Bandwidth Extrapolation of Audio Signals
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Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project
Bandwidth Extrapolation of Audio Signals
David Choi Sung-Won Yoon
March 15th, 2001
Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project
Outline
• Motivation• Characteristics of audio data• Proposed system
• Linear estimation• Principal component analysis
• Results• Conclusions
Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project
Bandwidth Extrapolation
• Results should be– Similar to original wideband signal– Perceptually better quality than narrowband
NarrowbandMDCT coefficients
Wideband MDCT coefficientsnonlinear system
X X Y
Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project
High Frequency Components
• At 5.5 kHz and above, the components:– Constitute small fraction of total energy– Effects of phase distortion almost negligible– Envelope is still important– Can be hidden using error concealment– Often uncorrelated with low frequency
components
Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project
CorrelationCello (single instrument) Voice (one person)
• Cello exhibits patterned correlation• Voice largely uncorrelated
Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project
System Diagram
Wideband Training Data
NarrowbandTest Data
MDCT
MDCT MDCT-1Estimation
LOW
HIGH
HIGH
Training
Reconstructed Wideband
Estimation Parameters
Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project
Linear Estimation
• Y : low frequency coefficients (zero mean)• X : high frequency coefficients (zero mean)• Want to estimate X given Y (stationary)
yxyyxyxx
yxxy
yyxy
RRRRMSE
YXERXYER
YRRX
1
**
1
,
ˆY
X
Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project
Principal Component Analysis
*YYERyy
),...,(
....
1
1
N
N
diag
yyR ,
Y
XTaking m eigenvectors,
YZ
m
*
*1
zxzzxzxx
zzxz
RRRRMSE
ZRRX
1
1ˆ
Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project
Results (Linear Estimation)• Cello
– Cutoff frequency: from 2.75kHz to 10kHz– Test/training data subsets of single sample
Signal energy Noise energy
Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project
Overfitting
• Same weights tested on new song– Same instrument, same performer
Setting the weights to zero Gave much better results
Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project
Reducing Overfit
• Low-order estimator was trained– Limited number of non-zero weights
Overfitting is reduced but poorS/N ratio results
Cutoff freq: 4.125 kHz
Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project
Results (PCA & Linear Estimation)
• Energy concentration well captured by PCA• Magnitude sufficient
Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project
S/N Ratio using PCA (1)
• Cello– Trained on one sample– Test data from new sample
Overfit begins around 60 eigenvectors
Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project
• Vega– Trained & tested on disjoint subsets of sample
S/N Ratio using PCA (2)
Y : 0 – 5.5 kHz Y : 3.48 – 5.5 kHz
Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project
Conclusions
• MSE criteria and perceptual criteria were not equivalent
• MDCT produced poorly correlated features which were difficult to predict
• Estimation degrades further when applied to data with inaccurate knowledge of statistics
• PCA provided poor description of low frequency for estimation