Section 7. Measurement Instructions
7-43
For a given sample rate,
SR
f
, if better frequency resolution is required (i.e.,
more bins, each covering a narrower frequency range) increase the number of
points in the FFT, N. If less resolution is required (i.e., fewer bins each
covering a wider frequency range) decrease the number of points in the FFT or
(to keep the minimum frequency from slipping into the DC bin) combine bins
as described below.
Spectral ReBinning
An FFT spectrum can be “rebinned” into a spectrum containing fewer bins
where each of the new bins contains a component that covers the frequency
range of the bins that were combined. The dc component (bin 0 of the original
FFT) is not combined with other bins but may be returned with a linear
rebinned spectrum. The first bin to be combined is the first ac component. Bins
can be combined in two different ways:
1)Linearly with the resulting bins all having a fixed bandwidth equal to the
distance between center frequencies of adjacent bins (as in a the spectrum
created by the FFT).
2)
Logarithmically with the bandwidth increasing with frequency.
The mathematical operations to combine bins depends on the spectrum type
(
SpectOption)
. Amplitude, RMS amplitude, and dB spectra are combined by
summing the power in the adjacent bins and then converting this summed
power to the desired spectrum type (amplitude, RMS amplitude, or dB). Power
spectral density (PSD) functions are combined by averaging adjacent
frequency-normalized bins into to give the frequency-normalized result.
Combining Real and Imaginary, or Amplitude and Phase spectra is not
allowed.
Fref
and
SBin
are constants that determine the type of spectral binning.
ILow
and
IHigh
are constants that determine which part of the rebinned spectrum is
returned.
Linear
Spectral
Rebinning
Linear spectral rebinning combines the spectral components from a fixed
number of adjacent bins into a single component of the final spectrum. Linear
spectral rebinning is selected by setting
Fref
equal to zero and
SBin
to two or
more. The parameter
SBin
determines the number of bins to combine.
Let
i
be the bin number of the rebinned spectrum. The center frequency of
each spectral component with linear spectral rebinning
is
( )
⎟
⎠
⎞
⎜
⎝
⎛
−
−
×
=
2
1
bin
bin
SR
c
S
S
i
N
f
i
f
Where
i
ranges from 0 for the DC component to
Floor
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
×
bin
S
N
2
for the bin containing the highest frequency component. where the
( )
x
Floor
is the largest integer that is not greater than
x
,
SR
f
is sample rate of the
original time series (parameter
FSampRate
),
N
is the length of the FFT
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