M00232

LOUDSPEAKER FAR-FIELD

EQU

ALTZATION

SYSTEM USING

DIGITAL

SIGNAL

PROCESSOR

Erisman Kriswandhani

Lim!,

Matias H.

w.

Budhianthor, F. Dalu setiajit

I _{Audio, Music,}

and Electroacoustic Laboratory, Electronics and Computer Engineering Faculfy,

Satya Wacana Christian University Diponegoro 52-60, Salatiga

Email: erisman2919@yahoo.comr, _{mbudhiantho@yahoo.comr, sotdaj@yahoo.coml}

ABSTRACT

Sound

reproduction

system

frequency response

at

listener position

in

the far-field

of

a loudspeaker

is

not

flat

due

to

the

imperfect frequency response

of

the

loudspeaker

and

the room itself. We design an onchip loudspeaker

far-field equalization system at a listener location

ia

a

room

using

TMS320C67l3

Digital

Signal

Processor.

Initially the

system

_{measures the} impulse response

using

a

MLS

signal.

The minimum-phase

of

measured impulse response is

found

b!

using

Hilbert

transform.

Least

mean

square algorithm is then used to calculate equalizer impulse response. Finaily, we used linear phase FIR

filter approach to minimized distortion of its output signal.

The

equalizer successfully decrease the

standard

deviation

of

the

system

magnitude

response from +6,19

dB to

+3,37

dB

at the audio frequency range of20-20000 Hz.

Kepvords: equalization,

DSP,

loudspeaker, far-field.

1

INTRODUCTION

Sound

reproduction system (consists of

audio amplifier, loudspeaker, and room) frequency

response

at

listener

position

in

the far-field of

loudspeaker is not

flat.

It

is

caused mai:rly

bii

the imperfect frequency response

of

the

loudspeaker

and the room itself [1].

A:ralog graphic and

parametric equalizer

may mediate this problem. However,

it

requires a

specific skill and equipment (spectrum analyzer) to determine which liequencies need

to

be equalized and

it

is

rather complicated

to

do

for a

non-technical people. Furthermore, those equalizers do

not equalize the phase response

of

the system, they

just equalize the magnitude response. The designed

equalizer equalizes the system automatically using

TMS320C67l3

Digital

Signal Processor (DSp), the magnitude as

well

as phase response

of

the sound reproduction system.

,

Least mean

square

is

used

to

solve

the

equalization

problem

of

loudspeaker's far-field

area. While

it

is not a real-time algorithm,

it

could deliver a solution that

is

close

to

Wiener solution.

Before

the

implementation

of

equalizer hansfer

function,

Hilbert

transform

is

used

to

convert

system transfer function

to a

minimum-phase system

to

avoid instability. Linear

phase Finite

Impulse

Response

(FIR)

filter

approach

and

windowing

is

adapted

to

obtain

a

constant group

delay and

undistorted

output.

This

filter

has

a

symmetric coefficients that lead

to

a decrement

of

multiplication operation and memory usage _[2].

The

equalization was able

to

improve the standard deviation of system magnitude response at the listener position by more than 50%o.

2

N{ODEL,

ANALYSIS,

DESIGN,

AND

IMPLEMENTATION

2.1

Loudspeaker

Far-field

Equalization

Sound

wavefront

at

the

listener

position depends

on

the

distance

between listener

and

loudspeaker.

In

loudspeaker's

far-field which

is

approximately

I

_{metre away from} the loudspeaker,

its radiation is omnidirectional and the wavefront is spherical [2].

Iflistener

faces the loudspeaker, the distance

between

the

loudspeaker

to

the

right

ear

is

equal

with

the

left

one.

The

difference

of

binaural perception

is

ignored

[3],

and the two

listening points at the listener position are identical.

The equalization uses a listening room with

an

area

of

25-40 m2

that

goes

to

fBt-OOZOS-t: standard.

The

positioning

of

loudspeaker and

listener

at

that

listening room goes

to

Golden Cuboid standard. According

to

those standard, the distance range between loudspeaker and listener is 1,97

-

2,49 m, ia the loudspeaker's far-field.

Therefore

the

equalization

of

loudspeaker

far-field

response

need

only

to

consider

the

VI-69

i

I

r'i

li

ti fi

$

The 6'h htJrnational Conference on Information

&

Communication Technology and Systems

characteristic

of

one

listening

point.

This characteristic is determined by the iirpulse response at the listening point.

2.2

Least

Mean

Square

Algorithm in

Measuring Equalizer's Impulse

Response

We used least mean square algorirhm

j1

1le

equalization by modifying system impulse response so that system output is as close as possible with the

ideal impulse response. The equalization is best

if

the

.

squared impulse

response

error

signal

is mlnlmum.

MLS

signal applied

to

measure system

impulse

response

and

calculated

the

cross-correlation between

the

input

MLS

signal

and

received

MLS

signal at the listener's position. The

ideal

impulse response

is

found from the

auto-correlation

of

the input

MLS

signal. There is time

delay

befween those

two

MLS

signals

which

is

accounted

the

distance between loudspeaker and

microphone.

We

compensated

the

delay

by

Z samples. The loudspeaker equalization using least

mean square

algorithm

is

shown

at

the

Figure

1 [image:2.595.50.251.413.483.2]

below.

Figure l. Loudspeaker's far-field equalization system using least mean square algorithm block diagram.

Which

hq[n] is

equalizer's impulse response,

l1n/

is

system's impulse

response,

6[nJ

is

impulse

signals, e[nJ

is

impulse response's error, and z-r is delay.

Equalization enor e[nJ

is

the

differenbe between output

of

serial system

(hofn] * h[n]) with

delayed Z-samples

ideal impuls

signal

6[n-L]. Equaiization

is

successful when the square

of efnl

is minimum.

Impulse response's

error

can

be

expressed

by the following equations:

elnl

=

6hi

- rl

-

(no["J

.

htn])

(l)

The equalization

is

successful when e2 yn1 ₌

0.

The

next step

is

to find

equalizer impulse response hq[nJ so that its convolution

with

h[nJ is

similar with ideal impuls signal 6[nJ.

The

least mean

square algorithm

is

implemented

in

matrix notation

[4].If

hq[n]

has a

length

of

M

samples,

h[nJ

has

a

length

of

N

samples, the required length

of

fik-Ll

and e[nJ is

M+N-l

samples

[2].

The column vector expression

of

h[nJ, he[nJ,

6[nJ

dan

e[nJ which have

the

elements

of

its

samples

are

expressed

at

the

following equations.

,n

=

(l[ol

hh]

htzl

rlru

-

1l)r

(3)

rro

=

qho[oJ

hah]

ha[2]...

halr{

-

1l)r

6

= qaloJ

6t1]

6[2]

.,,

dlllt+N-11)t

ds

=

(6[-I]

,r[1

-

r]

612

_

d[/lt+lf-I-1])r

e

-

1a[oJ

elr]

elzl

...

e[.af*N-1]jr

(4)

(s)

11..,

(6)

(1)

Equation

(2)

can

be

expressed

in

matrix form.

e

=

6L-

H.he

(8)

11

is a

(N+M-l)

by

M

matrix, synthetized

from

a column vector

h

so that equal to a convolution between h[nJ andhg[nJ.

The

square

of

e[nJ (error

energy) can be expressed at the following equation:

E =

er, e

=

6zr,6r-

2,hQr,

Hr.67+

hQr .Hr

.H.ha

(10)

Error

energy

is

minimum when

it,s

first derivative with lro is similar to zero.

d

(E\

,a-,

=

-?'Hr

't1+z'tf

'H,hq

= 0

(11)

it

is

H.ho

lh[0]000\

/r,irl htol

o .., o

\

r=lt1z1

hlll

/,tol

o

ltel

\i

\0

i : ". i

l

0 0

fttN_11/

H-t

f

nt

-

rnJ. hq

[mJ

(2)

Iti=0

elal

=

dla

- Il

Loudspeaker's Far-field EqualiTation System Using Digital Signal Processor-Erisman K.L.

And the column vector

of

equalizer impulse

response rs:

hn

=

(Hr.

I{)-',fit,6t

2.3

Hilbert

Transform's

Minimum-phase System

Concept

Most

of

the

measured

room's

impulse

response

is

a non minimum-phase. The inverse

of

non-minimum phase

transfer function result

in unstable transfer function.

The

equalizer transfer function

is

an inverse

of

system transfer function that

will

be equalized, therefore

to

create

a

stable

equalizer,

the

system

must

be

converted

to

a

minimum-phase system.

A

minimum-phase

system

G^(d')

has

a magnitude and phase that relates each other

in

a

Hilbert transform.

rr{tn

1c,"

(ei')

l} =

dco.(ei")

(13)

Magnitude

of

miaimum-phase system and

non

minimum-phase system

is

equal.

Using

that

fact,

we

can

find

the

phase

of

minimum-phase

system

by

using a

Hilbert

transform at the natural

logarithm

of non

minimum-phase

system's magnitude.

TMS320C6713 DSP doesn't have a specific software function or specific hardware processor to calculate the Hilbert transform, so Hilbert transform

wiil

be found

by

using

the properly

of

analytic

signal.

For a random real signal

g(t),

analylic srgnal

g"(t) canbe expressed at the following equation.

e.(t)

-

s(r)

+.rd(r)

While

d(t)

is Hilbert transform ot g(t).

(14)

The should:

G"(j0d)

Fourier transform

of

equation '(14)

Therefore Hilbert transform of a random real signal

g(t)

can

be

achieved

by

calculating the

Fourier transform of g(t) (G(j@)), forming G"Qa) as

in

equation

(15),

and calculating inverse Fourier transform

of

G,(a)

(C,0).The Hilbert

transform

of g(t) is the imaginary part of g.(t).

2.4

Digital Finite

Impulse

Response

Filter

Approach

in

Forming

of

Equalizer

Filter

Equalizer impulse

response

we

obtained

from

the least mean square algorithm

may

has a

non

linear

phasei response (non-constant group

delay)

that may

distort

the

input.

signal.

W*e implemented

the

equalizer

with

linear phase FIR hlter. We converted the equalizer impulse response

to a

linear phase

FIR digital filter by

windowing

process.

.

Hamming window related to a

filter with

the

smallest transition

band

and high

stop-band attenuation without producing Gibbs phenomenon.

2.5

Equalizer

Design

The

implemented loudspeaker far-field

equalizer system can be expressed at the

following

diagram (Figure 2).

The measurement of

initial

system response, the equalizer, and the equalization

ofthe

system

all

implemented

on

TMS320C6713 DSP and

a

short [image:3.595.193.512.20.750.2]

version of the algorithm was as follow.

Figure 3. TMS320C67l 3 DSP equalizer short algorithm

:. I

i

:;

a: i.. t'

(12)

tmtuk

ot

>

0

zmtuku=e

(15)

tmfuk

a;

<

0

(zc(i"D,

=l

c(1d

,

to

Figure 2. Loudspeaker's far-field equalizer system using TMS320C67l3 DSP block diagram.

Measuring system impulse respoose using MLS signal

Calculating minimum-phase system inpulse response using Hilbert transfomr

Calculating equalizer impulsc response using

least mean squarc algorithm

Calculating linear pliase FIR equalizer filter by rr,indos'i:rg

i.

.

The _{suggested SA.i value}

of MLS

_signals

to

the noise

is

30-50

dB

t6l.

_SnV

*ui*,

'.un

U.

increased

by

repeating

and

u".ruf"g

the measurement

[7].

SN

_{value has a}

3

_dB

lrr.i._"nt

for

every double _{timed increm.nt}

of

*ur,]r.*.rrt

amount [7].

.

Background noise level at the measurement

is

approximatety

50 dB,

_uuAio

---uirrfrin"r,,

amplification _{has been set so the}

MLS

sienat level

which is

received

at

_the

micropho".-*u-r8O

dB.

Therefore

ten

_amount

of

_{repeated unO-lu-"rug.a}

measurement

fulfills

_{the MLS signal SA.{}

standard. The length of

MLS

sipai

_{must be tho same}

y!

or

longer than

.oo-i,

reverberation _time

(RT(60)

to

avoid

_{time_aliasing}

ut

tfre

niisur"a

room's impulse _{response. The rJom,s}

,"u"rioution

time at the measurement _is

0,gl

,,

ro rh"

_t-""n-rth

of

shift register that is used to generare tf,"

fraiS'lignuf

11.1!

bir

It

produces

MLS

Jignal

*iifrlfr"

f.lre,n

"f

2'o

bir

=

65536

bit.

U^sing"44ti}

kH;,"_to,,r,

frequency,

the

MLS

-signat,s

d;#

is

(65536/44100)

s

=

_1,486

,

_JnO

ti-"_ufi^irg

rviff not _{occur at the measurement result.}

,

The DSp

generated

_MLS

signal

spectrum

can be seen at the following figure.

vl-/L

etoreribd

,=I*O-x++100

(16)

lhe

6"' lntematronal _{Conf'erence on}

.r; Information

&

_{Communication Techaology}

and Systems

the measwement

is l,g

_{m, therefore the value} of Z

is 234 samples.

After

minimum_phase

system

_impulse response

was found

by

using

HitUert transiorm, equalizer impulse _{response was approximated using} least mean square argorithm

",

;;;;;;

Jquutioo (12).

With the

65536- samples length

of

system

impulse response, _{the length}

of

"quifir".'impulse

response

is

determined

by

ln"

following consideration.

To

_eoualize

tn" t.qu"o"y^i.rpoor"

down

to

the low friquency 20 Hz,

_{the length}

of

equalizer's impulse

response

is

i/20

_{s,- which}

corresponded to

(l/20) x

₄₄₁₀₀

=

_{2205 rurnol"r.}

.

'

Ihe

length

of

Hamming

window

*ti"l

i,

used at the linear phase FIR nf

6,

upprouc

n'ii

_zzOS samples as well.

3

RESULT

.

Measurement _{and equalization}

test was done

in

a

room

with

the size

of

ZS

;r-'""i'

;,Sf ,

reverberation _{time. The position}

of

tourf.*1,

unA

hstener

went

to

_{the Gotden}

cri"ii,i{"{^ra,

tn"

distance between loudspeaker ana hstener was f ,S m, and the background _noise jevel

*u,

_SO

Og.-^""

,,I|"^r^ttem

frequency _{response measured by}

t.,lrr

was compared

with

_{the measurement}

of

the same system _{using a white noise}

by pC

_software. .

The

standard deviation

of

system fr.qu"nry

response

before and after

the

equatizatioi- _was

calculated.

|

""-:',0,

3.1

Yhi"l

Z

is

signal delay

at

the

cross_conelation

calculation (sample) _and

x

is

_{tne aistance}

-U-#""n

loudspeaker and microphone (m). The distance

x

at

lVstem'.s Frequency

Response

[image:4.595.34.247.387.522.2] [image:4.595.270.488.569.704.2]

Evaluation

Figure

5

below

_shows

the

_magnitude

of

.lllr.*,1_fr:quency

response measured Uy the

nSf

yrnq

MLS

signal, plotted

by

_Code

'Co_oor.,

Studio of

TMS320C6il3.

To

evaluate

the validity

of

that

_frequency response, another frequency response

of

the same

Figure 4. TMS320C67l _{3 DSp generaret MLS}

signal spectrum.

.

.

.

MLS

signal has almost the same _spectrum

*illi*it^l'"euls

_{signal which has}

th;

f; ,i..*_

at 20-20-000 Hz frequency

range.

.!

System's impulse response _{was obtained by}

cross-correlation _{between the input}

MLS

signal and

received signal at the listener p-osition.

Tirie

delay

between those

two

signals ^

which-'*"ii"j

_,rr" distance berween

loudSeaker

u;- _;;;;;.n",

express in samples are:

Loudspeaker's Far-field Equalization System Using Digital Signal Processor-Erisman K.L.

i

-/

system measured

using

a

white'

software.

VI-73

equalizer designed and implemented

on

DSP has

improved the magnitude

of

frequency response in

audio frequency range of20

-

20000 Hz.

Standard

deviation

of

system

frequency response magnitude before the equalization is 6,19

dB, and the one after the equalization

is

*3,37 dB.

By

considering-

both

of

the

standard deviation values,

it

was

concluded

that the

designed DSP equalizer has done itsjob.

4

CONCLUSION

AND

DISCUSSION

Equalizer

filter

designed

by

TMS320C67L3 can .decrease

the

standard

deviation

of

system

frequency response magnitude

from

+6,19

dB

to

*3,37 dB in

audio frequency range

of

20

-

20000 Hz.

The

successful

work

of

equalizer filter

shows

the

Hilbert

transform approach

using analytic signal properties works as well.

REFERENCES

tll

Hall,

Donald

E.

(1987) Basic

Acoustics. Canada : John Wiley

&

Sound, lnc.

l2l

Suwamo, Budhiantho

and

Setiaji

(2007) Penyamaan

Medan

Dekat

Penyuara untuk

Satu

Pendengar

di

Satu

Posisi

Tetap.

Electronics

and

Computer

Engineering

Faculty, Satyp Wacana Christian University.

t3l

B. Kapralos,

M.

R.

M.

Jenkin, and E.

Millios

(2003) Auditory Perception and Spatial (3D)

Auditory

Systems. Technical

Report

Department

of

Computer Science

York Universiry.

M. H.

Frank and

A. G. Arthur

(1985) Least

Square Estimation

with

Applications

to

Digital Signal

Processing.

AWiley-lnterscience publicatitln.

A. V.

Oppenheim and

R. W.

Schafer (1989)

Discrete-Time Signal

Processing. Prentice

Hall Signal Processing Series.

Griesinger,

David.

Impulse

Response Measurements Using All-Pass Deconvolution. Lexicon Inc., Massachusetts, USA.

Soren

Krarup

Olesen,

Jan

Plogsties, Pauli Minnaar, Flemming Christensen, and Henrik

Msller

(2000)

An

Improved

MLS Measurement System

for

Acquiring

Room Impulse Responses. Department of Acoustics,

noise

by

PC

".,,fri*fl,l,tt',-ft'fild

l

"'ii

G

I I

l l

g

[image:5.595.46.264.61.266.2] [image:5.595.46.255.500.640.2]

rta

Figure 6. PC software measured magnitude of system's frequency response using a u'hite noise.

By

comparing figure

5

and figure 6,

it

has

shown

that

beside

the

magnitude values

at

the frequencies around 20

Hz

and 20000 Hz, the other magnitude values

which

is

measwed

by DSP

is

similar

with

the one which

is

measured

by a

PC software.

3.2

Equalizer

System

Evaluation

To

evaluate the equalizer, system frequency response

is

measured

by PC

software before and

after the DSP which

takes

role as an

equalizer inserted at the system.

Figure

7

below

shows

the

magnitude

of

system frequency response using PC software with

a white noise after the equalization.

Figure 7. Magnitude ofsystem's frequency response

before and after the equalization.

By

comparing both of the magnitudes at the

figure 6 and figure 7,

it

has clearly shown that the

g

"'i

t -.,

I i *or

I I

i

L4l

t5l

t6l

L7l

''.r5orr{r/l/ii,{i$