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Bandwidth Extrapolation of Audio Signals. Sung-Won Yoon David Choi. February 8 th , 2001. Motivation Proposed system Lapped orthogonal transform (LOT) High frequency regeneration Experiment Expected results Workplan. Outline. Results should be Similar to original wideband signal

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Bandwidth extrapolation of audio signals

Bandwidth Extrapolation of Audio Signals

Sung-Won Yoon

David Choi

February 8th, 2001

Bandwidth Extrapolation of Audio Signals


Outline

Motivation

Proposed system

Lapped orthogonal transform (LOT)

High frequency regeneration

Experiment

Expected results

Workplan

Outline

Bandwidth Extrapolation of Audio Signals


Bandwidth extrapolation

Results should be

Similar to original wideband signal

Perceptually better quality

X

Y

Bandwidth Extrapolation

X

Narrowband

LOT coefficients

Wideband

LOT coefficients

nonlinear system

Bandwidth Extrapolation of Audio Signals


Proposed system
Proposed System

High Frequency

Regeneration

LOT

Narrowband signal

Wideband signal

LOT-1

LPF

2

LOT

Bandwidth Extrapolation of Audio Signals


Lapped orthogonal transform h malvar d staelin 1989
Lapped Orthogonal TransformH. Malvar & D. Staelin, 1989

2N

  • Avoids blocking artifact

  • No increase in bit rate

50% Overlap

2N

N

LOT coefficient

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

Y

X

High Frequency Regeneration

From narrowband signal

Regenerated high frequency

Bandwidth Extrapolation of Audio Signals


Linear estimation

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

Linear Estimation

  • Possible sparse representation of weights

  • Weights possibly chosen to exploit psychoacoustic phenomena (masking)

Bandwidth Extrapolation of Audio Signals


Principal components analysis

, combination of the low freq. coefficients

Principal Components Analysis

  • Quasi-stationarity of windowed audio signals

  • PCA applied on the LOT coefficients

  • Classification of LOT blocks may be necessary

Bandwidth Extrapolation of Audio Signals


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

Experiment

Bandwidth Extrapolation of Audio Signals


Expected results

Extrapolation should improve the quality instrument audio signals

However:

Expected Results

“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

Bandwidth Extrapolation of Audio Signals


Workplan

Week 1: instrument audio signals

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

Workplan

Bandwidth Extrapolation of Audio Signals


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