Measuring Spatial MIMO Impulse Responses in Rooms Employing Spherical Transducer Arrays

UNIVERSITÀ DEGLI STUDI DI PARMA

DIPARTIMENTO DI INGEGNERIA INDUSTRIALE

Measuring Spatial MIMO Impulse Responses in Rooms Employing Spherical Transducer Arrays

ANGELO FARINA, angelo.farina@unipr.it LORENZO CHIESI, lorenzo.chiesi@gmail.com

GOALS

 Room Acoustic Measurements based on IR recording and quantitative parameters analysis (Objective)

 Advanced auralization methods suitable for group listening or personal VR applications (Subjective)

 New trajectory visualization tools for understanding sound propagation inside room

 Spherical Microphone Array (AES-130 paper)

 Spherical Loudspeaker Array (AES-140 E-brief)

 M.I.M.O. IR measurement with Microphone and Speaker Arrays

 Advanced Auralization with rotation capability for source and receiver

 Graphical representation of trajectories of sound rays

METHODS

TRADITIONAL ROOM ACOUSTIC MEASUREMENTS (SISO)

Recording mono or stereo Room Impulse Responses

Dodecahedron with ESS signal Impulsive Sources

p(t)

t

• Direct Sound

• Early Reflection

• Late Reflection

Omnidirectional Microphone

Figure of 8

Microphone

TRADITIONAL ROOM ACOUSTIC MEASUREMENTS

ISO Acoustical Parameters computed from Room Impulse Response

RT

₆₀

Reverberation time Time needed for the sould level of a stationary sources abruptly interrupted to decay of 60dB

C

_50/80

Clarity index for speech and music

Ratio between energy associated to reflections arriving in the first 50/80ms and energy associated to the successive reflections

J

_LF

Lateral fraction index Ratio between energy associated to early reflections arriving from the side and energy associated to the early reflections arriving from all directions

For all these parameters, literature and experience define optimal values

depending on room target of use and size

TRADITIONAL ROOM ACOUSTIC MEASUREMENTS

In case measured acoustical parameters do not meet optimal value or room exhibits macroscopic acoustic problems, the acoustician should identify proper corrective actions.

Excess of reverb Adding absorbing material

Lack of reverb Adding diffusors, remove absorption

Poor Clarity Create early reflections and reduce reverb Poor Lateral fraction Add reflectors around the listener

Echoes Identify and inactivate reflection source

Quantity and position of acoustical correction devices and materials are critical and left to the acoustician’s experience

Need for "qualitative" Room Acoustic Analysys Tool which helps acousticians to deeply understand propagation of sound in space

and apply corrections where they are more effective.

Loudspeaker Arrays give us control over direction of sound emitted by the source while

Microphone Arrays reveal the direction of sound arriving to the receiver making easy to understand

sound propagation.

MICROPHONE ARRAYS

MH Acoustics Eigenmike™

• 8.2 cm Spherical Microphone Array

• 32 channel using Hi-Quality

Sennheiser Omnidirectional capsules

• Digital conversion inside sphere

 Microphone capsules mounted on spherical baffle provide quite poor directivity

 RAW capsule signals need to be processed to obtain “Virtual Microphones”

with specific directivity, ranging from omnidirectional to highly directive patterns

 Virtual microphones can be oriented in any direction

 Any number of Virtual Microphones can be extracted from recorded RAW capsule signals

Different strategies for processor filters synthesis exist:

 Theoretical method

(based on sound plane wave decomposition around object of simple shape)

 Numerical method based on inversion of spatial impulse response

(It can be applied to any shape and compensate for transducer non-ideality)

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Stepper Motor Stepper Motor

Custom control electronic

POE Ethernet

POE Injector

Control PC with MATLAB Audio Interface

Firewire

MICROPHONE ARRAYS

Automatic system for Microphone Array characterization

Custom 2 axis rotating holder:

• Axis1: B&K turntable (completely revamped)

• Axis2: Custom designed and manufactured

362 direction characterization with 10 second ESS test signal can be completed in 90 minutes

MICROPHONE ARRAYS

m = 1…M Microphones

d = 1…D Test directions

Characterization of Microphone Array Spatial Impulse Response

Array is subjected to impulsive sound wave coming from D = 362 test directions

uniformly distributed around it

For any test direction the IR of the 32 microphones is recorded populating a row of the Spatial Impulse Response

matrix

Microphone Array Beamformer Filter Sinthesis

Corresponds to determine the unknown filters h by imposing:

Where the known Q is a matrix of scalar gains arbitrarily defining the directivity of each of the V desired Virtual Microphones

in any of the 362 test directions

Frequency domain solution can be transformed back to time domain obtaining coefficients of beamformer FIR filters

Transformed to frequency domain, the system exhibits its linear nature and can be solved for each spectral row with Least Square numerical

method

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MICROPHONE ARRAYS

Real Microphone Nearly omnidirectional

Synthesized Virtual Microphone Cardioid 8^th order

Synthesized Virtual Microphone Omnidirectional

LOUDSPEAKER ARRAYS

 Speakers mounted on spherical buffle exhibit a nearly omnidirectional directivity at low frequency (wavelength larger than speaker size)

 At higher frequency (wavelength shorter than speaker size) speakers start beaming

 To obtain a controlled directivity source (Virtual Speaker) an input signal should be processed with a specific filter to feed each real speaker

 The structure of the Loudspeaker Array Beamforming Processor is the same as the Microphone Array Beamforming processor

 Numerical framework for FIR filter synthesis developed for the Microphone Array can be applied also to Loudspeaker Array

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LOUDSPEAKER ARRAYS

Characterization of Loudspeaker Array Spatial Impulse Response

Each of the S = 32 loudspeaker of the array generates an impulsive sound wave

s = 1…S Speakers d = 1…D Test directions

The IR is captured along any of the D = 362 test directions

populating a column of the Spatial Impulse Response matrix

Loudpeaker Array Beamformer Filter Sinthesis

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Where the known Q is a matrix of scalar gain arbitrarily defining the directivity of each of the W desired Virtual

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LOUDSPEAKER ARRAY #1

Elevation [deg]

Azimut [deg]

First Loudspeaker Array prototype: “Virtual Array”

 Cannot be used to simulate a virtual source with arbitrary directivity in realtime

 Can be used to simulate a real speaker array in room acoustic measurement application where the speakers of the array are used one by one

 25 cm PMMA sphere from garden lantern

 1 x 5” 80W Neodymium Full-Range CIARE speaker

 An automatic two-axes turntable used to simulate a 32-speakers array

LOUDSPEAKER ARRAY #1 (single loudspeaker + turntable)

Single Speaker (real)

Nearly omnidirectional

Synthesized Virtual Speaker Cardioid 8^th order

Synthesized Virtual Speaker Omnidirectional

Omnidirectional Virtual Speaker exhibits at least 1 octave wider bandwidth considering the same directivity ripple

Comparison with Dodecahedron Bruel&Kjaer 4292

 CNC machined aluminum design to dissipate heat

 Truncated icosahedron structure built with only 4 different element (hexagon and pentaghon) to optimize production cost

 20 cm diameter spherical array

 32 x RCF 2” 30W Neodymium Full-Range speakers Very high total power 32 x 30 = 960 W

LOUDSPEAKER ARRAY #2

Design and construction of 32 channel Spherical Loudspeaker Array

 Low cost hand crafted prototype made by wood

 Sphere obtained gluing a couple of IKEA bowl

32 channel professional amplification system with USB3 32 In + 32 Out

Audio interface (3000W, 50kg)

32 channels portable class-D amplifier packed in a light 3U trolley

With an Orion USB 32ch interface

1500W, 18 kg

LOUDSPEAKER ARRAY #2 (32 2’’ loudspeakers)

Single Speaker (real) – Directionality strongly depends on frequency

LOUDSPEAKER ARRAY #2 (32 2’’ loudspeakers)

Synthesized Virtual Speaker - Cardioid 4^th order

LOUDSPEAKER ARRAY #2 (32 2’’ loudspeakers)

Synthesized Virtual Speaker - Cardioid 8^th order

LOUDSPEAKER ARRAY #2 (32 2’’ loudspeakers)

Synthesized Virtual Speaker - Omnidirectional

LOUDSPEAKER ARRAY #2 (32 2’’ loudspeakers)

Synthesized Virtual Speaker – Beamwidth vs. Frequency for cardioids of increasing order

Spherical Harmonics vs. Spatial PCM Sampling

Whilst Sherical Harmonics are the “spatial” equivalent of the Fourier analysis of a waveform,

The SPS approach is the spatial equivalent of representing a waveform with a sequence of “spatial pulses”

(PCM, pulse code modulation)

1

2 32 3

32 directive beams

(spatial pulses)

Fourier for waveforms = HOA (B-format) for spatial distributions

A waveform can be expanded as the sum of a number of sinusoids (Fourier), Exactly as a balloon can be represented by the sum of a number of spherical

harmonics (High Order Ambisonics)

Composite spatial balloon

PCM in time = Spatial PCM Sampling (P-format) in space

A pulse sequence modelling a waveform and a spatial distribution

A waveform is represented by a sequence of pulses, a balloon is a “sea urchin” of spikes

M.I.M.O. ROOM MEASUREMENTS (raw emission and recording, A-to-A)

Recording Multiple Input Multiple Output Room Impulse Response

MIMO RAW

Impulse Response Matrix

Retro compatibility with traditional measurement ensured rendering

omnidirectional directivity for the source and omnidirectional and figure of 8 directivity for the receiver

32 channel Spherical Loudspeaker Array

32 channel Spherical Microphone Array

(Eigenmike™)

 Only one speaker of the array at a time is activated

 Impulse Response between active speaker and each microphone of the array is recorded populating a column of the matrix

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M.I.M.O. ROOM MEASUREMENTS (SPS to SPS)

s_pk

m_pk

 SPS beamformer (122 8^th order cardioid V.M.) for the microphone array can be computed (h_MA)

 SPS beamformer (122 8^th order cardioid V.S.) for the loudspeaker array can be computed (h_SA)

 SPS beamformers are applied to measured 32x32 RAW IR Matrix to compute the 122x122 SPS IR Matrix

 The SPS IR Matrix provides explicit directivity information, allowing for sound directions identification

 Each peak in the impulse response corresponds to a sound-ray travelling from source to receiver

For each peak/ray we know:

• Path length

• Direction of emission from source

• Direction of arrival at receiver

 For each peak, an Energy Spatial Distribution Matrix is computed from the SPS IR Matrix

 The peak of Energy Spatial Distribution Matrix identifies the Virtual Source (s_pk) and the Virtual Receiver (m_pk) that carries the most of the energy of the considered sound-ray.

 The direction in which the sound-ray is emitted and the direction in which is received can now be computed from the identified SPS components index (subpixel interpolation increases precision)

Processing MIMO Room Impulse Responses: a 122x122 SPS matrix

122 122

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MIMO

n h n IR n h n

IR

S R

(x_bp,y_bp,z_bp) (ϑ^’_vs,φ^’_vs) (ϑ^’_vs,φ^’_vs)

l_vs l_vr

Sv Rv

(x_r,y_r,z_r) (x_s,y_s,z_s)

S R

(ϑ_s,φ_s) (ϑ_r,φ_r)

Room 3D Model

l_ray

S R

= = (ϑ_vs,φ_vs) (ϑ_vr,φ_vr) = = (x_vr,y_vr,z_vr) (x_vs,y_vs,z_vs)

l_s

l_v

l_r

(ϑ_r,φ_r) (ϑ_r,φ_r)

l_ray

(x_r,y_r,z_r)

(x_r,y_r,z_r)

S R

Room 3D Model (x_vs,y_vs,z_vs)

(x_vr,y_vr,z_vr)

S R

l_s

l_r l_v

S R

(x_bp,y_bp,z_bp)

(ϑ^’_s,φ^’_s)

(ϑ^’_r,φ^’_r) l_s

l_r

(x_r,y_r,z_r)

S R

(ϑ_s,φ_s) (ϑ_r,φ_r)

l_ray

(x_s,y_s,z_s)

M.I.M.O. ROOM MEASUREMENTS

Sound ray path identification

Single Reflection propagation model

Double Reflection propagation model

Triple Reflection propagation model

Coarse 3D model of room is needed

Accurate 3D model of room for computation of specular

reflections

Identified Sound Ray can now be plotted inside the 3D model of the room

Filters can be applied based on:

• Reflection order

• Path length

• Ray energy

M.I.M.O. ROOM MEASUREMENTS

Single Reflection Path

Section View

Plant View 3D View

Poor Lateral Reflection

M.I.M.O. ROOM MEASUREMENTS

Double Reflection Path

M.I.M.O. ROOM MEASUREMENTS

Triple Reflection Path

Long path with high energy transfer:

possible audible echoes

CONCLUSION AND FUTURE DEVELOPEMENTS

Proposed Microphone and Loudspeaker Array technologies are demonstrated to be effective

for deeply understanding sound propagation in rooms Current high cost involved in these technologies

restricts their use to research applications

Their usability by professional acousticians could be reached by:

• Reducing hardware cost

• Developing easy-to-use analysis software

This work is dedicated to Alberto Amendola, who originated many of the fundamental ideas.

He sadly passed away this spring, but his memory will continue

inspiring us.