Bandwidth Extrapolation of Audio Signals

1. Bandwidth Extrapolation of Audio Signals David Choi Sung-Won Yoon March 15th, 2001 Bandwidth Extrapolation of Audio Signals

2. Motivation Characteristics of audio data Proposed system Linear estimation Principal component analysis Results Conclusions Outline Bandwidth Extrapolation of Audio Signals

3. 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

4. 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

5. Correlation Cello (single instrument) Voice (one person) • Cello exhibits patterned correlation • Voice largely uncorrelated Bandwidth Extrapolation of Audio Signals

6. 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

7. 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

8. , Principal Component Analysis Taking m eigenvectors, Bandwidth Extrapolation of Audio Signals

9. 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

10. 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

11. 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

12. Energy concentration well captured by PCA Magnitude sufficient Results (PCA & Linear Estimation) Bandwidth Extrapolation of Audio Signals

13. 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

14. 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

15. 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

16. 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