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Adaptive Time-Frequency Resolution for Analysis and Processing of Audio

A. Lukin, J. Todd

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Adaptive Time-Frequency Resolution for Analysis and Processing of Audio

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    1. Adaptive Time-Frequency Resolution for 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 ? can’t 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 ? can’t 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

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