Bandwidth Extrapolation of Audio Signals February 8th, 2001

Bandwidth Extrapolation of Audio Signals February 8th, 2001 Sung-Won Yoon David Choi Sung-Won Yoon, David Choi Bandwidth Extrapolation of Audio Signals EE368C Project Proposal

Outline Motivation Proposed system Lapped orthogonal transform (LOT) High frequency regeneration Experiment Expected results Workplan Sung-Won Yoon, David Choi Bandwidth Extrapolation of Audio Signals EE368C Project Proposal

Bandwidth Extrapolation X X Narrowband LOT coefficients Wideband LOT coefficients nonlinear system Y Results should be – Similar to original wideband signal – Perceptually better quality Sung-Won Yoon, David Choi Bandwidth Extrapolation of Audio Signals EE368C Project Proposal

Proposed System LOT High Frequency Regeneration Narrowband signal LOT -1 2 Sung-Won Yoon, David Choi LOT Wideband signal LPF Bandwidth Extrapolation of Audio Signals EE368C Project Proposal

Lapped Orthogonal Transform H. Malvar & D. Staelin, 1989 2N Avoids blocking artifact No increase in bit rate x t 50% Overlap 2N N LOT coefficient Sung-Won Yoon, David Choi Bandwidth Extrapolation of Audio Signals EE368C Project Proposal

High Frequency Regeneration Trained system Parameters p are chosen to fit the training data Mapping from narrowband signal to wideband signal – Estimate LOT coefficients – Magnitude only X Y Y fp X Sung-Won Yoon, David Choi From narrowband signal Bandwidth Extrapolation of Audio Signals Regenerated high frequency EE368C Project Proposal

Linear Estimation Each estimated high frequency coefficient is a weighted combination of the low freq. coefficients Y j w ji X i i Possible sparse representation of weights Weights possibly chosen to exploit psychoacoustic phenomena (masking) Sung-Won Yoon, David Choi Bandwidth Extrapolation of Audio Signals EE368C Project Proposal

Principal Components Analysis Quasi-stationarity of windowed audio signals PCA applied on the LOT coefficients Rzz , 1 . N diag ( 1 ,., N ) L H T Y H L X Classification of LOT blocks may be necessary Sung-Won Yoon, David Choi Bandwidth Extrapolation of Audio Signals EE368C Project Proposal

Experiment 1. For simplicity of analysis, initiate study with single instrument audio signals 2. Investigate the correlation among frequency components 3. Implement linear estimator and PCA 4. Compare results - Perceptual quality - Mean square error Sung-Won Yoon, David Choi Bandwidth Extrapolation of Audio Signals EE368C Project Proposal

Expected Results Extrapolation should improve the quality However: “Several approaches were considered to extrapolate the high frequency spectral envelope. In all cases, the subjective quality was not satisfactory. This suggests that the high frequency formant structure of speech cannot be accurately predicted from the narrowband formants.” - J. Valin & R. Lefebvre, Bandwidth Extension of Narrowband Speech for Low Bit-rate Wideband Coding, IEEE, 2000 Extensions may be necessary Sung-Won Yoon, David Choi Bandwidth Extrapolation of Audio Signals EE368C Project Proposal

Workplan Week 1: – Investigate the relationship between the low and high LOT coefficients – Quantify the relations that can be exploited Week 2: – Carry out the linear estimation based on the knowledge of the LOT coefficients Week 3: – Extend to PCA Week 4: – Compare the results – Prepare writeup and presentation Sung-Won Yoon, David Choi Bandwidth Extrapolation of Audio Signals EE368C Project Proposal