Digital equalization of a Digital equalization of a g q employing spectral employing spectral employing spectral
M Bi lli
1A Marco Binelli
1, A ,
1
U i i f P I d i l E D P
1
University of Parma, Industrial Eng. Dept., Parco y , g p ,
d b i @
drumboogie@ g @
2
University of Parma Industrial Eng Dept Parco
2
University of Parma, Industrial Eng. Dept., Parco farina@u farina@u
h b h f l h d f l f l
In this paper we investigate about the usage of spectral smoothed FIR filters for equalizing a car a limited computing power. The inversion algorithm is based on the Nelson‐Kirkeby method and limited computing power. The inversion algorithm is based on the Nelson Kirkeby method and Panzer and Ferekidis showed The filter is aimed to create a "target" frequency response not ne Panzer and Ferekidis showed. The filter is aimed to create a target frequency response, not ne
i id th ' k it A h l b li t i t t th d th h i f th i ht f
inside the car's cockpit. As shown also by listening tests, smoothness and the choice of the right f
Th f di i l i i h i i FIR fil l l h h d
The usage of traditional inversion techniques gives FIR filters longer or equal than the measured reduce the filter length by spectral smoothing, as previously observed by [1]. Other advantages ofg y p g, p y y [ ] g The smoothing algorithm is the same of [1]. It means that there is ang g [ ] We used some vari independent computing for magnitude and phase and this translates in Equivalent Rectang independent computing for magnitude and phase and this translates in
a non linear complex averaging
Equivalent Rectang (DOF) bands (1/24
a non‐linear complex averaging (DOF) bands (1/24
/
800 Hz, 1/3 octave
−1
L ∑ 1 [ ] [ ]
L ∑ [ α + ] [ ]
= M k i W i ]
k [ '
M [ k ] = ∑ M [ k − α + i ] [ ] ⋅ W i
M ∑ [ ] [ ]
i
] [
=0 i 0 i
M: variable (magnitude or phase) to be smoothed M: variable (magnitude or phase) to be smoothed M’: smoothed variable
M : smoothed variable L: window length
L: window length
α: half window length (L=2α+1) α: half window length (L=2α+1)
W i d h
W: window shape
Equation 1: magnitude/phase smoothingq g /p g
Figure 1: avgu e a
Figure 3: magnitude of a frequency response ag g q y p target curve
target curve
Fi 2 i d l h f fil i
Figure 2: magnitude plots shown after filter computation
W d l d hi M l b1 f i i I
We developed a graphic Matlab1 function suite. It allows to plot the measured frequency responsep q y p and set all the filter parameters (length spectral and set all the filter parameters (length, spectral
l ti t t l i ti t )
resolution, target curve, regularization parameters)
1 Figure 4: target curves used to build
1 Matlab is a registered trademark of The MathWorks, Inc. the test filters
F St d t’ t t t
Th l ti f th ti l j t 5 di t From Student’s t test we ca
The resolution of the questions scale was just 5 discrete
filters with “hard” target
steps, so it was hard to compare between average values g
best between the tested
p , p g
results because of the big standard deviation as you can see best between the tested
Y thi f th S
results because of the big standard deviation as you can see
in figure 7 You can see this from the S
in figure 7.
(raw A B, table 1) a
Likingg relationship between “sperelationship between spe
and “liking” (figure 8)
6 and liking (figure 8).
5 4 4
g Ra3
Likin Filter couple Ra
P
2
Filter couple
Perc
1 A B 0
1 A B 0,
0
A ft ERB B h d ERB C t filt d D ft DOF E h d CB B C < 0
A: soft ERB B: hard ERB C: not filtered D: soft DOF E: hard CB Filter type
B C < 0
Filter type
C D 0,
C D 0,
D E 16
A C 0
“f l l k ” h h d d d
A C < 0
Figure 7: “filter type‐liking” histogram with standard deviation
A D 34
indicators A D 34
It is difficult to establish directly if there is an averaging A E 1 It is difficult to establish directly if there is an averaging A E 1, window better than another but it is possible to say that B D 11 filters liking increases with the smoothness of the spectrum B D 11 filters liking increases with the smoothness of the spectrum
(figure 9) Further investigations will be done on smoothness B E 84 (figure 9). Further investigations will be done on smoothness
C E 0
types. C E < 0
Other interesting results come from subjective parametersg j p relationships We found 5 adjective well related to the global relationships. We found 5 adjective well related to the global
filt liki (t h h fi 10 d 11) Table 1: Student’s t test o
filters liking (two are shown here, figure 10 and 11) Table 1: Student s t test o parameter parameter
utomotive sound systems utomotive sound systems y l smoothed FIR filters
l smoothed FIR filters l smoothed FIR filters
A l F i
2 AES 125 ConventionAngelo Farina
2 AES 125 ConventionPaper 7575
g
A d ll S i 181/A 43100 PARMA ITALY
Paper 7575
o Area delle Scienze 181/A, 43100 PARMA, ITALY / , ,
@ il
@gmail.com
@g
o Area delle Scienze 181/A 43100 PARMA ITALY o Area delle Scienze 181/A, 43100 PARMA, ITALY
unipr it unipr.it
d h l b ld h f l h b d h
audio system. The target is also to build short filters that can be processed on DSP processors with on independent phase and magnitude smoothing, by means of a continuous phase method as on independent phase and magnitude smoothing, by means of a continuous phase method as ecessarily flat employing a little number of taps and maintaining good performances everywhere ecessarily flat, employing a little number of taps and maintaining good performances everywhere
f i th f f th di t
frequency response increase the performances of the car audio systems.
d i l B f h li i d DSP i i i fi ld i
d impulse response. Because of the limited DSP computing power in automotive field, we aim to f this method are a remarkable enlargement of the sweet spot and the stability of the equalizationg p y q
The inversion technique is based on [3]. This
iable window lengths rules: Critical Bands (CB), q [ ]
ensures a correct phase handling and
g ( ),
gular Bandwidths (ERB) Double Octave Fraction ensures a correct phase handling and absence of strong peaks in the filter gular Bandwidths (ERB), Double Octave Fraction
4 octave below the car Schroeder frequency ≈ absence of strong peaks in the filter 4 octave below the car Schroeder frequency, ≈
spectrum. The inverse filter S[k] can be above).
computed as follow:
computed as follow:
] k [ G *
] k [ ] T
k [ ] G
k [
S [ ] T [ k ]
] k [
S = 2 ⋅ [ ]
] k [ G ]
[ G [ k ] 2 + + ε ε
S[k]: Inverse filter
G[k] h d d ll d i d i f h
G[k]: smoothed and spectrally decimated version of the system measured transfer function
system measured transfer function.
ε: regularization parameter has been taken (typically) ε: regularization parameter. has been taken (typically) equal to 0.01q
T[k] : target curve.
Equation 2: Inverse filter synthesis veraging window length vs frequencye ag g do e gt s eque cy
We tested inverse filters with 2 target curves (“Soft” andg (
“Hard”) and 3 averaging windows (ERB CB DOF) OverHard ) and 3 averaging windows (ERB, CB, DOF). Over
th th ti d fi ti ( t filt d)
these, the native car sound configuration (not filtered) was inserted inside the listening test.g
A blind listening test was performed to This is the test filter set: A blind listening test was performed to
i ti t bj t’ filt liki Th This is the test filter set:
f investigate on subject’s filters liking. The
A – Soft + ERB;
9 involved persons were medium‐high
B – Hard + ERB; p g
skilled In detail we chose some target Hard R ;
C – Native (not filtered); skilled. In detail, we chose some target curves and averaging windows and C – Native (not filtered);
D S ft DOF curves and averaging windows and
D – Soft + DOF;
asked the subjects to fill a questionnaire E – Hard + CB.
nd
Figure 5: some measured spectra Figure 6: evaluation questionnaire
of test filters (D, E, F filter omitted)
th t th an say that the
curve are the configurations configurations.
St d t’ t t t Student’s t test nd from the ectral distance”
ectral distance
andom andom
Figure 8: “spectral distance ‐ Figure 9: “spectral roughness ‐
centage gu e 8: spect a d sta ce liking” relationship
gu e 9: spect a oug ess liking” relationship
22% liking relationship liking relationship
,22%
0 01%
0,01%
,01%
,01%
6,00%, 0 01%
0,01%
4 80%
4,80%
83%
,83%
1,54%
1,54%
Figure 10: “liking ‐ bass balance” Figure 11: “liking ‐ warmth”
4,87% g g
relationship
g g
relationship
,
0 01% relationship relationship
0,01%
Thi k
on “Liking”
This work was
on Liking
