EE1.el3 (EEE1023): Electronics III Acoustics lecture 20 Sound localisation Dr Philip Jackson www.ee.surrey.ac.uk/teaching/courses/ee1.el3
Sound localisation Objectives: calculate frequency response of a microphone array understand the factors affecting its resolution explain the primary cues in human sound localisation Topics: 2- and N- element microphone arrays Effects of spacing, frequency, and N Binaural cues Sound localisation in 3D S.1
Preparation for sound localisation What acoustic factors give us the ability to localise sounds with our two ears? identify and describe at least two acoustic cues that we use, based on the sound pressure signals arriving at the ears S.2
Microphone arrays Capabilities: localisation of individual sound sources enhancement of sounds from a given direction beamforming for steering the array Applications: directional microphone recordings speech enhancement in a car or meeting robot audition condition monitoring defence and surveillance S.3
Two element microphone array Two omnidirectional microphones are distance d apart in the free field of harmonic point source Q. d R r 0 r 1 θ Q d = dsinθ Each microphone signal depends on its distance r i from Q: p i (r, t) = Q r i e j(ωt kr i) (1) where the wave number is k = ω/c = 2πf/c = 2π/λ. In the far field, r i d and (θ) = d sin θ. At the centre of the array, we have r 0 = R 2 and r 1 = R + 2, or r i = R + ( i 1 2 ) θ S.4
Combining two microphone signals (broadside) From eq. 1 with (θ) = d sin θ, we obtain p i (R, θ, t) Q ( ( ( ))) R ej ωt k R+ i 1 2 = Q ( R ej(ωt kr) e jk 12 i ) (2) Consider output from array when we add the two signals: s 0 (R, θ, t) = Q R ej(ωt kr) (e jk 2 + e jk 2 ) = 2Q R ejωt e jkr cos ( k 2 (θ) ) (3) using cos x = cosh jx = 1 2 ( e jx + e jx) The effect is to steer the array in broadside direction with a directivity pattern that depends on k = 2π/λ = 2πf/c S.5
Directivity of 2-microphone array (broadside) 500 Hz 1 khz 2 khz Steering the array The steering angle φ defines a delay, τ φ = φ /c, where φ = d sin φ which we apply to the closer microphone signal: s φ (R, θ, t) = 2Q R ejωt e jk(r+ φ 2 ) cos ( k 2 ( (θ) φ )) (4) Hence, by adjusting τ φ, we can maximise the response of the array to sound coming from a given azimuth angle. S.6
Directivity of 2-microphone array, φ = 90 500 Hz 1 khz 2 khz Directivity of 2-microphone array, φ = 45 500 Hz 1 khz 2 khz S.7
A linear array of N microphones Extending the array to N microphones gives a more directed response: s N 0 (R, θ, t) = Q ( ( ))) R ej ωt k R+ ( N 1 N 1 2 e jki (5) i=0 (N 1) d = dsinθ θ Using trigonometry, we can write this as s N 0 (R, θ, t) = Q R ej(ωt kr) sin Nk 2 sin k 2 (6) S.8
Directivity of 8-microphone array, φ = {0, 90, 45 } S.9
Human sound localisation Effects of wave propagation and diffraction around a head: S.10
Binaural cues Inter-aural level difference the difference between the sound intensity level at the left and right ears Head acts as a barrier for mid and high frequencies, for D = 0.17 m, f crit = 1 khz -10 db ILD +10 db Inter-aural time difference the time difference of arrival (TDOA) between at the ears Added path up to 0.22 m is half wavelength at 750 Hz -1 ms ITD +1 ms S.11
Front-back disambiguation Movement of the head: can be used to determine whether the sound source is in front of, or behind, the head: Visual cues: if you can t see it, it must be behind you! Pinna: ear lobes act as HF barrier for sounds from rear. S.12
Perception of elevation Direct vs. reflected: sound from above provides reflections from the ground and shoulders. Pinna: variations in frequency response from different directions give information about incident angle of sound source. Perception of distance Overall intensity, spectral shape, direct vs. reflected sound S.13
Sound recordings Stereo recordings exploit summing localisation: spaced mics give time delay, 1 ms for hard panning mixer pan pots give level difference, 10 db for hard panning Binaural recordings Microphones placed in ear canals capture time, intensity and spectral changes, including effects of the pinnae. S.14
Sound localisation 2-element microphone array: effects of distance, spacing & frequency polar response, beams and nulls N-element microphone array: effect of N on aperture and resolution Human sound localisation: head shadowing interaural differences, ILD and ITD critical band processing & Duplex theory front-back disambiguation elevation Localising sound in recordings: stereo and binaural recordings S.15
Preparation for revision Read and digest lecture notes summarise topics identify areas for further study Practise on examples review worked examples complete exercises do additional exercises in books Rehearse exam technique attempt past exam paper S.16