Sung-Won Yoon

1
Bandwidth Extrapolation of Audio Signals
February 8th, 2001

• Sung-Won Yoon
• David Choi

2
Outline

• Motivation
• Proposed system
• Lapped orthogonal transform (LOT)
• High frequency regeneration
• Experiment
• Expected results
• Workplan

3
Bandwidth Extrapolation
X
Narrowband LOT coefficients
Wideband LOT coefficients
nonlinear system

• Results should be
• Similar to original wideband signal
• Perceptually better quality

4
Proposed System
High Frequency Regeneration
LOT
Narrowband signal
Wideband signal
LOT-1
LPF
2
LOT
5
Lapped Orthogonal TransformH. Malvar D.
Staelin, 1989
2N

• Avoids blocking artifact
• No increase in bit rate

50 Overlap
2N
N
LOT coefficient
6
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

From narrowband signal
Regenerated high frequency
7
Linear Estimation

• Each estimated high frequency coefficient is a
  weighted combination of the low freq. coefficients

• Possible sparse representation of weights
• Weights possibly chosen to exploit psychoacoustic
  phenomena (masking)

8
Principal Components Analysis

• Quasi-stationarity of windowed audio signals
• PCA applied on the LOT coefficients

• Classification of LOT blocks may be necessary

9
Experiment

• For simplicity of analysis, initiate study with
  single instrument audio signals
• Investigate the correlation among frequency
  components
• Implement linear estimator and PCA
• Compare results
• Perceptual quality
• Mean square error

10
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

11
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