Campbell CR9000, Instruction Manual

Page: 155 / 218

Section 7. Measurement Instructions
7-41
In terms of frequency:
To limit the lower end of the spectrum, select a minimum frequency of interest,
low
f
, and then set Ilow to:
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
low
SR
f
f
N
round
,
where
( )
x round
is
x
rounded to the nearest integer.
To limit the upper end of the spectrum, select a maximum frequency of
interest,
high
f
, and then set IHigh to:
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
high
SR
f
f
N
round
.
Not saving the higher frequency bins is particularly useful if you are used to
using some of the rules of thumb on over sampling that evolved to avoid
aliasing higher frequencies present because of the prolonged rolloff of analog
filters. For example, suppose you are interested in frequencies up to 1 kHz. To
get a 5 times oversample, FSampRate of 5 kHz is used with FiltOpt sampling
ratio = 5 and N=1024. The bin containing the 1 kHz information will be
Round((1024/5000)x1000) = 205. Bins containing spectra beyond the filter
stop frequency of 5000/3.37 = 1484 Hz will be drastically attenuated (
≥
90
dB). The bin containing the stop frequency is: I = Round ((1024/5000)x1484)
= 304). Set IHigh to bin 205 and only spectra up to 1 kHz will be returned. Set
IHigh to 304 get the spectra through the filter roll off but discard the 208 bins
containing spectra beyond the stop frequency.
The total number of spectral components (spectral pairs for real and
imaginary, or amplitude and phase, spectral options) loaded into the
destination array by FFTFilt
is IHigh - ILow + 1. Note that the bin numbers
ILow and IHigh are not the same as the array index numbers of the destination
array. For example, with a single (1Rep) 1024 point Amplitude FFT, if all the
bins were returned (ILow=0, and I High=512) into the destination:
FFTResult(1), FFTResult(1) would equal the amplitude for bin 0,
FFTResult(2) = bin(1), … FFTResult(513) = bin(512). If ILow were set equal
200 and IHigh equal 512, then FFTResult(1) = bin(200), FFTResult(2) =
Bin(201), … FFTResult(313) = bin(512).
Frequency Range
Maximum Frequency
The maximum non-attenuated frequency in the FFT is a function of the
Sampling Frequency,
SR
f
, ( FSampRate) and the Filter option ( FiltOption)
The maximum frequency in the spectrum calculated by an FFT is half the
sampling frequency (
2 /
SR
f
). This is also called the Nyquist frequency.
FSampRate must be at least twice the maximum frequency of interest,
high
f
.
Any frequencies higher than the Nyquist frequency that were present in the
time series will be aliased, contributing to the lower frequency components.
Aliasing is not a concern with the CR9052 because the Pass frequency
and the
stop frequency are both less than FSampRate/2 for all filter options except 1.