1. Coherent envelope detection for modulation filtering of speech Steven Schimmel Les Atlas

2. Modulation Filtering filter-bank analysis and reconstruction modulation filtering

3. Modulation Filtering sub-band processing envelope detector

4. Useful for what?

5. Hilbert envelope detector  Traditionally, people have used the “Hilbert envelope”  Based on the Hilbert transform, denoted by David Hilbert (1862-1943)

6. Definitions for the Hilbert envelope  “Analytic signal”: only positive frequencies  Phase signal:  Hilbert carrier:  Hilbert envelope:  PR:, or

7. Limitations of the Hilbert Envelope  Envelope non-negative: can’t be guaranteed after filtering [1]  Envelope real-valued: incorrect model for speech signals [1]  Hilbert carrier not narrow-band [2] [1] Li & Atlas, ICASSP 2004 [2] Ghitza, JASA 2001

8. Hilbert carrier not narrow-band spectrum of sub-band, envelope and carrier sub-band signalenvelopecarrier

9. Hilbert carrier not narrow-band spectra after low-pass filtering the envelope lpf envelopecarriermodified signal

10. Hilbert carrier not narrow-band final result of low-pass filtering the envelope original signalmodulation filtered

11. Quantitative evaluation [1] Goal Measure the effectiveness of a modulation filtering approach Method Average the modulation spectrogram of a processed signal across acoustic frequency

12. Quantitative evaluation [2] speech signal spectrogram modulation spectrogram

13. Quantitative evaluation [3] originalmodulation filtered

14. Effectiveness of Hilbert approach Severe low-pass modulation filter: 1 Hz cut-off, 40 dB suppression

15. Modification of the Hilbert approach  To reduce leakage into neighboring sub-bands the detected carrier should be narrow-band, or even monochromatic  First, we need to introduce the notion of instantaneous frequency (IF)

16. Instantaneous frequency (IF) From the definitions for the Hilbert transform, we have the analytic signal and the phase signal We define the instantaneous frequency signal

17. IF of Hilbert carrier in speech  The instantaneous frequency of a sub-band may look like this:  “Spikes” in the IF cause leakage into neighboring sub-bands

18. Coherent envelope Based on two ideas:  Two equivalent expressions for the envelope:  Smoothing the phase signal: 

19. IF of coherent carrier in speech  After smoothing the phase signal, the spikes of the IF are gone  And: coherent envelope is complex-valued, as desired original IF4 Hz lpf IF0 Hz lpf IF

20. Effectiveness of coherent approach Sub-bands are ~30 Hz apart. Neighboring sub- bands “modulate each other”. That’s life.

21. Improved IF estimator  In separate work, Atlas & Janssen [1] developed another coherent envelope detector based on a differential IF estimator  They applied it successfully to the task of musical instrument separation  To validate our findings, we implemented their estimator and tested it on speech [1] Atlas & Janssen, ICASSP 2005

22. Effectiveness of Atlas & Janssen approach “Better than ideal” is due to averaging.

23. Future work

24. Contact Steven Schimmel steven@ee.washington.edu on the web students.washington.edu/schmml Thanks Prof. Bishnu Atal Qin Li Supported by Washington Research Foundation