DAGA 2015 Nürnberg Spherical microphone array equalization for Ambisonics Franz Zotter1, Matthias Frank1, Christian Haar2 1Institut f¨ur Elektronische Musik und Akustik 1,2Kunstuniversit¨at Graz, Austria, Email: {zotter, frank}@iem.at Introduction 0dB 90° 135° 45° Microphone arrays on rigid spheres elegantly facilitate −12dB forming of higher-order spherical harmonic directivity patterns. Hereby, they also enable surround recording −24dB with height in higher-order Ambisonics [1]. While the 180° 0° necessary distortionless (either on-axis or diffuse-field b=0 equalized) and white-noise-gain constraints (WNG) for b=1 spherical-harmonic beamforming seem logical, we lack b=2 dependable knowledge about how to equalize spherical 135° 45° b=3 arrays for higher-order Ambisonic surround playback. 90° b=4 Processing based on the typical analytical superdirective 0 model of spherical beamforming [2] would heavily amplify −5 −10 noise and mismatch in higher-order directional signals free −15 at low frequencies. To avoid enormous noise boosts and diffuse −20 omni amplitude in dB strongly mislocalized signal components at low frequen- −25 cies, higher-order signals are gradually discarded towards 4 3 2 1 0 sph. exp. order low frequencies [1, 2, 3]. Figure 1: Spherical pickup pattern with gradually reduced Fig. 1 shows spherical harmonic pickup patterns with spherical harmonics expansion order and their amplitudes: gradually reduced expansion order, b =4...0. While the on-axis (free), diffuse-field, omnidirectional. Which amplitude omni-directional component remains unity, diffuse and on- represents loudness of the pattern in surround playback? axis amplitudes suffer amplitude loss when reducing the spherical harmonic expansion order b. Song proposes free- ceptual equalization curve on loudspeaker playback of field equalization [2] or measurements [4]; Baumgartner Ambisonically amplitude-panned band-limited noise. Pan- and L¨osler discuss diffuse-field equalization [5, 6]. ning was done in 2D as well as 3D (using AllRAP [7]). As this is most frequently done to obtain constant loudness Band-limited noise w./wo. order reduction in amplitude panning: Shouldn’t it be useful to assume that diffuse-field amplitude determines perceived loudness Listeners had to equalize the perceived loudness of a th in large-scale Ambisonic surround playback? Contrarily, reduced-order sound to a 4 -order reference sound, both ◦ bass over-emphasis dominated correspondingly processed encoded in the look direction ϕs =0 on the horizontal playback of EigenmikeTM recordings. Therefore, depend- plane, and both being band-limited noise signals of the able facts are going to be explored here for clarification. same frequency band. The set of Ambisonic pair compar- isons is described in Table 1. Except for N = 0, which Listening Experiment employed the same frequency range as N = 1, ranges were taken from [6] to fit the processing for a rigid-sphere array To clarify whether amplitude of the diffuse field, free field, of r =4.2 cm. Band limitation was achieved by 4th order omnidirectional component, or any quantity determines Butterworth band-pass filtering. perceived frequency response characteristics, we under- took a listening experiment at IEM’s anechoic chamber The continuous noise sounds of each comparison task and IEM’s CUBE. was periodically switched from one to the other of the comparison pair every 800 ms. Listeners could influence To defeat any uncuntrolled influence of an acoustic record- the loudness of the reduced-order sound by moving a ing situation, noise, microphone mismatch, etc., and to slider until they perceived a continuous sound without increase reproducibility, we based the search for a per- loudness modulation and then press the proceed button. Table 1: Comparison pairs: bands and Ambisonic orders N. Table 2: Environmental/algorithmic conditions. f A Ref c1 2D, 10 lspks, anechoic, center seat, ideal setup 68. 478 Hz N=0 N=4 c2 2D, 12 lspks, CUBE, center seat, delay comp. 68. 478 Hz N=1 N=4 c3 3D, 24 lspks, CUBE, center seat, delay comp. 478. 1405 Hz N=2 N=4 c4 3D, 24 lspks, CUBE, center seat 1405. 2727 Hz N=3 N=4 c5 3D, 24 lspks, CUBE, off-center seat 486 DAGA 2015 Nürnberg Experimental Setup 7 c c c c c c 1 2 3 4 5 2...5 The 10-channel loudspeaker arrangement in IEM’s ane- 6 2Deqd. 2Deqd. 3Deqd. 3D 3D,offc. pooled choic chamber uses ten 8020 Genelec loudspeakers at anechoic CUBE CUBE CUBE CUBE CUBE ear height, equally spaced at r =1.5m with ϕ = 5 0◦(front), 36◦,... from the subject’s perspective. IEM’s 4 CUBE is a permanent installation of 24 externally ampli- fied coaxial Tannoy System 1200 with the loudspeaker an- 3 gles documented, e.g., in [8]. We measured RT = 675 ms. 2 In total, we are interested in the influence of environments percept. equalization in dB and conditions of Table 2: IEM’s anechoic chamber (c1) 1 using 10 loudspeakers, IEM’s CUBE, in which the loud- speakers do not strictly have equal delays to the center 0 0 1 2 3 4|0 1 2 3 4|0 1 2 3 4|0 1 2 3 4|0 1 2 3 4|0 1 2 3 4 listening spot, with delay compensation in 2D (c2:12 Ambisonic order N horizontal loudspeakers), with and without delay com- Figure 2: Equalization perceived in medians and confidence pensationin3D(c3, c4: 24 loudspeaker hemisphere) at intervals making up for level differences in comparison pairs the center, and 2.5 m, i.e. half-radius, left-off-center (c5). Tab. 1. Conditions Tab. 2 are 2D/3D, anechoic/IEM CUBE, Ambisonic Panning/Decoding with equal, equalized, unequalized delays, or off-center. Noise signals were presented through Ambisonic panning Table 3: Estimators of perceptually correct c2...5 equalization. to ϕs = 0. The 2D max-rE-weighted [9] sampling Am- estimator N=0 N=1 N=2 N=3 bisonic panning of c1...2 used the weights g0,...,gL−1 omni (2D/3D) 0dB 0dB 0dB 0dB N CLL 4.7 dB 3.7 dB 2.3 dB 1.3 dB π perceived 5.3 dB 3.8 dB 2.3 dB 1.1 dB gl =1+2 cos(n 2(N+1) ) cos(n ϕl), (1) n=1 diffuse (2D) 6.4 dB 4.2 dB 2.4 dB 1.0 dB diffuse (3D) 10.1 dB 6.1 dB 3.6 dB 1.6 dB 2π to distribute the signal on L = 10 loudspeakers, ϕl = L l, free (2D) 15.2 dB 8.6 dB 4.7 dB 2.0 dB in c1, and L = 12, with ϕl corresponding to the azimuth free (3D) 23.4 dB 13.5 dB 7.7 dB 3.4 dB of the first 12 IEM CUBE loudspeakers, in c2. For 3D Ambisonic panning in c3...5, max-rE-weighted AllRAP, cf. [7, 10], was employed. Results Listeners and notes on the experiment The overview of the resulting perceptual equalization levels are depicted in Fig. 2. The level differences of For testing the condition c1, twelve listeners, average age the different-order bands are obvious, and there is a of 26, took part and needed 13 minutes on average to pronounced difference for the orders N = 0, 1 between finish 24 comparison tasks, of which we only used results anechoic c1 and IEM CUBE c2...5. What is more, multi- of nine listeners and 4(rep.) × 4(N) = 16 responses, here. variate ANOVA for c2...5 revealed there being no signif- Excluded conditions refer to alternative decoding of the icant influence of repetition, delay compensation, and N=0, 1 cases on fewer loudspeakers. The excluded 3 lis- listening position (0.13 ≤ p ≤ 0.44). By contrast, the teners gave repeated responses whose standard deviation 3D c3...5 and 2D c2 playback conditions as well as the reached 3 dB, three times as much as for the others. subjects have a significant influence (p ≤ 0.03). In experiments concerning the conditions c2...5, ten listen- ers, average age 31, took part and required 35 minutes The IEM CUBE conditions still resemble quite well, bear- on average to finish 4(rep.) × 4(c.) × 4(N) = 64 compari- ing in mind that 1 dB is often named as JND value for son tasks, whereof the last 16 were done after relocating levels. Therefore Fig. 2 shows the pooled statistics thereof to a 2.5 m left-shifted position c5. Listeners gave their in its right-most column c2...5. Median perceived equal- repeated answers with 0.6 dB average standard deviation. ization levels amount to 4=[5.3, 3.8, 2.3, 1.1] dB. All participants were experienced spatial audio listeners. Interestingly, the anechoic center-seat condition c1 seems To every listener, all comparison pairs for one listening to require much less equalization. We expect this result position ({c1}, {c2,c3,c4},{c5}) were presented four times, to apply to binaural rendering using anechoic HRIRs. each time in individual random order. For the N = 0 and N = 1 comparison tasks and the central Models listening positions, listeners reported to perceive timbre Analytic equalization differences, so that high- (or low-) frequency parts of the presented frequency bands were heard to be switched on From all analytical equalizations (diffuse-field, free-field, and off. At the off-center listening position, a different and omni-directional for max-rE 2D/3D, cf. Fig. 1), an amount of sound from the side was reported to cause analytic 2D diffuse equalizer comes closest to the experi- slight difficulties in equalizing the loudness levels. mental medians. For max N = 4, it is calculated by 487 DAGA 2015 Nürnberg 7 N=0 N=1 N=2 N=3 N=4 6 N 2 π 5 1+2 n=1 cos (n 2(N+1) ) 4 N,4 = .