Fig 1.
Standard circuit for LMS-based noise cancellation.
Fig 2.
ICO learning for active noise reduction.
A) Illustration of the active noise cancelling architecture. A set of control microphones, x1, x2 and x3, records ambient noise. ICO learning is used to learn parameters for mixing the recorded noise to produce a suitable anti-noise to cancel at the reference recording site (x0) that receives signals with a propagation delay Δt relative to the earlier-arriving signals at the control microphones. B) Schematic of the conventional ICO rule. The triangle represents a synapse with changing weight. C) Power spectrum of the noise used for all tests.
Fig 3.
Results for a linear microphone setup.
A Original mixed noise signal. B Microphone and noise-source geometry, α = 90°, d = 1.25 m. (C-E in arbitrary units and truncated after 12 s as there are no more changes visible afterwards). Learning rate: μ = 1.0 × 10−7. C effective noise at the reference site, D weight dynamics, green and orange curves are identical due to the symmetry of the microphone configuration and are here shifted a bit to make both visible, E development of the momentum, and F achieved noise reduction. G Noise reduction when scaling d in the configuration with different factors.
Table 1.
Abbreviation ‘mic.’ stands for microphone.
Fig 4.
We used the linear microphone setup from Fig 3B. After 10 s a parameter drift for 1 s has been introduced (dashed lines). (A-C in arbitrary units). Learning rate: μ = 1.0 × 10−7. A effective noise at the reference site. Before the parameter drift this curve is identical to Fig 3B, but here truncated in y-direction to make the effect of parameter drift visible. B weight dynamics, green and orange curves are identical due to the symmetry of the microphone configuration and are here shifted a bit to make both visible, C development of the momentum, and D achieved noise reduction for different drift rates k (only parts of the red and green curves are shown).
Fig 5.
Different microphone configurations.
Learning rate μ = 5 × 10−7. A quarter circle, B half circle, A-B with 3 control microphones. C full circle with 4 control microphones, D random configuration with 10 control microphones.
Fig 6.
Effect of shielding when using different noise sources.
Learning rate: μ = 7.5 × 10−8. Configuration is shown as inset in panel B, small red arcs show the shields against the non-predictive noise sources. Distance from S to x0 was 2.5 m. A Noise reduction without shielding, B with shielding.
Fig 7.
Learning rate: μ = 7.5 × 10−8. Configuration is shown as inset in panel B. It contains a similar shielding as in Fig 6, which for clarity, is not drawn. Distance from S to x0 was 3.5 m. A Using the original ICO rule, B Using the rule with momentum.
Fig 8.
Noise reduction when using low-pass filtered signals.
A Same geometrical configuration as in Fig 3 but now with split-up paths for the control microphones using different filters, where the cut-off for the reference microphone (so-called “unknown LP”) was 10 kHz. Learning rate: μ = 1.0 × 10−7. B Noise reduction for 3 conventional control microphones without path splitting, where only one low pass has been used with cut-off of 11 kHz. Note that the here-reached level was only about 16 dB. C Noise reduction for 3 paths from the control microphones. Path 1 with cut-off of 9 kHz, path 2 with 10 kHz and path 3 with 11 kHz. D Development of the synaptic weights of all paths. Path 2 shows weight growth and, thus, has been responsible for the resulting reduction of about 140 dB see in panel C.
Fig 9.
Influence of noise cancellation on a sine-wave signal.
Geometrical configuration as in Fig 3. Learning rate: μ = 1.0 × 10−7. A Control case without signal. B Sine wave with frequency 1/30 Hz and different amplitudes. C Same frequency as in B but amplitude reduced by a factor of 10. D Sine wave with frequency 100/30 Hz. The inset shows the ratio between the signal provided at x0 without noise and the signal obtained after filtering the noise with ICO for a large range of frequencies.