
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
log02
where
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
re
. Because the square of the RMS amplitude
is equal to power, an equivalent normalization to dB is
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
ref
P
P
10
log01
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 Pascals1020
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 cal
culation 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
if
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.
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