Campbell 21X Manual do Operador descarregar pdf (Página 116)

zerc to

pea

or

one

quarter

of

the

peak

to

value

of the

sinusoidal

signal.

MAGN

AND

PHASE

COMPONENTS

The result of the

FFT when the

magnitude and

phase

optiori

is selected is

N/2 input locations

containing

tlp magnitude components

(Mi)

followed by

llli2 input locations containing

the

phase

comppnents

(P1).

Magnitude

is half

of the

zero to

peak

amplitude or one

quarter

of

the

peak

to

pea(

value of the sinusoidal

signal.

There

is

a

magnitude and a

phase

component

for each

bin.

The value

of

ivaries

from 1

to

N/2.

The

magnitupe

and

phase

components

are

related

to thQ

real

(R;)

and

imaginary

(11)

components

1as

shown below:

Mi= SQRTI(Ri.Ri)

+

(l;"1)l

arctan

(l;/R;)

To

calculatelthe

magnitude and

phase

the 21X's

FFT a

must first compute

the real

and

Conversion

from

real

to the magnitude and

phase

requires

quitb

a bit

more

datalogger

execution

time and

no

new

information is

gained.

lf

datalogger

dxecution time

is limiting,

program

the

dataloggpr

to store the real and

imaginary

results and have

a

computer

do the

conversion

to

magnitud4 and

phase

during

the data

reduction

pl'iase.The

FFT assumes

the

signal

was samplefl

at the beginning

of each of N

intervals. Sifice

the FFT assumes

the

signal

is

periodic

witfria

period

equalto

the total sampling

period,

the

rpsult of its

phase

calculation at each

frequency component

is the average

of

the

phase

atthd,

beginning of the

first interval with

the

phase

a! the

endof

the

last

interval.

The

phase

is the

angle

(0

360 degrees)

of

the

cosine

wave that describes the

signal at a

pafticular

point

in time.

POWER SPECTRA

The

result of the

FFT

when

the

power

spectra

option

is selpcted

is

N/2 bins

of spectralenergy

(PSi)

represBnting

frequencies

from 0 Hzto 1/2

the

samplin$

frequency. The

value of i varies

from

1 to N/2.

The result in each

bin i,

is

related

to

the

magnltude

(M;)

of the

wave

in

the

following

m4nner:

14)

15I

SECTION 10.

PROCESSING INSTRUCTIONS'

where

the

magnitude

is

half

of the

zero to

peak

amplitude or one

quarter

of the

peak

to

peak

value

of

the sinusoidal signal.

The

power

spectra

can

also

be expressed as

either

of

the

following:

PSi=

N*(Ui*Ui)

l7l

PS;= F*1*19'*g';

t8l

U1 is

defined

as the

root mean square

(RMS)

value

of

the sine component

of frequency

i

(f,)

(Ui

=

magnitude

(M;)

of

the sine

wave

multiplied

by

the

square

root of 2)

in units

of the

input

signal

multiplied

by the

scaling

multiplier.

In

equation 8, F

is

the sampling

frequency

(Hz)

and

T is

the duration

of the

original

time

series data

(seconds).

When

the

FFT results

are expressed

in

terms of

the

power

spectra,

a multiplier of

1 will cause

the

average

of allthe bins to be

very nearly

equal

to twice

the variance of the original data.

FFT

RESULTS

WITH

BIN

AVERAGING

When

bin averaging

is

specified,

the

FFT

results

can

only

be calculated in terms

of the

power

spectra.

The rest of this

section

deals

with

the

DC

component,

bin frequency, and the

power

spectra results.

An example showing

bin

averaging FFT results is

given

in Section 8.8.2.

DC

COMPONENT

Before

the

FFT is applied,

the

average of the

originaltime series data

is

subtracted

from

each

value. This is done to maintain the

resolution of

the

math

in the rest of

the

FFT calculations.

When

bin

averaging

is

specified then

the DC

component is not output.

BIN

FREQUENCY

The

band

width or the frequency

covered

by

each

averaged

bin

is

equalto

FA/N where F is

the

sample

frequency in Hz

(1/scan

interval in

seconds)

and

A is the number of bins

being

averaged.

The

frequency

(f,)

of

any

given

averaged bin i

where i ranges from 1

to

(N/2A)-1

is

given

by

the

following

equation:

i-1

*F*A/N<fi<i*F*A/N

tgl

PSi- 2.N.(Mi.Mi)

t6l

10-9

1 2 ... 111 112 113 114 115 116 117 118 119 120 121 ... 190 191

Comentários a estes Manuais

Sem comentários