Hearing and Deafness 2. Ear as a frequency analyzer

1. Hearing and Deafness 2. Ear as a frequency analyzer Chris Darwin

2. 1.0 0 -1.0 0 0.05 Time (s) Frequency: 100-Hz Sine Wave Spectrum Amplitude against frequency 1 Waveform Amplitude against time amp 100 Hz frequency

3. 1.0 0 -1.0 0 0.05 Time (s) Frequency: 500-Hz Sine Wave Spectrum Amplitude against frequency 1 1 Waveform Amplitude against time amp amp frequency 100 500 500 frequency

4. 0 0 0 0 0.05 0.05 Time (s) Time (s) Amplitude: 500-Hz Sine Wave Spectrum Amplitude against frequency 1 1 amp amp frequency 100 500 500 frequency

5. 1 1 amp amp frequency 100 500 500 frequency Phase: 500-Hz Sine Wave sine The amplitude spectrum does not show phase cosine

6. 1 1 amp amp frequency frequency 1 1 amp amp frequency frequency adding sine waves Spectrum of Sum

7. 5.0 1 1 0 amp amp -1.7 0 0.05 Time (s) frequency 100 500 500 frequency 100-Hz fundamental Complex Wave Spectrum Amplitude against frequency Waveform Amplitude against time

8. Adding nine sine waves Frequency Spectrogram Time 5s Frequency Time 5s

9. The linear vs log scales • Linear • equal distances represent equal differences 0 100 200 300 400 500 • Log • equal distances represent equal ratios 100 200 400 800 1600 3200 -1 0 1 2 3 4 e.g. Piano keyboard frequencies Octave = doubling of frequency basilar membrane has log repn of frequency

10. deciBel (dB) scale Sound A is x dB more intense than sound B when: x = 10*log10 (energy of A / energy of B) or x = 20*log10 (amp of A / amp of B) So if A is 20 watts and B is 10 watts x = 10*log10 (20/10) = 10*0.3 = 3dB You can usually just hear a difference of 1dB (jnd)

11. 0 0 0.05 Time (s) 1 1 1 1 amp amp amp amp frequency 100 500 500 frequency frequency 100 500 500 frequency Bandpass filtering (narrow) 5.0 0 -1.7 0 0.05 Time (s)

12. 5.0 1 1 0 amp amp -1.7 0 0.05 Time (s) frequency 100 500 500 frequency Bandpass filtering (wide) 1 1 amp amp frequency 500 frequency 100

13. Beats Repetition rate is the difference in frequency between the two sine-wave components 1/3 second 505 - 500 = 5 Hz 1 1 amp amp frequency 500 frequency 100

14. Beats Repetition rate is the difference in frequency between the two sine-wave components 1/100th second 500 - 400 = 100 Hz 1 1 amp amp frequency 400 500 frequency 100

15. Reponse of basilar membraneto sine waves Each point on the membrane acts like bandpass filter tuned to a different frequency: high freq at base, low at apex. Each point vibrates at frequency of pure tone (-> phase locking)

16. Excitation patterns(envelope of excitation) Basilar membrane excitation pattern is like a spectrum

17. Auditory filter bandwidth (ERB)

18. Excitation pattern of complex tone on bm

19. 1000 Hz 250 Hz Broadband Noise frequency 2000 Hz Measurement of auditory bandwidth with band-limited noise Amadeus

20. A gardening analogy

21. A gardening analogy

22. A gardening analogy Tone Noise Auditory bandwidth Noise bandwidth Detection mechanism

23. Wider auditory filter

24. Auditory tuning curves Inner hair-cell damage Healthy ear

25. Outer-hair cell damage

26. Human auditory bandwidth At 1 kHz the bandwidth is about 130 Hz; at 5 kHz the bandwidth is about 650 Hz. BW = freq / 8 roughly

27. Normal auditory non-linearities • Normal loudness growth (follows Weber’s Law, which is logarithmic, not linear) • Combination tones • Two-tone suppression • Oto-acoustic emissions

28. Conductive vs Sensori-neural deafness Mostly a combination of OHC and IHC damage Becomes linear, so No combination tones Or two-tone suppression

29. Symptoms of SNHL • Raised thresholds: helped by amplification • Wider bandwidths: no help possible • Recruitment (restricted dynamic range): partly helped by automatic gain controls in modern digital aids • Often accompanied by tinnitus

30. Normal vs Impaired Dynamic Range