplingRate determines the sampling rate factor between
core coder and SBR, where 0 stands for single rate and 1 for dual
rate.
© ISO/IEC 2008 – All rights reserved 19
ISO/IEC 14496-3:2005/Amd.9:2008(E)
eldExtType A four bit code that identifies the extension type according to Table
AMD9.14.
eldExtLen Length descriptor of eld extension configuration in bytes
eldExtLenAdd First additional length field of eld extension configuration in bytes
eldExtLenAddAdd Second additional length field of eld extension configuration in bytes
other_byte Helper variable for parsing over unknown configuration payload
Table AMD9.14 — ELD extension_type
Symbol Value of Purpose
extension_type
ELDEXT_TERM ‘0000’ Termination tag
/* reserved */ ‘0001’ /* reserved */
… … …
/* reserved */ ‘1111’ /* reserved */
Add the following tables to 4.A.2:
Table AMD9.15 — Window coefficients wLD for low delay filterbank for N=1024
n w (n) N w (n) nw (n) nw (n)
LD LD LD LD
0 0,00000000 512 1,000282151024 0,160989741536 -0,01310123
1 0,00000000 513 1,000843191025 0,158965611537 -0,01306470
2 0,00000000 514 1,001404721026 0,156960261538 -0,01302556
3 0,00000000 515 1,001966651027 0,154972591539 -0,01298381
4 0,00000000 516 1,002528891028 0,153001511540 -0,01293948
5 0,00000000 517 1,003091391029 0,151045901541 -0,01289255
6 0,00000000 518 1,003654041030 0,149104661542 -0,01284305
7 0,00000000 519 1,004216791031 0,147176661543 -0,01279095
8 0,00000000 520 1,004779541032 0,145260811544 -0,01273625
9 0,00000000 521 1,005342211033 0,143355991545 -0,01267893
10 0,00000000 522 1,005904741034 0,141461111546 -0,01261897
11 0,00000000 523 1,006467131035 0,139575701547 -0,01255632
12 0,00000000 524 1,007029451036 0,137699931548 -0,01249096
13 0,00000000 525 1,007591791037 0,135833991549 -0,01242283
14 0,00000000 526 1,008154241038 0,133978061550 -0,01235190
15 0,00000000 527 1,008716781039 0,132132291551 -0,01227827
16 0,00000000 528 1,009279301040 0,130296821552 -0,01220213
17 0,00000000 529 1,009841691041 0,128471781553 -0,01212366
18 0,00000000 530 1,010403841042 0,126657291554 -0,01204304
19 0,00000000 531 1,010965751043 0,124853531555 -0,01196032
20 0,00000000 532 1,011527471044 0,123060741556 -0,01187543
21 0,00000000 533 1,012089101045 0,121279161557 -0,01178829
22 0,00000000 534 1,012650701046 0,119509001558 -0,01169884
20 © ISO/IEC 2008 – All rights reserved
ISO/IEC 14496-3:2005/Amd.9:2008(E)
23 0,00000000 535 1,013212261047 0,11775043 1559 -0,01160718
24 0,00000000 536 1,013773651048 0,11600347 1560 -0,01151352
25 0,00000000 537 1,014334781049 0,11426820 1561 -0,01141809
26 0,00000000 538 1,014895511050 0,11254465 1562 -0,01132111
27 0,00000000 539 1,015455841051 0,11083292 1563 -0,01122272
28 0,00000000 540 1,016015821052 0,10913318 1564 -0,01112304
29 0,00000000 541 1,016575531053 0,10744559 1565 -0,01102217
30 0,00000000 542 1,017135021054 0,10577028 1566 -0,01092022
31 0,00000000 543 1,017694271055 0,10410733 1567 -0,01081730
32 0,00000000 544 1,018253161056 0,10245672 1568 -0,01071355
33 0,00000000 545 1,018811541057 0,10081842 1569 -0,01060912
34 0,00000000 546 1,019369291058 0,09919240 1570 -0,01050411
35 0,00000000 547 1,019926391059 0,09757872 1571 -0,01039854
36 0,00000000 548 1,020482891060 0,09597750 1572 -0,01029227
37 0,00000000 549 1,021038881061 0,09438884 1573 -0,01018521
38 0,00000000 550 1,021594411062 0,09281288 1574 -0,01007727
39 0,00000000 551 1,022149451063 0,09124964 1575 -0,00996859
40 0,00000000 552 1,022703871064 0,08969907 1576 -0,00985959
41 0,00000000 553 1,023257511065 0,08816111 1577 -0,00975063
42 0,00000000 554 1,023810251066 0,08663570 1578 -0,00964208
43 0,00000000 555 1,024362041067 0,08512288 1579 -0,00953420
44 0,00000000 556 1,024912951068 0,08362274 1580 -0,00942723
45 0,00000000 557 1,025463041069 0,08213540 1581 -0,00932135
46 0,00000000 558 1,026012381070 0,08066096 1582 -0,00921677
47 0,00000000 559 1,026560921071 0,07919944 1583 -0,00911364
48 0,00000000 560 1,027108531072 0,07775076 1584 -0,00901208
49 0,00000000 561 1,027655081073 0,07631484 1585 -0,00891220
50 0,00000000 562 1,028200411074 0,07489161 1586 -0,00881412
51 0,00000000 563 1,028744491075 0,07348108 1587 -0,00871792
52 0,00000000 564 1,029287371076 0,07208335 1588 -0,00862369
53 0,00000000 565 1,029829131077 0,07069851 1589 -0,00853153
54 0,00000000 566 1,030369811078 0,06932667 1590 -0,00844149
55 0,00000000 567 1,030909371079 0,06796781 1591 -0,00835360
56 0,00000000 568 1,031447681080 0,06662187 1592 -0,00826785
57 0,00000000 569 1,031984601081 0,06528874 1593 -0,00818422
58 0,00000000 570 1,032520001082 0,06396833 1594 -0,00810267
59 0,00000000 571 1,033053841083 0,06266065 1595 -0,00802312
60 0,00000000 572 1,033586171084 0,06136578 1596 -0,00794547
61 0,00000000 573 1,034117071085 0,06008380 1597 -0,00786959
62 0,00000000 574 1,034646591086 0,05881480 1598 -0,00779533
63 0,00000000 575 1,035174701087 0,05755876 1599 -0,00772165
64 0,00000000 576 1,035701281088 0,05631557 1600 -0,00764673
65 0,00000000 577 1,036226201089 0,05508511 1601 -0,00756886
66 0,00000000 578 1,036749341090 0,05386728 1602 -0,00748649
67 0,00000000 579 1,037270661091 0,05266206 1603 -0,00739905
68 0,00000000 580 1,037790241092 0,05146951 1604 -0,00730681
69 0,00000000 581 1,038308151093 0,05028971 1605 -0,00721006
70 0,00000000 582 1,038824461094 0,04912272 1606 -0,00710910
© ISO/IEC 2008 – All rights reserved 21
ISO/IEC 14496-3:2005/Amd.9:2008(E)
71 0,00000000 583 1,039339141095 0,047968551607 -0,00700419
72 0,00000000 584 1,039852061096 0,046827091608 -0,00689559
73 0,00000000 585 1,040363121097 0,045698251609 -0,00678354
74 0,00000000 586 1,040872171098 0,044581941610 -0,00666829
75 0,00000000 587 1,041379201099 0,043478171611 -0,00655007
76 0,00000000 588 1,041884281100 0,042387041612 -0,00642916
77 0,00000000 589 1,042387481101 0,041308681613 -0,00630579
78 0,00000000 590 1,042888881102 0,040243181614 -0,00618022
79 0,00000000 591 1,043388451103 0,039190561615 -0,00605267
80 0,00000000 592 1,043886101104 0,038150711616 -0,00592333
81 0,00000000 593 1,044381701105 0,037123521617 -0,00579240
82 0,00000000 594 1,044875151106 0,036108901618 -0,00566006
83 0,00000000 595 1,045366451107 0,035106791619 -0,00552651
84 0,00000000 596 1,045855691108 0,034117201620 -0,00539194
85 0,00000000 597 1,046342971109 0,033140131621 -0,00525653
86 0,00000000 598 1,046828381110 0,032175601622 -0,00512047
87 0,00000000 599 1,047311921111 0,031223431623 -0,00498390
88 0,00000000 600 1,047793501112 0,030283321624 -0,00484693
89 0,00000000 601 1,048273031113 0,029354941625 -0,00470969
90 0,00000000 602 1,048750421114 0,028437991626 -0,00457228
91 0,00000000 603 1,049225681115 0,027532301627 -0,00443482
92 0,00000000 604 1,049698911116 0,026637881628 -0,00429746
93 0,00000000 605 1,050170221117 0,025754721629 -0,00416034
94 0,00000000 606 1,050639741118 0,024882831630 -0,00402359
95 0,00000000 607 1,051107461119 0,024022321631 -0,00388738
96 0,00000000 608 1,051573321120 0,023173411632 -0,00375185
97 0,00000000 609 1,052037211121 0,022336311633 -0,00361718
98 0,00000000 610 1,052499071122 0,021511241634 -0,00348350
99 0,00000000 611 1,052958891123 0,020698661635 -0,00335100
100 0,00000000 612 1,053416761124 0,019899221636 -0,00321991
101 0,00000000 613 1,053872771125 0,019113591637 -0,00309043
102 0,00000000 614 1,054327001126 0,018342411638 -0,00296276
103 0,00000000 615 1,054779481127 0,017585631639 -0,00283698
104 0,00000000 616 1,055230181128 0,016842481640 -0,00271307
105 0,00000000 617 1,055679061129 0,016112191641 -0,00259098
106 0,00000000 618 1,056126081130 0,015393981642 -0,00247066
107 0,00000000 619 1,056571241131 0,014687261643 -0,00235210
108 0,00000000 620 1,057014591132 0,013991671644 -0,00223531
109 0,00000000 621 1,057456161133 0,013306871645 -0,00212030
110 0,00000000 622 1,057896011134 0,012632501646 -0,00200709
111 0,00000000 623 1,058334261135 0,011968711647 -0,00189576
112 0,00000000 624 1,058771091136 0,011316091648 -0,00178647
113 0,00000000 625 1,059206691137 0,010675271649 -0,00167936
114 0,00000000 626 1,059641251138 0,010046841650 -0,00157457
115 0,00000000 627 1,060074441139 0,009430771651 -0,00147216
116 0,00000000 628 1,060505421140 0,008826411652 -0,00137205
117 0,00000000 629 1,060933351141 0,008233071653 -0,00127418
118 0,00000000 630 1,061357461142 0,007650111654 -0,00117849
22 © ISO/IEC 2008 – All rights reserved
ISO/IEC 14496-3:2005/Amd.9:2008(E)
119 0,00000000 631 1,061779091143 0,00707735 1655 -0,00108498
120 0,00000000 632 1,062201641144 0,00651513 1656 -0,00099375
121 0,00000000 633 1,062628581145 0,00596377 1657 -0,00090486
122 0,00000000 634 1,063063091146 0,00542364 1658 -0,00081840
123 0,00000000 635 1,063500501147 0,00489514 1659 -0,00073444
124 0,00000000 636 1,063928371148 0,00437884 1660 -0,00065309
125 0,00000000 637 1,064333911149 0,00387530 1661 -0,00057445
126 0,00000000 638 1,064704431150 0,00338509 1662 -0,00049860
127 0,00000000 639 1,065029961151 0,00290795 1663 -0,00042551
128 0,00338834 640 1,064810761152 0,00244282 1664 -0,00035503
129 0,00567745 641 1,064697651153 0,00198860 1665 -0,00028700
130 0,00847677 642 1,064450041154 0,00154417 1666 -0,00022125
131 0,01172641 643 1,064080021155 0,00110825 1667 -0,00015761
132 0,01532555 644 1,063613821156 0,00067934 1668 -0,00009588
133 0,01917664 645 1,063077191157 0,00025589 1669 -0,00003583
134 0,02318809 646 1,062494531158 -0,00016357 1670 0,00002272
135 0,02729259 647 1,061883651159 -0,00057897 1671 0,00007975
136 0,03144503 648 1,061256121160 -0,00098865 1672 0,00013501
137 0,03560261 649 1,060622911161 -0,00139089 1673 0,00018828
138 0,03972499 650 1,059994181162 -0,00178397 1674 0,00023933
139 0,04379783 651 1,059371321163 -0,00216547 1675 0,00028784
140 0,04783094
...








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