Campbell Scientific CR9000X Measurement and Control System - Manual (Page 279)

Section 7. Measurement Instructions
7-55
determine the number of values returned by FFTFilt. The units of the RMS
amplitude spectrum are mV RMS.
deciBell
The deciBell (dB) spectrum normalizes the RMS amplitude spectrum
according to
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
ref
A
A
10
log 0 2
where A is value from the RMS amplitude spectrum, and
ref
A is RMS
amplitude reference level. The inverse of the multiplier parameter (Mult -1 ) of
the FFTFilt instruction gives A
ref
. Because the square of the RMS amplitude
is equal to power, an equivalent normalization to dB is
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
ref
P
P
10
log 0 1
where P is the value from the power spectrum, and
ref
P is power reference
level. The square of the inverse of the multiplier parameter (Mult -2 ) gives
ref
P . The multiplier parameter of the FFTFilt performs two functions for the
dB spectrum option. The first function is to convert the raw signal
measurements from mV to the units in which the dB reference is specified, and
the second function gives the dB reference. For example, users may convert
signals from a microphone to sound pressure level (SPL) spectra in dB relative
to 20 μPascals RMS, by setting Mult to:
RMS Pascals 10 20 6 − ×
k
where k is the microphone calibration in Pascals per mV. The FFT calculation
produces FFTLen/2 +1 deciBell components. ILow and IHigh, described
below, determine the number of values returned by FFTFilt. The dB spectrum
is unitless.
FFT Spectral Bins
The FFT calculation produces N/2 +1 spectral bins, where N is the number of
points in the original time series. These bins may contain a single value (i.e.,
amplitude) or a pair of values (i.e., Real and Imaginary). Each of these bins
represents a frequency range. Let
i be the bin number, ranging from 0 for the
DC component to N/2 for the highest frequency range. The center frequency of
each range is:
( )
i
N
f
i f SR
c
=
where
SR
f is the sample rate of the time series processed by the FFT
(parameter FSampRate), and N is the length of the FFT (parameter
FFTLen).
( )
0
c
f is the center frequency of the first spectral component
calculated by the FFT,
( )
1
c
f is the center frequency of the second spectral
component, and so on.