• In DFT mode, they are computed by taking the inverse DFT of the Doppler power
spectrum in the frequency domain.
In the DFT case, only the first 3 terms must be calculated.
The time domain and frequency domain techniques are nearly identical except that the
method of taking the inverse DFT of the power spectrum relies on the assumption that the
time series is periodic. Another
dierence is that for time domain calculation only a
rectangular weighting is used.
Table 49 Time Domain Calculation of Autocorrelations and Corresponding Physical Models
Parameter and Definition Physical Model
0
=
1
= 1
*
+ +
0
=
1
= 1
′
* ′
+
1
=
1
1
= 1
1
′
* ′
+ 1
+
′
2
2
2
2
=
1
2
= 1
2
′
* ′
+ 2
+
′ 2
2
2
where M is the number of pulses in the time average. Here, s' denotes the clutter-filtered
time series, s denotes the original unfiltered time series and the * denotes a complex
conjugate. gr and gt represent the transmitter and receiver gains, that is, their product
represents the total system gain.
Since the RVP900 is a linear receiver, there is a single gain number that relates the
measured autocorrelation magnitude to the absolute received power. However, since many
of the algorithms do not require absolute calibration of the power, the gain terms are
ignored in the discussion of these. T
o
for the
unfiltered time series is proportional to the sum
of the meteorological signal S, the clutter power C and the noise power N. R
0
is equal to the
sum of the meteorological signal S and noise power N which is measured directly on the
RVP900 by periodic noise sampling. T
o
and R
0
are used for calculating the dBZ values- the
equivalent radar
reflectivity factor which is a calibrated measurement. The physical models
for R
0
, R
1
and R
2
correspond to a Gaussian weather signal and white noise. W is the
spectrum width and V' the mean velocity, both for the normalized Nyquist interval on [-1
to 1].
The autocorrelation lags above and the corresponding physical models have
five unknowns:
N, S, C, V', W. Because the R
1
and R
2
lags are complex, this yields, eectively, 5 equations in
5 unknowns using the constraint provided by the argument of R
1
. This closed system of
equations can be solved for the unknowns which is the basis for calculating the moments
from the autocorrelations.
RVP900 User Guide M211322EN-J
188
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