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- The initial approach was to use directive microphones for gathering some
information about the spatial properties of the sound field “as
perceived by the listener”
- Two apparently different approaches emerged: binaural dummy heads and
pressure-velocity microphones:
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7
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- It was attempted to “quantify” the “spatiality” of a room by means of
“objective” parameters, based on 2-channels impulse responses measured
with directive microphones
- The most famous “spatial” parameter is IACC (Inter Aural Cross
Correlation), based on binaural IR measurements
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8
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- Other “spatial” parameters are the Lateral Energy ratios: LE, LF, LFC
- These are defined from a 2-channels impulse response, the first channel
is a standard omni microphone, the second channel is a “figure-of-eight”
microphone:
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9
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- Experiment performed in anechoic room - same loudspeaker, same source
and receiver positions, 5 binaural dummy heads
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- Diffuse field - the difference between the heads is now dramatic
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- Experiment performed in the Auditorium of Parma - same loudspeaker, same
source and receiver positions, 5 pressure-velocity microphones
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- At 25 m distance, the scatter is even larger....
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- The Soundfield microphone allows for simultaneous measurements of the
omnidirectional pressure and of the three cartesian components of
particle velocity (figure-of-8 patterns)
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15
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16
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- Current 3D IR sampling is still based on the usage of an
“omnidirectional” source
- The knowledge of the 3D IR measured in this way provide no information
about the soundfield generated inside the room from a directive source
(i.e., a musical instrument, a singer, etc.)
- Dave Malham suggested to represent also the source directivity with a
set of spherical harmonics, called O-format - this is perfectly
reciprocal to the representation of the microphone directivity with the
B-format signals (Soundfield microphone).
- Consequently, a complete and reciprocal spatial transfer function can be
defined, employing a 4-channels O-format source and a 4-channels
B-format receiver:
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- If only spherical harmonics of order 0 and 1 are taken into account, a
complete spatial transfer function measurement requires
16 impulse responses:
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- Albeit mathematically elegant and easy to implement with
currently-existing hardware, the 1st-order method presented
here cannot represent faithfully the complex directivity pattern of an
human voice or of an human ear:
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19
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- The polar pattern of a binaural dummy head is even more complex, as
shown here (1 kHz, right ear):
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- The answer is simple: analyze the spatial distribution of both source
and receiver by means of higher-order spherical harmonics expansion
- Spherical harmonics analysis is the equivalent, in space domain, of the
Fourier analysis in time domain
- As a complex time-domain waveform can be thought as the sum of a number
of sinusoidal and cosinusoidal functions, so a complex spatial
distribution around a given notional point can be expressed as the sum
of a number of spherical harmonic functions
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- Employing massive arrays of transducers, it is nowaday feasible to
sample the acoustical temporal-spatial transfer function of a room
- Currently available hardware and software tools make this practical up
to 4° order, which means 25 inputs and 25 outputs
- A complete measurement for a given source-receiver position pair takes
approximately 10 minutes (25 sine sweeps of 15s each are generated one
after the other, while all the microphone signals are sampled
simultaneously)
- However, it has been seen that real-world sources can be already
approximated quite well with 2°-order functions, and even the human HRTF
directivites are reasonally approximated with 3°-order functions.
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- Arnoud Laborie developed a 24-capsule compact microphone array - by
means of advanced digital filtering, spherical ahrmonic signals up to 3°
order are obtained (16 channels)
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24
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- Jerome Daniel and Sebastien Moreau built samples of 32-capsules
spherical arrays - these allow for extraction of microphone signals up
to 4° order (25 channels)
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25
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- Plogue Bidule can be used as multichannel host software, running a
number of VST plugins developed by France Telecom - these include
spherical harmonics extraction from the spherical microphone arrays,
rotation and manipulation of the multichannel B-format signals, and
final rendering either on head-.tracked headphones or on a static array
of loudspeakers (high-order Ambisonics)
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- Sebastien Moreau and Olivier Warusfel verified the directivity patterns
of the 4°-order microphone array in the anechoic room of IRCAM (Paris)
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- University of California Berkeley's Center for New Music and Audio
Technologies (CNMAT) developed a new 120-loudspeakers, digitally
controlled sound source, capable of synthesizing sound emission
according to spherical harmonics patterns up to 5° order.
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- Class-D embedded amplifiers
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- The spatial reconstruction error of a 120-loudspeakers array is
frequency dependant, as shown here:
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- A complete 24-inputs, 24-outputs system can now assembled for less than
2000 USD
- Low-noise PC case, RME Hammerfall sound
card, 3 Behringer Ultragain Pro-8 digital converters slaved to
the same master clock
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- A set of digital filters can be employed for sinthesizing the required
spatial pattern (spherical harmonics), either when dealing with a
microphone array or when dealing with a loudspeaker array
- Whatever theory or method is chosen, we always start with N input
signals xi, and we derive from them M output signals yj
- And, in any case, each of these M outputs can be expressed by:
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- The sound field is sampled in N points by means of a microphone array
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- The processing filters hij are usually computed following one
of several, complex mathematical theories, based on the solution of the
wave equation (often under certaing simplifications), and assuming that
the microphones are ideal and identical
- In some implementations, the signal of each microphone is processed
through a digital filter for compensating its deviation, at the expense
of heavier computational load
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- No theory is assumed: the set of hij filters are derived
directly from a set of impulse response measurements, designed according
to a least-squares principle.
- In practice, a matrix of filtering coefficients, is formed, and the
matrix has to be numerically inverted (usually employing some
regularization technique).
- This way, the outputs of the microphone array are maximally close to the
ideal responses prescribed
- This method also inherently corrects for transducer deviations and
acoustical artifacts (shielding, diffractions, reflections, etc.)
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36
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- For computing the matrix of N filtering coefficients hi0, a
least-squares method is employed.
- A “total squared error” etot is defined as:
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- DPA-4 A-format microphone
- 4 closely-spaced cardioids
- A set of 4x4 filters is required for getting B-format signals
- Global approach for minimizing errors over the whole sphere
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39
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- A set of 16 inverse filters is required
(4 inputs, 4 outputs = 1°-order B-format)
- For any of the 84 measured directions, a theoretical response can be
computed for each of the 4 output channels (W,X,Y,Z)
- So 84x4=336 conditions can be set:
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- Traditional methods for measuring “spatial parameters” proved to be
unreliable and do not provide complete information
- The 1°-order Ambisonics method can be used for generating and recording
sound with a limited amount of spatial information
- For obtaining better spatial resolution, High-Order Ambisonics can be
used, limiting the spherical-harmonics expansion to a reasonable order
(2°, 3° or 4°).
- Experimental hardware and software tools have been developed (mainly in
France, but also in USA), allowing to build an inexpensive complete
measurement system
- From the complete matrix of measured impulse responses it is easy to
derive any suitable subset, including an highly accurate binaural
rendering over head-tracked headphones.
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- Anecoic room, one source, one
receiver
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- The frequency-dpendent directivity of the human voice has been
approximated with first-order components:
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- Reverbersnt room, one source, one
receiver
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Notes
