This document proposes using lapped orthogonal transforms and high frequency regeneration techniques to extrapolate audio signals from narrowband to wideband. It outlines using LOT decomposition on narrowband signals, then training a system to map the narrowband LOT coefficients to estimated wideband LOT coefficients through linear estimation or principal component analysis. An experiment is proposed using single instrument audio signals to investigate frequency component correlations and implement the techniques. Expected results note extrapolation may improve quality but not be fully satisfactory based on prior research.

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

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

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

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

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

6. Sung-Won Yoon, David Choi EE368C Project Proposal
Bandwidth Extrapolation of Audio Signals
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
f
Y p



X Y
From narrowband
signal
Regenerated
high frequency

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

8. Sung-Won Yoon, David Choi EE368C Project Proposal
Bandwidth Extrapolation of Audio Signals
Principal Components Analysis










H
L
X
Y T
L
H





 
)
,...,
(
....
1
1
N
N
diag 










zz
R ,
• Quasi-stationarity of windowed audio signals
• PCA applied on the LOT coefficients
• Classification of LOT blocks may be necessary

9. Sung-Won Yoon, David Choi EE368C Project Proposal
Bandwidth Extrapolation of Audio Signals
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

10. Sung-Won Yoon, David Choi EE368C Project Proposal
Bandwidth Extrapolation of Audio Signals
Expected Results
• Extrapolation should improve the quality
• However:
• Extensions may be necessary
“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

11. Sung-Won Yoon, David Choi EE368C Project Proposal
Bandwidth Extrapolation of Audio Signals
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