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

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

Bandwidth Extrapolation Y Narrowband MDCT coefficients Wideband MDCT coefficients nonlinear system Results should be Similar to original wideband signal Perceptually better quality than narrowband 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 Bandwidth Extrapolation of Audio Signals

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

Bandwidth Extrapolation of Audio Signals System Diagram Wideband Training Data NarrowbandTest Data MDCT MDCT-1 Estimation LOW HIGH Training Reconstructed Wideband Estimation Parameters Bandwidth Extrapolation of Audio Signals

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) Bandwidth Extrapolation of Audio Signals

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 Signal energy Noise energy Bandwidth Extrapolation of Audio Signals

Bandwidth Extrapolation of Audio Signals Overfitting Same weights tested on new song Same instrument, same performer Setting the weights to zero Gave much better results Bandwidth Extrapolation of Audio Signals

Bandwidth Extrapolation of Audio Signals Reducing Overfit Low-order estimator was trained Limited number of non-zero weights 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 Bandwidth Extrapolation of Audio Signals

Bandwidth Extrapolation of Audio Signals 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 Signals

Bandwidth Extrapolation of Audio Signals S/N Ratio using PCA (2) Vega Trained & tested on disjoint subsets of sample Y : 0 – 5.5 kHz Y : 3.48 – 5.5 kHz Bandwidth Extrapolation of Audio Signals

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 Bandwidth Extrapolation of Audio Signals

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 Bandwidth Extrapolation of Audio Signals