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

Bandwidth Extrapolation of Audio SignalsSung-Won Yoon, David Choi EE368C Final Project

Future Directions

• Better transform to capture relevant characteristics of audio signals

• Employ models based on the audible physics of audio signals

• Divide signal windows into different classes