USER’S MANUAL__________________________________________________________________
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acceptable assumption) and that the signal-to-noise ratio is large.
Specifically we have (similar to Srivastava, et al 1979):
where "ln" represents the natural logarithm. This can be compared to the
expression in the preceding section for SQI to illustrate that this expression
for the variance is only valid when:
which occurs when the SNR is large.
This variance estimator is normalized to the Nyquist interval in units of [-
π, π]. Thus, for example, a variance of π
2
/25 would be obtained from a
Gaussian spectrum having a standard deviation equal to one fifth of the
total width of the plotted spectral distribution. For scientific purposes, the
spectrum width (standard deviation) is more physically meaningful than
the variance, since it scales linearly with the severity of wind shear and
turbulence. For these reasons, the width W is output by the RVP900:
Again, for efficient packing in 8-bits, width is normalized to the Nyquist
interval [-1, 1 ]. For the example given above, the output width W would
be (1/5). To obtain the width in meters per second, one multiplies the
output width by V
u
.
R0, R1, R2 Width Algorithm
The width algorithm in this case is similar except that the addition of R
2
extends the validity of the width estimates to weak signals. In this case the
variance is:
The output width W is then defined as in the previous section.
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