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Engineering Faculty University of Parma ITALY
ASK Automotive Industries Reggio Emilia - ITALY
Inverse numerical filters for linearisation of loudspeaker’s response
A. Farina, E. Ugolotti, A. Bellini, G. Cibelli, C. Morandi
First COST-G6 Workshop on Digital Audio Effects
(DAFX98)
Automotive Industries Group
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Angelo Farina
Outline Outline
z
Loudspeaker physical conformation;
z
Loudspeaker non-linear modeling;
z
Digital audio Processor for distortion compensation;
z
DSP implementation;
z
Measured distortion results;
Automotive Industries Group
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Angelo Farina
Basic loudspeaker Basic loudspeaker
conformation conformation
z Electric- mechano-acoustic transducers:
– p(t) = k e(t)
z Non-linear behavior:
– The magnetic induction B is not constant with displacement
– non ideal suspension stiffness – R = R(T)
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Angelo Farina
Loudspeaker
Loudspeaker modeling modeling
Acoustic signal
Re
Rm
Cm Mm
Za
Bl:1 1:Sd
i(t) F(t) p(t)
Audio electric signal
Automotive Industries Group
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Loudspeaker
Loudspeaker modeling modeling
Audio signal
e(t)
p(t)
) (
) ) (
ˆ
(
s e
s s p
xn
=
ϕ
) (
) ) (
(
0 ˆ
ˆ
s
s
ns
n
x
x
ϕ
ψ = ϕ
z Non-linear loudspeaker I/O relation is linearized around fixed displacements xn
z ψ xn accounts only for non- linear behavior
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Angelo Farina
Loudspeaker non Loudspeaker non - - linear linear
modeling modeling
Audio signal e(t)
p(t)
) ) (
( ) ) (
0
( n
s e
s
s p ϕ
SPLϕ = →
z
is similar to SPL measurements
)
ψ (n
H(n)
)
SPL
(n
ϕ
Non-linear model
displacement x(t)
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Mathematical formulation Mathematical formulation
1
n 2 n
n n
e
n r
xˆ a ~J(s)
) xˆ ( sL R
s ) xˆ ( ) Bl
xˆ ( ) K
xˆ ( sL R
) xˆ ( sBl ) s ( S~ ) s (
~z ) s
n(
−
⎥⎥
⎦
⎤
⎢⎢
⎣
⎡ +
+ +
= + ϕ
A set of diplacement-dependent transfer functions is derived from the Thiele-Small formulation, allowing for the dependance of Bl, L and K from the displacement x.
n different values of x are considered, and around each of them the variation of the parameters is considered linear. A separate inverse filter is computed for each of the n not-linear responses, and each sample is convolved with the proper inverse filter, which is chosen by first computing the estimated instantaneous displacement x.
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Angelo Farina
Audio processor Audio processor
Audio signal e(t)
p(t)
z The more critical part is the synthesis of the H(n) filter, which makes it possible to estimate the instantaneous displacement
(Non-linear model) -1
Audio processor
Automotive Industries Group
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DSP implementation DSP implementation
Audio signal e(t)
p(t) (Non-linear
model) -1
Audio processor
Power Audio amplifier
Automotive Industries Group
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Angelo Farina
DSP implementation DSP implementation
z
Audio processor implemented with a 320C54x DSK;
z
40 MIPS, 10Kword Dual Access RAM;
z
Sampling frequency 23148 Hz;
z
Converter resolution 14 bit.
Automotive Industries Group
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Multirate
Multirate Audio processor Audio processor
e(t)
HPF ϕSPL−1(n) Delay
+
LPF Decimator LPF
)
1(
− n ψ
H(n)
)
1(
SPL n ϕ −
Interpolator
{
Non-linear processing
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Angelo Farina
Audio processor Audio processor
measurements measurements
Power Audio amplifier
Anechoic room Audio analyzer B&K 2012
Electric
signal Acoustic pressure
Audio
processor
Automotive Industries Group
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Response (SPL) Results Response (SPL) Results
80 85 90 95 100 105 110 115
100 1000
SPL (dB)
f [Hz]
digital pre-processed normal
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Angelo Farina
Distortion (THD) Results Distortion (THD) Results
50 100 150 200 250 300 350 400
20 60 100 140 180
Distortion [mV]
f [Hz]
Amplitude input 4 V
normal digital pre-processed
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Distortion (THD) Results Distortion (THD) Results
20 40 60 80 100 120 140
20 60 100 140 180
Distortion [mV]
f [Hz]
Amplitude input 5 V
normal digital pre-processed
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Angelo Farina
Conclusions Conclusions
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Definition of a non-linear model for low frequency loudspeaker systems;
z
Design of a parametric audio processor for the compensation of non-linear distortion of
loudspeaker;
z
Implementation of the audio processor with a low cost commercial DSP;
z
Measured reduction of Distortion with the
insertion of the audio processor;
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Angelo Farina
The future The future
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New Hardware (Analog Devices SHARC on the EZ-KIT stand-alone board)
z
Inverse filters computed with the Kirkeby regularization technique
z
Full-band linearization by means of “warping”
instead of dual-band processing
z
The inverse filter will include also the acoustics behaviour of the car compartment
Automotive Industries Group
