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Basics of Audio Signal Processing
Sudhir K
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Summary Slide
 Digital Representation of Audio
 Psycho-Acoustic principles
 Lossy Compression of Audio (MP3 and AAC)
 Lossless compression of Audio (general principles with example)
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Digital Representation of Audio
 PCM Data
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Sampling audio input at discrete intervals and quantizing into discrete
number of evenly spaced levels.
Sampling Frequency
Bits per sample
Number of Channels
Interleaved and block format
 Audio CD
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44.1 KHz, 2 channels , data-rate is 1.4 Mbits per second
ADC
Digital
Processing
DAC
speakers
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Psycho-Acoustic Principles
 Sound Pressure Level
 Perceptual and Statistical redundancy
 Absolute Threshold of Hearing
 Critical Bands
 Masking in Time domain
 Masking in Frequency domain
 Perceptual Entropy
 Pre-echo Effect
 Psycho-Acoustic Model 1
 Psycho-Acoustic Model 2
 Filter Banks and Transforms
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Sound Pressure Level
 Standard metric to quantify intensity of acoustical stimulus
 Measured in decibels (dB) relative to an internationally defined reference level
 LSPL is the SPL of stimulus p
 P0 is the standard reference level at 20 µPa
 150-dB SPL is the dynamic range of human
auditory system
 140-dB SPL is typically the threshold of pain
 Human auditory system can hear frequencies
ranging from 20 Hz to 20 KHz frequency
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Absolute Threshold of Hearing
 Characterizes the amount of energy needed in a pure tone such that
it can be detected by a listener in a noiseless environment
 This can be interpreted naively as a maximum allowable energy
level for coding distortions introduced in frequency domain
 Note that the absolute threshold of hearing is a function of
frequency
 Response of a human ear for a pure tone is dependant on the
frequency of the tone
 Sensation Level : intensity level difference for stimultus relative to
detection threshold (quantifies listener’s audibility)
 Equal SL components can have different SPL’s
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Absolute Threshold of Hearing
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Human Ear Model
 Frequency to place
transformation
Sound wave moves the eardrum and
attached bones
 The eardrum and the bones transfer
mechanical vibrations to Cochlea
 Oval window of cochlear membrane
induces traveling waves along length of
basilar membrane.
 Traveling waves generate peak
responses at frequency specific
membrane positions
 Specific positions of membrane provide
peak responses for specific frequency
band
 Cochlea can be considered as a set of highly
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overlapped band-pass filters.
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Critical Bands
 Cochlea can be considered as a set of
highly overlapped band-pass filters.
 Critical bandwidth is a function of
frequency that quantifies the cochlear
bandwidth
 Loudness (percieved intensity)
remains same when the noise energy
in present within a critical band
 One bark corresponds to distance of
one critical band
 Critical bandwidth tends to remain 0
constant up to 500Hz and then
increases to 20% of center frequency
above 500 Hz
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Frequency (KHz)
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Simultaneous Masking
 Process where one sound is rendered inaudible by presence of another sound
 Frequency domain masking
Masker
Maskee
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Tone masking Noise (TMN)
Noise Masking Tone
Noise Masking Noise
In-band Phenomenon (occurs within same critical band)
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Simultaneous Masking
 SMR (signal to mask ratio)
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smallest difference between intensity
of masking signal and the intensity of
masked signal
SMR for NMN is 26dB, TMN is 24dB
and NMT is 5dB
Noise is a better masker than tone
 Spread of Masking
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Inter-band Masking
Triangular spreading function
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Temporal (Non-simultaneous) masking
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Masking in time-domain
Pre-Masking : Masking occurs prior to the signal
Post-Masking: Masking following the occurrence of signal
Pre-masking is usually less (approx 1-2 ms)
Post-masking is of longer duration (50 to 300ms)
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Just Noticeable Difference (JND)
 Also called as global masking threshold
 Global Masking threshold is a combinaton of individual masking
thresholds (threshold due to NMT, TMN and absolute threshold)
 Quantization noise should be kept below the JND to keep it
inaudible.
Signal
Masking curve
Noise
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Perceptual Entropy
 Measure of perceptually relevant information
 Expressed in bits per sample
 Represents a theoretical limit on compressibility of a particular
signal
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Pre-Echo
 Pre-echoes occur when a signal with sharp attack begins near end of
a transform block immediately following a region of low energy
Inverse quantization spreads evenly throughout the reconstructed block
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Pre-Echo control
 Bit-reservoir
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Store surplus bits, which can be used during periods of attack
 Window Switching
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Switch between long and short time-window
Short window for transients to minimize spread of noise.
Long window for normal case to increase compression efficiency
 Gain Modification
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Smoothes transient peaks by changing gain of signal prior to the
transient
 Temporal Noise Masking
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Linear prediction on frequency domain spectrum
Flattened residual and quantization noise.
The quantization noise is suchthat it follows original signal enveope
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Stereo coding
 MS-Stereo (Middle/Side Stereo)
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One channel to encode information identical between left and right
channel
One channel to encode differences between left and right channel
Transmit sum and difference of the original signals in left and right
channels
 Intensity Stereo
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Lossy Coding technique
Replace left and right channel with a single representing signal plus
directional information
Usually used only in higher frequencies (since human ear is less
sensitive to signal phase at these frequencies)
Used only at low bit-rates
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Psycho Acoustic Model1
1. Spectral analysis and SPL normalization
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Normalize input samples and segment into blocks
2. Identification of Tonal and Noise maskers
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Energy from 3 adjacent spectral components combined to form single
tonal masker
Energy of all other spectral lines not within a range of Δ combined to
form noise masker
 Decimation and reorganization of maskers
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Any tonal or noise threshold below absolute threshold are discarded
Adjacent pair of maskers are compared and is replaced by stronger of
the two.
 Calculation of individual Masking Threshold
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Calcullate threshold due to tonal and noise maskers
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Pyscho Acoustic Model 1
Threshold due to tonal maskers
Threshold due to noise maskers
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Psycho Acoustic Model 1
 Calcullation of global masking threshold
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Individual masking threshold are combined to estimate global masking
threshold
Assumes masking effects are additive
Sum of absolute threshold of hearing, threshold from tonal masker and
threshold from noise masker
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Filter Bank Characteristics
 Lossless (analysis and synthesis should be invertible)
 Aliasing errors should cancel for perfect or near-perfect
reconstruction
 Low computational complexity
 Bandwidth should replicate critical bands of human ear.
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QMF Filters
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Pseudo-QMF
 Cosine Modulation of low-pass prototype filter to implement
parallel M-channel filter banks with nearly perfect reconstruction
 Overall linear phase and hence constant group delay
 Complexity = one filter + modulation
 Critical sampling
Analysis & synthesis filters satisfy mirror image conditions to
eliminate phase distortion
Analysis filter
Synthesis filter
MPEG1 uses a 32-channel PQMF bank for spectral decomposition in layer
I and Layer II
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MDCT (TDAC)
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De-correlate signal by mapping to an orthogonal basis functions
Lapped orthogonal block transform
Successive transform block overlap each other
Overall linear phase
Forward MDCT
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50% Overlap between blocks
Block transform of 2M samples and block advance of M samples
Basis functions extend across 2 blocks (blocking artifacts elimination)
Critically sampled M samples output for 2M input samples
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Lossy Audio Compression techniques
 Decoded output is not bit-exact with original input
 Decoded output is perceptually same as original input
 More compression achieved
 Extensive use of psycho-acoustic model to discard perceptually
irrelevant audio data
 Examples : MP3 and AAC
Time to
Frequency
Filter Bank
Allocate bits
&
Quantize
Format
Bitstream
PsychoAcoustics
Model
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Audio Decoder
Usually Encoder Complex and Decoder less complex
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MPEG Compression
 ISO 11172-3 ISO (MPEG 1)
 Mainly specifies the bit-stream and hence leaves the flexibility of Encoder
design to individual developers
 Lossy and perceptually transparent
 Sampling frequencies of 32, 44.1 KHz and 48 KHz supported
 Various bit-rates from 32-192 kbps per channel supported
 Supports following channel modes
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Mono, Stereo, Dual Mono, Joint Stereo
 Based on complexity 3 independent layers of compression
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Layer 1 (around 192 kbps per channel)
Layer 2 (around 128 kbps per channel)
Layer 3 (MP3) (around 64 kbps per channel)
 Complexity increases as we go from Layer 1 to Layer 3
 CRC (optional) for error checking
 Ancillary Data support
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MPEG 1 layer1 and layer 2
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MPEG Layer 1 and Layer 2
 Sub-band filtering
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Polyphase filter bank
Decompose input signal into 32 sub-bands
Sub-bands are equally spaced (for ex : 48KHz signal, each subband is
750 Hz)
Critically sampled (output of each sub-band is down sampled such that
the number of input and output samples are the same)
sub-bands do not reflect the human ear’s critical band
Prototype filter chosen such that high side lobe attenuation (96 dB) is
achieved
Not perfectly Lossless (error is small)
 FFT
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Done for psycho-acoustic analysis and determination of JND thresholds
Done in parallel with the sub-band filtering
Layer 1 : 512 and Layer 2 : 1024 point
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MPEG 1 Layer 1 and Layer 2
 Block companding
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Sub-band filtering output is block-companded (normalized by a scale
factor) such that the maximum sample amplitude in each block is unity.
This operation is done on a block of 12 samples (8 ms at 48 KHz)
 Psycho-Acoustic analysis
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Output of the FFT block is input to the psycho-acoustic block
This block outputs the masking threshold for each band
 Quantization and bit-allocation
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This procedure is iterative
Bit-allocation applies JND threshold to select an optimal quantizer
from a pre-determined set
Quantization should satisfy both masking and bit-rate requirements
Scale factors and quantizer selections are also coded and sent in the
bitstream
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MPEG Layer 1 and Layer 2
 Psycho-Acoustic Model
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Separate spectral values into tonal and non-tonal components or
calcullate tonality index
Apply spreading function
Set lower bound for threshold values
Find masking threshold for each sub-band
Calculate Signal to Mask Ratio and pass it to the bit-allocation block.
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MPEG 1 Layer 1 and Layer 2
 MPEG1 Layer 1
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Frame length of 384 samples
32 sub-bands of length 12.
Each group of 12 samples gets a bit-allocation and a scale-factor
 MPEG 1 Layer 2
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Enhancement of Layer 1
More compact code for representing scale-factors, quantized samples
and bit-allocation
Frame length of 1152 samples
Each sub-band = 3 groups of 12 samples each
Each sub-band has a bit-allocation and upto 3 scale-factors
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MPEG 1 Layer 1 and Layer 2
 Bitstream
SCFSI : Scale factor Selection information. Number of scale
factors for each sub-band.
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MPEG 1 Layer 3
Diag from fhg site
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MPEG 1 Layer 3
Main blocks
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Filter Bank
Perceptual acoustic model
Quantization and Coding
Encoding of bit-stream
Features
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Mono and stereo support
Bit-rates upto 320 kbps
Sampling frequencies => 32 KHz, 44.1 KHz and 48 KHz
CBR and VBR coding
MS-stereo and IS-stereo coding
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Enhancements over Layer 1 and Layer 2
 Higher frequency resolution due to MDCT
 Non-uniform quantization
 Uses scale-factor bands, which resemble human ear model (unlike
sub-bands used in Layer 1 and Layer 2)
 Entropy Coding (Variable length Huffman codes)
 Better Handling of Pre-echo artifacts
 Use of Bit-reservoir
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Hybrid Filter Bank
FilterBank
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Hybrid filter bank
Better approximation of critical
bands of human ear
Poly-phase filter followed by
MDCT filter bank
Poly-phase filter bank
 Compatible to Layer 1 and Layer
2
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MDCT filter bank
 Each poly-phase frequency band
into 18 finer sub-bands
 Higher frequency resolution
 Pre-echo control
 Better Alias reduction
 Block Switching
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BEGIN
for i=511 downto 32 do
X[i]=X[i-32]
for i=31 downto 0 do
X[i]=next_input_audio_sample
Window by 512 Coefficients
Produce Vector Z
for i=0 to 511 do
Z i =C i *X i
Sub-band Filtering
Partial Calculation
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for i=0 do 63 do Yi =
Z i + 64 j
j=0
Calculate 32 Samples by
Matrixing
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M ik * Yk
for i=0 do 31 do Si =
k=0
Output 32 Subband
Samples
END
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Window Switching
 Window Switching
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Short and long windows
Adaptive MDCT block sizes of 6 and 18 points
Short windows to prevent pre-echo (pre-masking to hide pre-echoes)
Long window of length 1152 samples
Short window of length 384 samples
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Quantization and Coding
 Uses Bit-reservoir
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Bits saved from one frame are used for encoding other frame
 Non-linear quantization
((
xr(i)
ix(i) = nint
4
qquant+quantanf
0.75
)
)
- 0.0946
2
 Huffman encoding
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32 different huffman code tables available for coding
Each table caters for different Max value that can be coded and the
signal statistics
Different code books for each sub-region
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Quantization and
Coding
 Inner iteration loop
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Rate control loop
Assigns shorter code to more
frequently used values
Does huffman coding and quantization
Keeps increasing global gain till
quantization values are small enough to
be encoded by available number of bits
Layer III Outer Iteration Loop
BEGIN
Inner Iteration Loop
Calculate the distortion for each
critical band
Save scaling factors of the critical bands
Preemphasis
Amplify critical bands with more than the
allowed distortion
 Outer Iteration loop
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Noise Control loop
If quantization noise exceeds masking
threshold in any band then it increases
the scale factor for that band
Executed till noise is less than masking
threshold
All critical bands amplified ?
y
n
Amplification of all bands below
upper limit ?
y
n
At least one band with more than the
allowed distortion ?
y
n
Restore scaling factors
RETURN
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Bit-reservoir and Back-frames
 Encoder can donate bits to bit-reservoir and can borrow bits from
the bit-reservoir
 9-bit pointer for pointing to main data begin (starting byte of audio
data for that frame)
 Theoretically the main data begin cannot be greater than 7680 bits
(frame length for frame of 320 kbps at 48 KHz)
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Advanced Audio Coding (AAC)
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AAC Features
 Sampling Rate (8 kHz to 96 kHz)
 Bit Rates (8 kbps to 576kbps)
 Mono, Stereo and multi-channel (Upto 48 channels)
 Supports both CBR and VBR
 Multiple profiles or Object Types
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Low Complexity (LC)
SSR
HE (High Efficiency)
HEv2 (High Efficiency with Parametric Stereo)
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AAC-Basic Features and Modules
 High frequency resolution transform coder (1024 lines MDCT with
50% overlap)
 Non-uniform quantizer
 Noise shaping in scale factor bands
 Huffman Coding
 Temporal Noise Shaping (TNS)
 Perceptual Noise Substitution (PNS)
 Modules
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FilterBank
Perceptual Model
Quantization and Coding
Optional tools like TNS, PNS, prediction etc
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Improvements over MP3
 Higher efficiency and simpler filter bank
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Only MDCT vs hybrid filter bank of MP3
 Higher Frequency Resolution (1024 vs 576 of MP3)
 Improved Huffman Coding table
 Window Shape adaptation (Sine and KBD)
 Enhanced Block Switching
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The window length is dynamically changed between 2048 and 256
samples (Against 1152 and 384 of MP3). This leads to better coding
efficiency for long blocks and less pre-echo artifacts for short blocks.
 Use of following tools only in AAC
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Temporal Noise Shaping
Perceptual Noise Substitution
Long Term Prediction
 More flexible joint stereo (separate for every scale band)
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Filter Bank
 MDCT supporting block lengths of 2048 and 256 points
 Dynamic switching between long and short blocks
 50 % overlap between blocks
 Windows are of two types
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Kaiser Bessel Window (KBD)
Sine shaped Window
 In case of short blocks 8 short transforms are performed in a row to
maintain synchronicity
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Temporal Noise Shaping (TNS)
 Forward Prediction
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Correlation between subsequent input samples exploited by quantizing
the prediction error based on unquantized input samples
Quantization error in the final decoded signal is adapted to PSD (Power
Spectral Density) of the input signal
Forward prediction done on spectral data over frequency. The temporal
shape of the quantization error signal will appear adapted to the
temporal shape of input signal at output of the decoder.
Temporal shape of Quantization noise of a filter bank is adapted to the
envelope of the input signal by TNS and in case of No TNS the
quantization noise is distributed almost uniformly over time.
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Temporal Noise Shaping (TNS)
 Tool for handling transient and pitched input signals
 Duality between time and frequency domains
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Un-flat spectrum can be coded efficiently by coding spectral values or
by applying predictive coding methods to time-domain signal
Duality : Efficient coding of transient signals (un-flat in time-domain)
is efficient in time-domain or by applying predictive methods to the
spectral data
 TNS uses a prediction approach in the frequency domain to shape
the quantization noise over time
 Quantized filter coefficients transmitted
 TNS tool can be dynamically switched on and off in the stream
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Perceptual Noise Substitution (PNS)
 Available only in MPEG-4 and not in MPEG-2
 Based on the fact that the fine structure of a noise signal is of minor
importance for the subjective perception of signal.
 Instead of transmitting actual spectrum transmit the following
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Information that this frequency region is noise-like.
Total power in that frequency band
 PNS can be switched on and off on a scale-factor basis.
 In decoder when a region is coded using PNS, then the decoder
inserts randomly generated noise.
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Spectral Band Replication (SBR)
 Recreate High-frequencies from decoded base-band signal.
 Enhancement Technology (needs a base audio codec)
 Base codec operates at half the sampling frequency of SBR
 The bit-stream of the basic encoder + control parameters
transmitted.
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SBR Decoder
1. Decoded low-band Signal analyzed using
QMF
2. High Frequency Reconstruction from Lower
bands
3. Reconstructed signal adaptively filtered to
ensure spectral characteristics of each subband
4. Envelope adjustment
5. Addition of low-band signals with envelope
adjusted high-band signals
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Parametric Stereo (PS)
 Mono Signal is encoded along with stereo Parameters as side
information in the encoded bit-stream
 3 types of parameters are employed in parametric stereo
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Inter-Channel Intensity Difference (IID)
Inter-Channel Cross Coherence (ICC)
Inter-Channel Phase Difference (IPD)
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Lossless Audio Compression
Sudhir K
Multimedia Codecs
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Main Features
 No Loss in Quality
 Perfect Reconstruction
 Less Compression
 No Psycho-Acoustic Model required
 Applications
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High-end Audio
Home-Theatre
DVD Audio
 Examples
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MLP, WMA Lossless, OptimFrog, Real Lossless, Monkey’s audio,
FLAC, LTAC, Apple Lossless, TTA Lossless audio, MPEG4 lossless
Coding (ALC)
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Types of Lossless Coding
 Time domain lossless Coding
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Audio data in time-domain
Most of the current lossless compression techniques are of this type
 Frequency domain lossless Coding
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Operate on audio data in Frequency domain
Very few schemes like LTAC
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Time Domain Lossless compression
Block
Decomposition
Inter-Channel
Decorrelation
Signal
Modelling
Entropy
Coding
 Block Decomposition
 Inter-Channel Decorrelation
 Signal Modelling
 Entropy Coding
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Inter-Channel Coding
 Redundancy between various channels
 Various Techniques
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Difference Channel Coding
Mid-Side Stereo Coding
Intensity Stereo Coding
Inter-Channel Matrixing
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Signal Modeling and Prediction
 Model input audio signal
 Difference between original and predicted audio signal minimal
 Model parameters and error coefficients transmitted
 Computationally most complex block
 Various Techniques
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Linear Prediction
LMS Filter or Adaptive filter
Polynomial Curve fitting techniques
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Entropy Coding
 Remove redundancy between bits in the bit-stream
 To compress residue or error signal further
 Many schemes
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Huffman coding
Run length Coding
Golomb Rice coding
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References
 TED PAINTER, ANDREAS SPANIAS, “Perceptual Coding of Digital Audio”, in Proc IEEE Vol 88, No 4,
April 2000
 Davis Yen Pan, “Digital Audio Compression”, Digital Technical Journal, Vol 5, No 2, Spring 1993
 Heiko Purnhagen, “Low Complexity Parametric Stereo Coding in MPEG-4”, Proc of 7th Int Conference on
Digital Audio Effects, Naples Italy, Oct 5-8, 2004
 TED PAINTER, ANDREAS SPANIAS, “A review of Algorithms for Perceptual Coding of Digital Audio
Signals”,
 Davis Pan, “A Tutorial on MPEG/ Audio Compression”
 Seymour Shlien, “Guide to MPEG-1 Audio Standard”
 ISO 11172-3, Information Technology- Coding of moving pictures and associated audio for digital storage
media Part-3
 ISO 13818-3
 ISO 14496-3
 Jurgen Herre, “Temporal Noise Shaping, Quantization and Coding methods in Perceptual Audio Coding: A
Tutorial Introduction”, AES 17th International conference on high quality audio coding.
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Deleted Slides
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Filter Banks
 Time-frequency analysis block
 Parallel bank of bandpass filters covering entire spectrum
 Divide signal spectrum into frequency sub-bands
Band-pass analysis output
Upsampling in Decoder
Output is identical to
input with delay
Decimation by factor M
Critically sampled or maximally decimated
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Parametric Stereo
 Encoder
Decoder
C= 10IID/20
α= arccos(ICC/2)
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