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A. Lukin, J. Todd
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1. Adaptive Time-Frequency Resolutionfor Analysis and Processing of Audio
2. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 2/15 Short-Time Fourier Transform
Most commonly used transform for audio:
Spectral analysis
Noise reduction (spectral subtraction algorithms)
Time-variable filters and other effects
Very fast implementation for large number of bands via FFT
Good energy compaction for many musical signals
Many oscillations in basis functions ? ringing (Gibbs phenomenon)
Uniform frequency resolution ? inadequate resolution at lows
3. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 3/15 Filter banks
4. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 4/15 Suggested approach
Imitation of time-frequency resolution of human hearing
Adaptation of resolution to local signal features
5. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 5/15 Spectrograms
Problems:
Most perceptually meaningful energy is concentrated in the narrow band below 4 kHz ? cant see useful details
Time/frequency resolution trade-off
6. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 6/15 Spectrograms
Problems:
Poor frequency resolution at low frequencies ? cant separate bass harmonics from bass drum
Time/frequency resolution trade-off
7. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 7/15 Spectrograms
Problems:
Poor time resolution at transients ? time-smearing of drums
8. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 8/15 Spectrograms Simple solution: combine spectrograms with different resolutions
Take bass from spectrogram with good freq. resolution
Take treble from spectrogram with good time resolution
9. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 9/15 Spectrograms
Simple solution:
Combine spectrograms with different resolutions: take bass from spectrogram with good frequency resolution, take treble from spectrogram with good time resolution
10. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 10/15 Spectrograms Better approach: select best resolution for each time-frequency neighborhood
Criteria?
Better frequency resolution at bass (reflects a-priori psychoacoustical knowledge)
Maximal energy compaction (to minimize spectral smearing in both time and frequency)
11. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 11/15 Spectrograms Calculation of energy compaction
(energy smearing in the given block
for all given resolutions)
12. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 12/15 Spectrograms
Benefits:
Sharper bass drum hits and other transients, even in mid-frequency range
Sharper guitar harmonics in high frequencies
13. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 13/15 Spectrograms
14. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 14/15 Spectrograms
15. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 15/15 Processing framework General framework for
multi-resolution processing
Perform processing with
several different resolutions
Adaptively combine (mix)
results in time-frequency space
Mixing is controlled by a-priori
knowledge of psychoacoustics
and analysis of local signal features
(e.g. transience)
16. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 16/15 Noise reduction Spectral subtraction algorithm modifications
Better frequency resolution at low frequencies (according to the human hearing resolution)
Better temporal resolution near signal transients (for reduction of Gibbs phenomenon)
17. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 17/15 Noise reduction Results of single-resolution and multi-resolution algorithms
18. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 18/15 Noise reduction Results of single-resolution and multi-resolution algorithms
19. A. Lukin, J. Todd Adaptive Time-Frequency Resolution 19/15 Your questions