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BRUEL & KJAER 2031 User manual

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Instruction
Manual
2031
Narrow
Band Spectrum Analyzer Type
2031
033-0267 .
A
narrow
band spectrum analyzer featuring·
almost entirely digital construGtion. The
spectral analysis takes place in
400
con-
stant bandwidth lines across a frequency
range
which
is selectable from
0-
10Hz
to
0-
20kHz
in a
1-2-5
sequence, and ex-
tensive
transient
recording facilities make
the
2031
equally
at
home
with
continuous
and impulsive signals. The analysis takes
place in real-time
for
all frequency ranges
up to
0-
2kHz.
The results produced can
be exponentially or linearly averaged prior
to display on an
11"
calibrated display
screen,
which
may also be used
to
show
the
time
function,
the
instantaneous spec-
trum,
and a hold max. spectrum.
+
BrUel
&
Kjcer
BROEL &
KJ~R
instruments cover the
whole
field of sound and vibration measurements.
The main groups are:
ACOUSTICAL
MI;ASUREMENTS
Condenser
Microphones
Piezoelectric Microphones
Microphone
Preamplifiers
Hydrophones
Sound Level
Meters
Precision Sound Level
Meters
Impulse Sound Level
Meters
Noise Dose
Meters
Noise Level Analyzers
Standing Wave Apparatus
Calibration Equipment
Reverberation Processors
Sound
Sources
ACOUSTICAL
RESPONSE TESTING
Sine
Generators
Random Noise Generators
Sine-Random Generators
Artificial
Voices
Artificial
Ears
Artificial
Mastoids
Hearing
Aid
Test Boxes
Audiometer Calibrators
Telephone
Measuring
Equipment
Audio
Reproduction Test Equipment
Tapping
Machines
Turntables
VIBRATION
MEASUREMENTS
Accelerometers
Force Transducers
Impedance Heads
Accelerometer Preamplifiers
Vibration
Meters
Accelerometer Calibrators
Magnetic
Transducers
Capacitive Transducers
Complex
Modulus
Apparatus
Bump
Recorders
VIBRATION TESTING
Exciter
Controls-
Sine
Exciter
Controls-
Sine-
Random
Exciter Equalizers, Random or Shock
Exciters
Power
Amplifiers
Programmer Units
Stroboscopes
STRAIN
MEASUREMENTS
Strain
Gauge Apparatus
Multipoint
Selectors
MEASUREMENT
AND
ANALYSIS
Voltmeters
Phase
Meters
Deviation Bridges
Measuring
Amplifiers
Band-Pass Filter Sets
Frequency Analyzers
Real Time Analyzers
Heterodyne Filters and Analyzers
Distortion
Measuring
Equipment
Psophometers
Statistical Distribution Analyzers
Tracking Filters
RECORDING
Level Recorders
Frequency Response Tracers
Tape Recorders
Alphanumeric
Printers
Digital Event Recorders
DIGITAL
EQUIPMENT
Computers
Tape Punchers
Tape Readers
Bruel
&
Kjcer
DK-2850 NJERUM, DENMARK ·
Telephone:
+ 45 2 80 05 00 ·
Telex:
37316
bruka
dk
1
Instruction
Manual
2031
Narrow
Band Spectrum Analyzer Type
2031
033-0267 .
'I
r
---~--..-
..
•:
..
" . ·
•·
··
wr·
A
narrow
band spectrum analyzer featuring
almost entirely digital construction. The
spectral analysis takes place in
400
con-
stant bandwidth lines across a frequency
range
which
is
selectable from
0-
10Hz
to
0-
20kHz
in a
1-2-5
sequence, and ex-
tensive transient recording facilities make
the
2031
equally at home
with
continuous
and impulsive signals. The analysis takes
place in real-time for all frequency ranges
up to
0-
2kHz. The results produced can
be exponentially or linearly averaged prior
to
display on an
11"
calibrated display
screen,
which
may also be used
to
show
the
time
function, the instantaneous spec-
trum
, and a hold max. spectrum.
+ BrUel &Kjrer
"'r
q··
L
~-
--
--
-- , - -
-~
--~--
--
-!
~
'~-
-
-
- - - -
--
·-
- - - - - -
.../
NARROW
BAND
SPECTRUM
ANALYZER
TYPE
2031
September 1
978
This
apparatus has been designed and tested according to class
II
of
IEC
publication
348,
Safety Requirements
for
Electronic
Measuring
Apparatus, and has been supplied
in
safe condition. The present
instruction
manual
contains
information
and
warnings
which
should
be
followed
by the user
to
ensure safe operation and to retain
the
apparatus in
safe condition.
CONTENTS
1.
INTRODUCTION
AND
SPECIFICATIONS
(PRODUCT
DATA)
.................................................
1
2.
CONTROLS
..........................................................................................................................
13
2.1.
FRONT PANEL
OF
NARROW
OF
NARROW BAND SPECTRUM ANALYZER
TYPE
2031
.............................................................................................
13
Controls used
for
Analog Input and General Operation
..
.. ..
..
.. .. ..
..
.. ..
..
..
..
.. .. ..
13
Controls used to set the Triggering Conditions
..
.
........
..
....
.
.. .. .. ..
..
.. .. .. ..
...
....
. 15
Controls used in Recording and Transformation of Data
...............................
16
Controls used in Averaging
of
Data ...
.... .. ....
..
.
..
..
....
....
..
.
..
.. .. .. ..
..
..
...
..
..
....
.
..
17
Controls used in
the
Display
of
Data ..
.... .. ....
..
.
..
..
.... ..
.
.. .. .. .. .. .. .... ..
..
.. .. .. .. ....
18
Controls used in•.
the
Input/Output
of
Data ..
.... ..
.
..
.. .. .. .. .... .. ..
.
.... .... .... .. .... ..
.
20
2.2.
THE
2031
DISPLAY
SCREEN
....................................................................
21
The
2031
Display Screen in Display of a Time Function .
.... .. .... ..
..
........
..
....
.
21
The
2031
Display Screen in Display of a Spectrum
..
.
.. ..
..
.. ..
...
........ .... ..
..
....
.
22
2.3.
REAR
PANEL
OF
THE
NARROW BAND SPECTRUM ANALYZER
TYPE
2031
.............................................................................................
23
3.
OPERATION
.........................................................................................................................
27
3.1.
PRELIMINARY ADJUSTMENTS
.................................................................
27
3.2.
CALIBRATION
.........................................................................................
28
Calibration using a Sinusoidal Reference
...................................................
29
Calibration using an External Noise Source
..
..
....
.. ..
..
..
..
.. .. .. .. ..
.
......
..
..
.
.. .. .. ..
30
3.3.
GENERAL OPERATIONAL PROCEDURE
......................................................
31
3.4
. CONTROL OF TRIGGERING
......................................................................
31
Selection of Triggering Source
..
....
..
.
....
.
..
.. ..
.
..
....
..
.
..
.. .. .. .. .. .. .... .. .. .. .. .... .. .. ..
31
Use of the "Records after
Trig."
Control
.... .. ............ .. ....
..
.... ..
.
..
.. ..
..
.. .. .. .... ..
32
3.5.
CONTROL
OF
RECORDING
.................
..
....................................................
33
3.6.
CONTROL
OF
AVERAGING
.......................................................................
34
Linear Averaging .....................................................................................
34
Exponential Averaging .
..
.. .. .. .. .. ..
....
.
..
.
....
.. ..
....
..
....
.. ..
..
.. .. ..
...
..
..
....
.
.. .. .. ..
..
..
36
Hold. max. ..............................................................................................
36
3.7.
USE
OF
THE
DISPLAY CONTROLS
.. .. .... ....
.. ..
..
.. ..
....
.
..
.
..
.. ..
.
..
..
....
.
.. ..
..
.. ..
..
..
36
Display
of
a Time Function ......
.... .. ..
..
.... .. ..
......
....
.
.. ..
..
.. .. .. ..
..
.. ..
...
..
...........
37
Display of a Spectrum
..
.. .. .. .. .. ..
....
..
.... .. ..
.. ..
.... .... ....
.. ..
....
.. .. ..
..
.. .. .. ..
..
.. ..
..
..
39
Use of a Reference
Memory
..
.... .. ......
.
....
.. ..
.
........ ..
.
..
.
..
..
....
.
..
.. ..
...
........
.
..
..
39
Display
of
Difference Spectra ....................................................................
40
3.8.
ANALYSIS
OF
TRANSIENTS
.....................................................................
40
Analysis of Single Transients
..
..
.
.... .. ..
.
.... .. ..
.
........ .... .. ....
..
....
.
..
..
.
......
....
..
.
..
42
Automatic
Transient Averaging
..
.....
.... .. ..
.. ..
....
..
.... ..
..
.
..
..
.... ..
.
..
.. .. .. ..
..
.. .. ..
..
43
Manual Averaging of Transients
with
Rejection
of
Bad Data ..
..
.
..
.. .. .. ..
..
.. ..
....
43
3.9.
ANALOG OUTPUT FROM THE
2031
..........................................................
43
Analog
Output
to a Level Recorder Type
2307
............................................
44
Analog
Output
to an
X-Y
Recorder Type
2308
..........................................
46
Exchange
of
the
Level Recorder and
X-Y
Recorder interfaces
......................
48
3.1
0.
USE
OF
AN EXTERNAL SAMPLING FREQUENCY
........................................
49
Use
of
the
Tracking Frequency
Multiplier
Type
1901
with
the
2031
.....
..
..
....
50
3.11.
RACK MOUNTING
OF
THE
2031
.................. .. ........................
..
....
..
..
.. ..
....
50
4.
DIGITAL
DATA
TRANSFER
AND
REMOTE
CONTROL
OF THE
2031
VIA
THE
IEC
INTERFACE
.....................................................................................................
52
4.1 .
IEC
FUNCTIONS IMPLEMENTED
.................
.
...............................................
52
4.2.
SELECTION
OF
ADDRESSES
.....................................................................
52
4.3.
CODES
FOR
ADDRESSING
2031
CONTROLS
..............................................
53
F.S. FREQUENCY
.....................................................................................
54
TRIGGER "Records a.
Trig."
.............................................
..
.......
................
54
AVERAGING
"No.
of
Spectra"
.
..................................................................
55
TRIGGER
''Level''
.............
..............................................
..
........................
55
INPUT
''Att
0-100
dB''
............................................................................
55
TIME FUNCTION
"Move"
...........................................................................
56
SPECTRUM GAIN
.....................................................................................
56
LINE SELECTOR
.......................................................................................
57
Other
Controls, Upper Front Panel
of
2031
.............................
.
...................
57
Other
Controls,
Lower
Front Panel
of
2031
.......................
..........................
58
Differences Between Remote and
Manual
Control
of
the
2031
..........
....
........
59
4.4.
REQUIRED FORMATS
FOR
DIGITAL INPUT
AND OUTPUT OVER
THE
2031
IEC
INTERFACE
...........................................
60
Mode#
0,
Digital
Input/Output
of
an ASCII Encoded Spectrum
......................
60
Mode#
1, Remote Setting
of
Pushkeys and
Output
of
Pushkey Settings
..........
61
Mode#
2, Digital
Input/Output
of
Time Function
..........................................
62
Mode#3.
Block Transfers MSBY-LSBY
to
and
from
the
2031
.......................
62
Mode#4.
ASCII Sensing
of
Pushkeys
.........................................................
63
Mode#
5, Digital
Output
of
2's
Complement Encoded
Spectrum
....................
64
Mode#
6, Block Transfers LSBY to and
from
the
2031
.................................
64
Mode#
7, Block Transfers MSBY
to
and
from
the
2031
................................
64
Mode#8,
Carry On Processing
......................................
.
...........................
64
Other
Input/Output
Modes,
Manual
Digital
Input/Output
.............................
65
Other
Input/Output
Modes,
Input
of
Alphanumeric
Text to
the
Display Screen
65
4.5.
USE
OF
INTERRUPTS
IN
2031
DATA TRANSFERS
.......................................
66
Read-out of
the
Time Function
with
Interrupt
Control
...................................
66
Read-out of
the
Complex Spectrum
with
Interrupt
Control
.............................
67
Read-out of
the
Averaged
or
Instantaneous
Spectrum
with
Interrupt
Control
.................................................................
67
4.6.
FORMATS USED
IN
BLOCK TRANSFERS
....................................................
68
Format
of
the
16-bit
Time Function
.........................................
.........
..........
68
Format
of
Complex Spectrum
.....................................................................
68
Format
of
Instantaneous Power Spectrum
...................................................
68
Format
of
Averaged
MS
Spectrum
..............................................................
69
Format
of
Spectrum Display
Buffer
.............................................................
69
Format of Reference
Memory
.....................................................................
70
Format of the
8-bit
Time Function
..............................................................
70
4.7.
SPEED
OF
DIGITAL INPUT AND OUTPUT
....................................................
71
FEATURES:
•
High
resolution,
constant
bandwidth
frequency
analysis
in
400
frequency
channels
• Eleven selectable
frequency
ranges
from
0-
10
Hz
through
0-20
kHz
• Full
transient
recording
facilit
ies
with
internal,
external,
or
free
running
trigger
and
control
of
after
trigger
recording
•
Display
of
time
signal,
instantaneous
spectrum,
averaged
spectrum,
and
spectrum
difference
on
11"
display
screen
•
Greater
than
70
dB
dynamic
range
plus
9 dB
crest
factor
capabiI
ity
•
Built-in
antialiasing
filters
• Exponential and
linear
averaging
over
1
to
2048
spectra
• Hold max.
facility
allows
maximum
level in each
channel
to
be held
• Selectable
flat
(rectangular)
or
Hanning
weighting
•
Display
of
spectrum
over
80
dB,
40
dB,
or
20
dB
display
range
•
Memory
allows
storage
of
spectrum
for
comparison
with
later
data
• First
estimate
transfer
function
measurements
18-200
type
2031
Narrow
Band Spectrum Analyzer
possible
using
memory
subtract
feature
•
Alphanumeric
read-outs
directly
from
display
screen
using
line
selector
• Read-outs
using
line
selector
can be made
relative
to
values
in
other
channels
or
lines
•
Output
of
displayed data
via analog
output
•
Digital
input
and
output
via
IEC
interface
•
Settings
of
major
controls
shown
on
display
screen
via
alphanumeric
displays
• Pushkey
controls
externally
programmable
via
IEC
interface
,..,_
• ...,f;ti'K'tOW<OANI\>a
..
l'"aol'
r
:;-:::
1 1
;~,
--
L-
y~oo,.,_,._
_.:J
' '
.:
.:
..
:
.:
.
kll'l
...
_
........,.,
•
Connection
to
IEC
or
IEEE
Std.
488
interface
bus
via
IEC
interface
USES:
•
Analysis
of
acoustical and
vibrational
signals
•
Analysis
of
transients
and
shocks
• Preventive
maintenance
and
machine
monitoring
• Speech
analysis
and
phonetics
•
Order
analysis
• Physiological and
Neurological
research
Introduction
The
Narrow
Band
Spectrum
Anal-
yzer Type
2031
is an
instrument
de-
signed
for
the
narrow
band
fre-
quency
analysis
of
continuous
and
transient
data
coming
from
acousti-
cal,
vibrational,
and
other
signal
sources.
It
calculates
a
400
channel
constant
bandwidth
RMS
power
spectrum,
in
dB,
of
the
input
signal.
The
frequency
range
of
the
instru-
ment
is
pushkey
selectable
in
a
1-2-
5 sequence
from
0-10
Hz
to
0-
20
kHz.
Alternatively,
by
using
an
external
sampling
source,
the
fre-
quency
range can be made
to
float,
allowing
the
2031
to
track
pheno-
mena
of variable
frequency,
as in,
e.g.
order
analysis
. The
time
taken
to
generate
a
single
spectrum
is
less
than
200
ms,
giving
real-time
operation
up
to
greater
than
2kHz.
The
2031
operates by
Fourier
transforming
records
of
1
024
sam-
ples
of
the
input
signal
into
the
fre-
quency
domain.
The
recording takes
place
in
a
transient
recorder
having
two
parallel
memories
.
The
trigger-
ing
facilities
available on
the
recor-
der
enable
the
2031
to
be used in
the
analysis
of
a
wide
range
of
sig-
nals.
The
transient
recorder's
free
run-
ning
mode
is used
to
analyze
contin-
uous
signals. Here,
new
records are
continuously
taken and
trans-
formed
.
Where
the
signals
to
be an-
alyzed are
intermittent
or
transient,
the
triggered
mode is used. Here,
transformation
only
takes place on
receipt
of
a
trigger,
the
source
of
which
may
be
internal,
with
a
trig-
ger
level variable in
200
steps ac-
ross
the
input
voltage range,
or
ex-
ternal
from
a TTL pulse.
In
the
triggered
mode,
the
after
trigger
recording
setting
selects pre-
cisely
which
record is
transformed
with
respect
to
the
trigger.
Its
wide
range
of
adjustment,
namely
0,0
to
9,9
record
lengths
in steps
of
0,1
record
lengths,
enables
transient
data
to
be analyzed even
when
they
are
quite
remote
from
the
precise
moment
of
triggering.
Further,
in
the
analysis
of
cyclic processes,
it
allows
part
of
the
signal
to
be gated
and analyzed
independently
from
the
rest, e.g.
the
opening or closing
of
a valve in a
machine
cycle.
2
The
2031
can be set
such
that
each
new
record taken is
trans-
formed.
Alternatively,
in
the
analy-
sis
of
single
transients,
recording
and
transformation
may
be stopped
as soon as
the
first
record has been
transformed
.
Transformed
data can be
exponen-
tially
or
linearly
averaged over 1
to
2048
spectra. Exponential averag-
ing is
useful
in looking at
running
processes,
where
changes
are
im-
portant,
while
linear
averaging be-
comes preferable
where
it
is
import-
ant
that
all data being
input
has an
equal
influence
on
the
final
average
generated, e.g.
in
spatial averaging
or
averaging
of
cyclic processes.
Note
that
linear
averaging is con-
trolled
such
that
a
true
average is al-
ways
displayed,
this
converging
on
the
final
result.
A hold max. mode
is also available,
allowing
the
maxi-
mum
value
occurring
in
each
chan-
nel
to
be held.
Exponential and
linear
averaging
and
the
hold
max
. mode are
equally
applicable
to
the
analysis
of
continu-
ous
and
transient
data. This
means
that,
e.g.
in
the
previous
example,
the
signal
generated
by
the
opening
or
closing
of
the
valve could be aver-
aged over
many
cycles.
Display
of
the
analyzed
spectrum
takes place on an
11"
calibrated
dis-
play screen,
which
may
also be
used
to
show
the
time
function.
Both
the
instantaneous
and
the
av-
eraged
spectrum
can be
shown
,
and
either
can be
entered
into
a ref-
erence
spectrum
memory
and re-
called later
for
comparison
with
new
,
incoming
data. A
further
dis-
play mode gives
the
difference
be-
tween
new,
incoming
data and
the
stored data.
This
allows
changes
in
spectra
to
be
identified,
and
where
sufficient
stationarity
exists,
allows
the
magnitude
of
a
transfer
function
to
be measured.
Read-outs
from
the
display
can be
plotted
using
a Level Recorder Type
2307
or, (optional), an
X-Y
Recor-
der
Type
2308
via
the
analog
out-
put,
or
digitally
transferred
to
an
IEC
compatible
peripheral
via
the
IEC
interface.
This
interface
also
permits
the
digital
read-in
and read-
out
of
data, and
the
reading and
the
setting
of
the
front
panel
controls,
as used
in
the
remote
programming
of
the
2031.
The
frequency
and RMS
ampli-
tude
of
any
channel
in
the
spec-
trum,
or
the
relative
position
of
any
sample
in
the
time
function
can be
read
from
alphanumeric
displays on
the
display
screen, by
using
the
line
selector. (Note
that
when
external
sampling
is used, spectral read-outs
are
in
terms
of
amplitude
and
chan-
nel
number.)
Further
alphanumeric
displays give
the
settings
of
the
ma-
jor
controls
such as
the
full
scale le-
vel,
full
scale
frequency,
etc.
Amplitudes
are read
from
the
2031
in
terms
of
dB. The reference
level is
usually
set
to
1
JJV
RMS,
but
may
be varied
throughout
a
range
of
±
50
dB
from
that
level.
Alt-
ernatively,
the
RMS level
in
any
channel
of
a displayed
spectrum
can be
set
to
0 dB, and all
the
fol-
lowing
amplitude
measurements
made
relative
to
that
level. Like-
wise,
the
position
of
a
sample
in
the
time
function
can be read
in
ab-
solute
terms,
or
relative
to
the
posi-
tion
of
any
other
sample, as a
sam-
ple
number
and as a
time
in
sec-
onds.
The
amplitude
display
range
of
the
2031
can be set
to
80
dB,
40dB,
or
20dB
. The
full
scale level
can be varied over
80
dB
in
10
dB
steps. Hence,
this
allows
a
40
dB
or
a
20
dB
amplitude
window
from
the
displayed
spectrum
to
be expanded
to
fill
the
entire
display
screen.
Simi-
larly,
when
a
time
function
is
dis-
played,
the
time
axis can be ex-
panded by a
factor
of
3.
Input
to
the
2031
is via a
stand-
ard B & K
measuring
amplifier
in-
put,
allowing
connection
of
most
B & K
microphone
preamplifiers
and
other
signal
sources.
An
internal
amplitude
reference
is provided
to
ease
calibration
. Frequency calibra-
tion
is made
unnecessary,
since
all
measurements
are referenced
to
an
internal
crystal
controlled
oscillator
.
Prior
to
recording and
transforma-
tion,
the
input
signal
is passed
through
an
antialiasing
filter,
auto-
matically
selected
with
the
fre-
quency
range.
This
filter,
which
cuts
off
at
the
selected
full
scale
fre-
quency,
is
to
prevent
the
introduc-
tion
of
aliasing
distortion,
and
may
be bypassed
if
required. For
exter-
nal
sampling,
either
the
internal
or
external
antialiasing
filters
may
be
used.
Before
transformation,
the
time
records
may
be
weighted
using
a
Hanning
weighting.
This
is
usually
used
in
the
analysis
of
continuous
signals
to
improve
selectivity.
For
the
analysis
of
transients,
however,
where
the
Hanning
weighting
might
modify
the
data
under
analysis,
a
flat
weighting,
(i.e.
rectangular
or
no
weighting),
may
be
selected
.
Frequency Analysis
The
mathematical
basis
for
all
fre-
quency
analysis
procedures
is
the
so-called
Fourier
Transform.
In its
most
genera
I
form,
it
is
expressed
by
the
Fourier
integral
pair
as
fol-
lows:
1 1
00
F(w)
= -
f(t)
exp
(-jwt)
dt
21T
-oo
(1)
f(t)
=
~-~
F(w)
exp
(jwt)
dw
(2)
Equation
1
transforms
the
time
function
f(t)
into
its
complex
fre-
quency
components
F(w)
for
each
(angular)
frequency
w
radians
/s,
(w = 21rf,
where
f
is
the
frequency
in
Hz).
Equation
2
shows
how
the
original
time
signal
f(t)
can
be
com-
pletely
synthesized
from
its
original
frequency
components.
It
is
possible
to
write
discrete
equivalents
of
equations
1
and
2 as
follows:
1
N-
1 ( 21rnk)
F(k) = - L
f(n)
exp
-j
--
N n=O N
(3)
f(n)
=
N-1
I
k=O ( 21rnk)
F(k) exp j
-N-
(4)
These
two
equations
are
known
as
the
Discrete
Fourier
Transform,
or
DFT,
and
each
of
the
continuous
functions
F(w)
and
f(t),
extending
from
+
oo
to
-oo,
is
replaced
by
a
fi-
nite
number,
N,
of
discrete
sam-
ples,
these
being
F(k)
and
f(n)
respec-
tively.
If
Af
is
the
frequency
incre-
'
ment
between
the
samples,
and
At
is
the
time
increment,
then
kAf
is
the
frequency
corresponding
to
F(k),
750177
Fig.1.
Discrete
Fourier
Transform
of
Complex
Time
Function,
(real
part
only).
Note
the
periodic-
ity
of
the
spectrum
Real
Imaginary
761025
Fig.2.
Discrete
Fourier
Transform
of
Real-valued
Time
Function.
Note
the
symmetry
of
the
real
part
and
the
antisymmetry
of
the
imaginary
part
and
nAt
is
the
time
corresponding
to
f(n).
The
infinite
integrals
are
hence
replaced
by
finite
sums,
but
many
of
the
properties
of
the
DFT
are
parallel
to
those
of
the
integral
transform.
Equation
3
is
known
as
the
forward
transform,
and
equa-
tion
4 as
the
inverse
transform.
Although
it
is
of
a
discrete
na-
ture,
and
hence
lends
itself
to
digi-
tal
computation,
direct
evaluation
of
the
DFT
is
a
lengthy
and
inefficient
procedure
requiring
some
N2
com-
plex
multiplications
to
perform
an
N
point
transform.
Fast
Fourier
Trans-
form,
or
FFT, is
an
algorithm
which
allows
a
more
efficient
means
of
evaluation,
reducing
the
number
of
multiplications
required
to
approxi-
mately
N log2 N.
In
the
generalized
forward
trans-
form,
N
complex
time
domain
points
are
transformed
into
N
complex
fre-
quency
domain
points,
where
N is
usually
chosen
to
be a
power
of
2.
The
N
complex
frequency
domain
points
are
evenly
distributed
from
DC
to
the
sampling
frequency.
Fur-
ther,
the
spectrum
becomes
peri-
odic,
with
a
period
equal
to
the
sam-
pling
frequency,
i.e.
the
N
complex
points
are
repeated
up
and
down
the
frequency
axis
with
a
period
equal
to
the
sampling
frequency.
Taking
this
periodicity
into
~
account,
and
referring
to
Fig.1,
it
is
evident
that
those
points
falling
between
the
Nyquist
frequency,
(i.e
.
half
the
sampling
frequency),
and
the
sam-
pling
frequency
represent
the
nega-
tive
frequency
components
of
the
spectrum,
while
those
points
from
DC
up
to
the
Nyquist
frequency
re-
present
the
positive
frequency
com-
ponents.
A
simplification
leading
to
an
in-
crease
in
efficiency
occurs
whe
·n
it
is
assumed
that
the
time
domain
points
can
only
be real
valued,
(as
is
usually
the
case).
The
spectrum
will
then
be
conjugate
even,
mean-
ing
that
the
positive
frequency
com-
ponents
can
be
generated
from
the
negative
ones,
and
vice
versa,
i.e.
only
the
positive
or
the
negative
components
are
needed
to
define
the
whole
spectrum.
Using
this,
it
enables
N
real-valued
time
doniain
points
to
be
transformed
as
N/2
complex
points,
a
manipulation
be-
ing
made
on
the
results
to
obtain
the
spectrum
of
the
original
time
function
from
DC
to
the
Nyquist
fre-
quency.
Each
of
the
points
generated
by
the
above
process
wi
II
have
the
form
F(i) = ai +
jbi.
For
each
positive
component
F(i),
there
must
be
a
ne-
gative
frequency
component
F(-i)
=
3
ai-
jbi.
The
power
at
this
fre-
quency
is
the
sum
of
the
powers
of
the
positive
and
negative
frequency
components,
i.e.
2(ai2
+
bi2).
This
value
may
then
be
averaged
over
multiple
spectra
to
form
the
MS
value,
and
the
square
root
taken
to
form
the
RMS
value.
Description
A
simplified
block
diagram
of
the
2031
is
given
in
Fig
.3
.
It
can
be
split
into
four
sections,
the
Analog
Input,
the
Processor
,
the
Display
and
Analog
Output,
and
the
IEC
In-
terface
.
Its
architecture
is based
on
two
16
bit
buses,
the
Y-bus
and
the
D-bus,
over
which
all
data
flow
be-
tween
the
various
sections
takes
place
.
Analog
Input
Section
A
block
diagram
of
the
Analog
In-
put
Section
of
the
2031
is
shown
in
Fig.4.
The
Input
Amplifier
has
two
inputs.
One,
the
Preamplifier
In-
put,
is
the
standard
B & K
7-pin
type,
allowing
the
connection
of
most
B & K
Microphone
Preamplifi-
ers,
to
which
it
also
supplies
power
and
microphone
polarization
volt-
ages.
The
input
of
signals
from
other
sources
is
made
via
the
Direct
Input
.
Both
inputs
have
separate
sensitivity
adjustments,
such
that
differing
transducer
sensitivities
can
be
accommodated
.
Calibration
of
the
Input
Amplifier
and
the
rest
of
the
2031
can
be
checked
using
an
internal
Refer-
ence
Oscillator,
whose
frequency
is
controlled
such
that
the
calibration
signal
appears
in
channel
256
of
the
resulting
analysis.
Its
amplitude
is
100
dB
referred
to
1
J1V
RMS.
(Alternatively,
an
external
calibra-
tion
signal
can
be used.)
The
1
11V
RMS
reference
level
can
be
altered
by±
50
dB
in
steps
of
10
dB.
The
Input
Attenuation
setting
gov-
erns
the
level
setting
for
the
rest
of
the
analyzer
.
It
can
be
used
to
re-
duce
the
input
signal
level
in
steps
of
10
dB
over
a 1
00
dB
range,
us-
ing
the
front
panel
controls.
When
set
to
0
dB,
full
scale
deflection
corresponds
to
1
mV,
and
since
the
4
Front
Panel
Controls
Analog
Output
To
Level Recorder
Digital
Input
and
Output
Remote Programming
Information
over I
EC
Bus
770258
Fig.3.
Simplified
Block
Diagram
of
the
2031
Y-Bus
l[
Mode Set Register Master
Oscillator
1 l
·~
Reference
Oscillator Sample Rate Divider
Sa
~
Ext
.
mpling
,~,
L l
~
~
~
!
D
I
nput
o---
eamp.o---
Pr
I
nput
Input
f---
Amplifier
Input
Anti-
Attenu-
I--
aliasing
ation Filter
Sample
lnt
I--
and
I--
ADC
....__
errupt
Hold
Jl
D-Bus
770264
Fig.4.
Analog
Input
Section
of
the
2031
lowest
measurable
voltage
is
1
J1V,
this
gives
a
total
operating
range
of
1
60
dB.
Any
input
over-
load is
indicated
by
an
overload
indi-
cator,
and
an
upper
10
dB
indicator
shows
when
the
input
signal
is
within
10
dB
of
full
scale.
From
the
Input
Attenuation,
the
signal
enters
the
Antialiasing
Filter
.
This
is a
7-pole
elliptical
low
pass
filter
having
a
roll-off
of
113
dB/octave,
automatically
se-
lected
with
the
frequency
range
so
that
it
cuts
off
at
the
fu
II
seale
fre-
quency.
Its
purpose
is
to
avoid
alia-
sing
errors
when
the
input
signal
is
later
sampled,
and
it
may
be
by-
passed,
if
required
.
The
Antialiasing
Filters
may
also
be
used
when
sam-
pling
is
externally
controlled.
In
this
case,
the
cut-off
frequency
of
the
connected
filter
will
correspond
to
the
frequency
range
setting
.
The
low
pass
filtered
signal
now
enters
the
Sample
and
Hold
net-
work
and
Analog
to
Digital
Conver-
ter,
(ADC),
where
it
is
sampled
at
a
frequency
2,
56
times
the
full
scale
frequency,
the
sampling
frequency
being
derived
from
a
crystal
con-
trolled
Master
Oscillator.
Alterna-
tively,
an
external
sampling
fre-
quency
can
be
used,
whereupon
the
full
scale
frequency
becomes
the
sampling
frequency
divided
by
2,56
. Each
sample
taken
is
entered
into
the
ADC,
where
it
is
converted
into
a 1
2-bit
two's
complement
word.
Processor
Section
The
block
diagram
of
the
Proces-
sor
section
of
the
2031
is
given
in
Fig.5.
The
functions
of
the
Proces-
sor
are
to
control
the
input
of
data,
to
Fourier
transform
the
data,
to
av-
erage
the
spectra
produced
,
to
con-
trol
the
display
of
data,
and
to
sense
the
front
panel
controls
.