Campbell CR9000, Instruction Manual

Page: 151 / 218

Section 7. Measurement Instructions
7-37
Window Function
TSWindow is a constant designating whether the CR9052 should apply a
window (also known as taper, or apodization) function to the time series
snapshot before performing the FFT. Typical window functions give more
weight to the middle of the time series while tapering the ends to avoid spectral
leakage caused by a non-integral number of periods of a repetitive signal in the
snapshot.
The CR9052 applies the selected window function by multiplying each point
of the original time series by the corresponding point of the window function.
Because this windowing process removes some of the original signal variation,
the CR9052 uses the following procedure to correct the resulting spectra.
The CR9052 first computes the mean and standard deviation of the original
time series for use in additional processing. Next, the CR9052 subtracts the
mean from each point of the original time series, and then multiplies the mean-
subtracted time series by the selected window function. The CR9052 then
computes the standard deviation of this windowed time series. The CR9052
then computes the FFT of the windowed time series, and multiplies each ac
component of the complex spectrum by the ratio of the standard deviations of
the time series computed before and after the window function was applied.
The CR9052 then sets the dc component of the spectrum to the mean of the
original time series, normalized for the FFT length.
The CR9052 computes the Hanning window function from:
⎟
⎠
⎞
⎜
⎝
⎛
−
−
1
2
cos 5 . 0 5 . 0
N
k
π
for
( )
1 0
− ≤ ≤
N k
.
N
is the length of the original time series ( FFTLen) .
The CR9052 computes the Hamming window function from:
⎟
⎠
⎞
⎜
⎝
⎛
−
−
1
2
cos 46 . 0 54 . 0
N
k
π
for
( )
1 0
− ≤ ≤
N k
.
The CR9052 computes the Blackman window function from
⎟
⎠
⎞
⎜
⎝
⎛
−
+
⎟
⎠
⎞
⎜
⎝
⎛
−
−
1
4
cos 08 . 0
1
2
cos 5 . 0 42 . 0
N
k
N
k
π π
for
( )
1 0
− ≤ ≤
N k
.
The Kaiser-Bessel window function is calculated using:
( )
β
β
0
2
2
1
2
1
0
I
1 I
⎟
⎟
⎟
⎠
⎞
⎜
⎜
⎜
⎝
⎛
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛ −
−
−
−
N
N
k