Campbell Scientific CR9000X Measurement and Control System - Manual (Page 284)

Section 7. Measurement Instructions
7-60
IHigh to:
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛ −
+
×
2
1 1
round bin
SR
high
bin
S
f
f N
S
.
The total number of spectral components returned by the FFTFilt instruction is
IHigh - ILow + 1.
Logarithmic Spectral ReBinning (1/n Octave Analyses)
Logarithmic spectral rebinning combines the spectral components from a
variable number of adjacent bins into a single component of the final spectrum.
The number of bins that are combined increases logarithmically with
frequency. FFTFilt is programmed to return a logarithmic spectrum by setting
Fref to a non-zero value and SBin between one and twelve. The parameter
SBin determines the number of bins per octave in the rebinned spectrum. An
octave is a factor of two increase in frequency.
The dc component is never part of the final logarithmic spectrum.
Let i be the bin number of the rebinned spectrum. The center frequency of
each spectral component with logarithmic spectral binning is
( )
bin
S
i
ref c
f i f 2 =
for
high low
i i i ≤ ≤
where
ref
f is an arbitrary reference frequency selected by the user (parameter
Fref), and
bin
S is the bins per octave in the final logarithmic spectrum
(parameter SBin). In many acoustic applications, Fref is set to 1 kHz.
The ratio (not the difference) between center frequencies of adjacent spectral
components in the logarithmic spectrum is bin
S
1
2 . The absolute bandwidth of
each spectral component is not constant, but rather, increases with increasing
frequency. The bandwidth of each spectral component, expressed as a fraction
of the center frequency, is bin bin
S S 2
1
2
1
2 2
−
−
.
Many acoustic applications call for 1/3 octave analyses (three points per
octave). For this case, the center frequency of a given bin is a factor of about
1.26 greater than the center frequency of the preceding bin. The bandwidth of
each bin is about 23 percent of the bin’s center frequency.
Note that in this logarithmic spectrum the integer bin number,
i
, may be
negative as well as positive. Fref is the center frequency of bin 0,
( )
ref
S
ref c
f f f
bin
= =
0
2 0
This is not to say that bin 0 is always a valid output. The valid frequency bins
to output are determined by frequency range of the original FFT and the values
entered for Sbin and Fref (e.g., if the original sample rate (FSampRate) was
1kHz and Fref was entered as 1 kHz bin 0 (1 kHz center frequency) could not
be output because the highest frequency in the original FFT is 500 Hz.)