Campbell 21X Manuale dell'Operatore Scaricare il pdf (Pagina 115)

SECTION 10. PROCESSING

INSTRUCTIONS

power

spectral

is

output. Parameter

3 is equal

to the log base

2 of

A where A is

the number

of

bins

to

be averaged.

For example,

if

there are

1024

samples in

the

originaltime

series data

and the

resulting

512

spectral bins are

averaged

in

groups

of 8

(Parameter

3

=

3

=

log

base 2

of

B) then 63

(=5724

1)

averaged bins will

be

produced.

PARAMETER

4

defines which input

location

will

contain the first

value

at the original

time series

data. Once

the FFT

program

has

executed,

this

location willcontain

the first resulting

value.

PARAMETER

5 is

a scaling

multiplier

that is

applied to

the

FFT

results

(i.e.,

after the FFT

cornputation has

been done).

The

multiplier

is

not

applied to the DC

component.

MEMORY REQUIREMENTS

The

number of Input Memory Locations

allocated

must

be

enough

to

accommodate

the

N

sampled

values,

where N

is

defined

under

Parameter 1. The

number of lntermediate

Memory Locations

allocated must be

greater

than

or

equal

to

(N/8

+ 2).

lf insutficient

Input

or

Intermediate Memory

Locations

have

been

allocated, the

datalogger will

flag

an E60

or E04,

respectively.

NOTE:

The

21X has

1

lntermediate

Location that is

not available for

use

by

Processing

or Output

Instructions

so

the number

of lntermediate

Locations allocated must exceed

the

indicated total requirement by

at

least 1.

FFT RESULTS WITHOUT BIN

AVERAGING

When

no bin averaging

is specified, the FFT

results may

be calculated

in terms of the

real/imaginary

components, the

magnitude/phase

components, or

the

power

spectra. The rest

of this section deals with

the

DC

component, bin frequency, and

the FFT

results

just

mentioned.

An example

showing

each

of

the

possible

results is

given

in

Section

8.8.1.

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

the math

in

the rest

of the FFT calculations.

lf the real and imaginary

or the

magnitude

and

phase

results are specified

by

Parameter

2

the

DC

component is the

average of the original

time series data. lf

power

spectra

results

are

specified, the DC

component is equal

to the

square

of the average

of the original time series

data

times

2N.

The DC

component

is

stored in the first input

location

specified by

Parameter 4 which

corresponds

with

the frequency at 0 Hz

(bin

0).

BIN FREQUENCY

The

band

width

or the frequency covered

by

each bin is equalto F/N where

F is

the sample

frequency in Hz

(1/scan

interval in seconds).

The frequency

(f;)

of any

given

bin iwhere i

ranges from 0 to

(N/2)-1

is

given

by the

equation:

(i-1

.F)/N

<

fi<

(i.F)/N

For

example,

given

that the

power

spectra resu

shows

that

the energy

peak

of

a signal falls in

bin

'128

when

it is sampled

at a

frequency of 10

Hzlor

1024

samples,

the frequency of the sig

is:

127 "

10

I

1024<

fi

<

128

*

10

/

1024

1.24H2.

fi. 1 .25H2

REAL AND

IMAGINARY

COMPONENTS

The result of the

FFT

when

the

real

and

imaginary option is

selected

is N/2 input

locations

containing

the realcomponents

(R;)

followed

by

N/2 input locations containing

the

imaginary components

(l;).

There

is

a

real

and

an imaginary component for

each

bin. The

value

of

ivaries from 1

to

N/2. The realand

imaginary results

at each frequency

i,

are

related

to the

magnitude

(M;)

and

phase

(P,)

as

shown

below:

Ri

=Mi

*cosP;

li

=Mi

*sinPi

where

M; is

the magnitude

and

P; is

the

phase

the signal in degrees. Magnitude is half of the

10-8

1 2 ... 110 111 112 113 114 115 116 117 118 119 120 ... 190 191

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