Campbell CR23X Specifikace stáhnout pdf (Strana 174)

SECTION 10. PROCESSING INSTRUCTIONS

10-10

BIN FREQUENCY

The band width or the frequency covered by

each averaged bin is equal to 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 [9]

For example, given that the power spectrum

result shows that the energy peak of a signal

falls in bin 32 when it is sampled at a frequency

of 10 Hz for 1024 samples and that the bin

averaging specified is 4, the frequency of the

signal in bin i is:

31 * 10 * 4 / 1024 < f

< 32 * 10 * 4 / 1024

1.21 Hz < f

< 1.25 Hz

POWER SPECTRUM

The result of the FFT with A bins averaged, are

(N/2A)-1 bins of average spectral energy (APSn)

representing frequencies from 0 Hz to 1/2 the

sampling frequency. The value of i varies from

1 to (N/2A)-1. The results are found in

consecutive input locations starting with the first

one specified by Parameter 4. The value for

average bin n (APS

) is related to the spectral

bin values (PS

see previous section) by the

following equation:

APS

=(Σ PS

+0.5(PS

nA-A/2

+PS

nA+A/2

))/A [10]

where i goes from nA-(A/2-1) to nA+(A/2-1)

The following table illustrates how bin averaging

is done given a time series of 1024 values taken

at one per second with the resulting 512 spectral

bins averaged in groups of 4 (Parameter 3 = log

base 2 of 4 = 2) to produce 127 averaged bins.

TABLE 10-1. Example of FFT Power Spectrum Bin Averaging (Assuming 1024 time series values

starting in Location 1)

No Bin Averaging Averaged in Groups of 4

BIN NO. LOC. REPRESENTATIVE AVERAGED LOC. REPRESENTATIVE

FREQUENCY BIN NO. FREQUENCY

01 DC

1 2 1/1024

2 3 2/1024

3 4 3/1024

4 5 4/1024 ------------------------1 1 4/1024 or 1/256

5 6 5/1024

6 7 6/1024

7 8 7/1024

8 9 8/1024 ------------------------2 2 8/1024 or 2/256

9 10 9/1024

10 11 10/1024

11 12 11/1024

. . .

502 502/1024

503 503/1024

504 504/1024 -------------------- 126 126 504/1024 or 126/256

505 505/1024

506 506/1024

507 507/1024

508 508/1024 -------------------- 127 127 508/1024 or 127/256

509 509/1024

510 510/1024

511 511/1024

Examples of the use of the FFT are given in Section 8.

1 2 ... 169 170 171 172 173 174 175 176 177 178 179 ... 373 374

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