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Bandwidth Extrapolation of Audio Signals. David Choi Sung-Won Yoon. March 15 th , 2001. Motivation Characteristics of audio data Proposed system Linear estimation Principal component analysis Results Conclusions. Outline. Results should be Similar to original wideband signal

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bandwidth extrapolation of audio signals

Bandwidth Extrapolation of Audio Signals

David Choi

Sung-Won Yoon

March 15th, 2001

Bandwidth Extrapolation of Audio Signals

outline
Motivation

Characteristics of audio data

Proposed system

Linear estimation

Principal component analysis

Results

Conclusions

Outline

Bandwidth Extrapolation of Audio Signals

bandwidth extrapolation
Results should be

Similar to original wideband signal

Perceptually better quality than narrowband

X

Y

Bandwidth Extrapolation

X

Narrowband

MDCT coefficients

Wideband

MDCT coefficients

nonlinear system

Bandwidth Extrapolation of Audio Signals

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

High Frequency Components

Bandwidth Extrapolation of Audio Signals

correlation
Correlation

Cello (single instrument)

Voice (one person)

  • Cello exhibits patterned correlation
  • Voice largely uncorrelated

Bandwidth Extrapolation of Audio Signals

system diagram

LOW

Wideband Training Data

MDCT

Training

HIGH

Estimation Parameters

NarrowbandTest Data

HIGH

Reconstructed Wideband

MDCT

Estimation

MDCT-1

System Diagram

Bandwidth Extrapolation of Audio Signals

linear estimation
Y : low frequency coefficients (zero mean)

X : high frequency coefficients (zero mean)

Want to estimate X given Y (stationary)

Linear Estimation

Bandwidth Extrapolation of Audio Signals

principal component analysis

,

Principal Component Analysis

Taking m eigenvectors,

Bandwidth Extrapolation of Audio Signals

results linear estimation
Cello

Cutoff frequency: from 2.75kHz to 10kHz

Test/training data subsets of single sample

Results (Linear Estimation)

Signal energy

Noise energy

Bandwidth Extrapolation of Audio Signals

overfitting
Same weights tested on new song

Same instrument, same performer

Overfitting

Setting the weights to zero

Gave much better results

Bandwidth Extrapolation of Audio Signals

reducing overfit
Low-order estimator was trained

Limited number of non-zero weights

Reducing Overfit

Overfitting is reduced but poor

S/N ratio results

Cutoff freq: 4.125 kHz

Bandwidth Extrapolation of Audio Signals

results pca linear estimation
Energy concentration well captured by PCA

Magnitude sufficient

Results (PCA & Linear Estimation)

Bandwidth Extrapolation of Audio Signals

s n ratio using pca 1
Cello

Trained on one sample

Test data from new sample

S/N Ratio using PCA (1)

Overfit begins around 60 eigenvectors

Bandwidth Extrapolation of Audio Signals

s n ratio using pca 2
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 Signals

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

Conclusions

Bandwidth Extrapolation of Audio Signals

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

Future Directions

Bandwidth Extrapolation of Audio Signals

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