=
2
=
= 0
2
2
Typically a weighting function or "window" wm is applied to the input time series s
m
to
mitigate the
eect of the DFT assumption of periodic time series. RVP900 supports
dierent windows such as the Hamming, Blackman, Von Han, exact Blackman, and the
rectangular window for which all spectral components are weighted equally.
The following
figure shows the typical form of a spectrum window to illustrate how the edge
points of the time series are de-emphasized and the center points are over emphasized. The
dashed line corresponds to the rectangular window. The gain of the window is set to
preserve the total power.
Weight
1
0
Time/Sample Index
M
Rectangular
Figure 39 Typical Form of Time Series Window
Although the window gain can be adjusted to conserve the total power, there is an eective
reduction in the number of samples which increases the variance (or uncertainty) of the
moment estimates. For example the variance of the total power is greater when computed
from a spectrum with Blackman weighting compared to using a rectangular window. This is
because there are
eectively fewer samples because of the de-emphasis of the end points.
This is a negative side to using a window.
The DFT of the window itself is known as its impulse response which shows all of the
frequencies that are generated by the window itself. A generic example is shown in the
following
figure which illustrates that these side lobe frequencies can have substantial
power. This is not a problem for weather signals alone, but if there is strong clutter mixed in,
then the side lobe power from the clutter can obscure the weaker weather signals. The
rectangular window has the worst sidelobes, but the narrowest window width. However, the
rectangular window provides the lowest variance estimates of the moment parameters (in
the absence of clutter.
RVP900 User Guide M211322EN-J
186
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