1. Figures for Chapter 7 Advanced signal processing Dillon (2001) Hearing Aids

2. Front  (a)  Output + - T Figure 7.1 (a) Block diagram of a subtractive directional microphone comprised of either a single microphone with two ports, or two separate microphones with one port each. The negative sign next to one of the inputs of the summer indicates that the two signals are subtracted. (b) A delay-and-add directional microphone array with four ports. Source: Dillon (2001): Hearing Aids Fixed directional arrays Subtractive array Front  (b) + T + + Output T T Additive array

3. Figure 7.2 Frontal sensitivity of a two-port (or two-microphone) subtractive directional microphone relative to the sensitivity of an equivalent single-port microphone. The parameter shown is the port spacing. The internal delay needed to produce a cardioid polar response has been assumed. Source: Dillon (2001): Hearing Aids Frontal sensitivity and port spacing

4. Figure 7.3 End-fire and broadside microphone arrays. Source Array electronics Output Broadside array Source Array electronics Output Endfire array Source: Dillon (2001): Hearing Aids

5. Adapter Front   Output + - T Figure 7.4 A simple adaptive directional microphone with steerable nulls. Source: Dillon (2001): Hearing Aids Adaptive directional microphone

6. Figure 7.5 The Widrow Least Mean Squares adaptive noise reduction scheme, based on a reference microphone that picks up only the noise. The fixed delay compensates for the delay inherent in the adaptive filter. Speech + Noise  - + Delay Source: Dillon (2001): Hearing Aids Widrow LMS noise reduction

7. Figure 7.6 A Griffiths-Jim adaptive noise canceller, whereby the two microphone outputs are added in the top chain but subtracted in the bottom chain.   + + - + Front Left Right  - + Delay Source: Dillon (2001): Hearing Aids Griffiths Jim adaptive noise reduction

8. Figure 7.7 Improvement in speech reception threshold for an adaptive array relative to a single microphone. The experiment used frontal speech and a single noise masker at 45 degrees from the front in three simulated environments that differed in the amount of reverberant sound relative to the direct sound. From Hoffman et al (1994). Source: Dillon (2001): Hearing Aids Microphone array benefit

9. Figure 7.8 Blind source separation of two sources, S 1 and S 2, occurs when the two adaptive filters, G1 and G2, adapt to the response shapes that compensate for the room transmission characteristics, R1, R2, R3 and R4, from each source to each microphone. Note that everything to the right of the dotted line is in the hearing aid, whereas the blocks to the left are the transfer functions of the transmission paths within the room. When properly adapted, the response of G1 = R3/R1 and G2 = R4/R2. The output Y 1 then does not contain any components of S 2. The blocks G1 and G2 can alternatively be feed-forward blocks rather than feed-back blocks. + S1S1 S2S2  +  + Adaptor G2 G1 R1 R4 R3 + + + R2 Y1Y1 Y2Y2 Source: Dillon (2001): Hearing Aids Blind source separation

10. Figure 7.9 A Wiener Filter incorporating a Fourier Transform (F.T) to calculate the spectrum of the combined speech and noise. A speech/non-speech detector classifies the spectrum as noise or speech plus noise, and thus enables the average spectral power of the speech to be estimated. Averager F.T. Speech/non-speech detector Averager - + Avg speech Spectrum Avg speech plus noise spectrum Speech plus noise Switch Input  ÷ Noise Source: Dillon (2001): Hearing Aids Wiener filter noise reduction

11. Figure 7.10 A Spectral Subtraction noise reduction system incorporating a Fourier Transform to calculate the power spectrum, a speech/non-speech detector to enable the average spectral power of the noise to be estimated, and an Inverse Fourier Transform to turn the corrected spectrum back into a waveform. Speech/non-speech detector SwitchAverager -  + F.T. Avg noise Spectrum Phase I.F.T. Magnitude Source: Dillon (2001): Hearing Aids Spectral Subtraction

12. Figure 7.11 The gain-frequency response of a (hypothetical) four-channel hearing aid, where feedback oscillationhas been avoided by decreasing the gain of the band from 2 kHz to 4 kHz (solid line) from the original response (dotted line). Source: Dillon (2001): Hearing Aids Feedback management

13. Figure 7.12 Gain-frequency and phase-frequency response of the complete feedback loop for an ITE hearing aid. Redrawn from Hellgren et al., (1999). Source: Dillon (2001): Hearing Aids Feedback-loop response

14. Figure 7.13 Internal feedback path added to cancel the effects of the external, unintentional leakage path.  Internal feedback path - External leakage path + Source: Dillon (2001): Hearing Aids

15. Frequency Intensity Frequency Intensity 10002504000 1000 250 4000 Figure 7.14 Input and output spectra for a frequency transposition scheme in which the output frequency equals half the input frequency. The amplifier also provides some high frequency pre- emphasis. The arrows show the reduction in frequency of each formant. Source: Dillon (2001): Hearing Aids Transposition

16. Time (seconds) Spectral enhancement Figure 7.15 Spectrograms of the syllable /ata/ (a) unprocessed and (b) spectrally enhanced, showing more pronounced formants (Fisher, Dillon & Storey, in preparation). Frequency (kHz) (b) Time (ms) 0 2 4 0 2 4 0200400600800 (a) Source: Dillon (2001): Hearing Aids