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John Hubbert, Greg Meymaris, Mike Dixon, Scott Ellis
NATIONAL CENTER FOR ATMOSPHERIC RESEARCHBoulder, Colorado
NEXRAD TAC MeetingNorman OK
29 April 2019
Rethinking Clutter Filteringand
Improving Signal Statistics
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Time (sec)
Clutter signal
2 sec.
Spectra-Based Clutter filtering• Since the advent of fast digital receivers this has been the
standard, e.g., GMAP• Replaced time domain filters• Very common in weather radars
Discrete Fourier Transform
Fourier Transform pairFrequency domain
Time domain,i.e., sum of sinusoids
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Real Part of a S-Pol Time Series.
Raw Time series
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Time (ms)
Real Part of a S-Pol Time Series. DFT creates a periodic signal
Raw Time series
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Time (ms)
Raw Time series In order to create a
sum of sinusoids that can replicate this jump discontinuity, many higher frequency sinusoids are required.
Real Part of a S-Pol Time Series. DFT creates a periodic signal
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Time (ms)
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Time (ms)
Raw Time series
HanningWindowedTime series
In order to create a sum of sinusoids that can replicate this jump discontinuity, many higher frequency sinusoids are required.
HanningWindowedTime series
Real Part of a S-Pol Time Series. DFT creates a periodic signal
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Raw spectrumHanning windowed
spectrum
m/s m/sVelocity Velocity
Window Effects on SpectraRaw Hanning windowed
The smooth curve spectrum is an artifact of the jump discontinuity
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Time (sec)
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Time (sec)
(a) (b)
Scan of Rocky Mountains by S-Pol at 8 deg/sec.
(16 degrees az.)
Typical Clutter I and Q Signals
I Q
Degs.
What is Regression Filtering?
Clutter + Weather Weather Only
Represent the I and Q Signals as a Sum of These Orthogonal PolynomialsFast, low round off error algorithm: http://jean-pierre.moreau.pagesperso-orange.fr/
Regression Clutter filtering• Regressions filters have a history in biomedical field
•
• And weather radar• Torres, S. and D. Zrnic ́, 1999: Ground clutter canceling with a
regression filter. J. Atmos. Oceanic Technol.
Regression Filter Example on S-Pol Data
Power Spectrum Time series
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Time (ms)
RealPart
Raw dataFitted data
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Raw dataFitted data
8th order polynomial fit
Subtracting the polynomial fit from the time series…..
Regression Filtered versus Raw Spectrum
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Blackman Window and Notch Technique
Regression Window and NotchComparison
Regression versus Window and Notch
• WHY USE A REGRESSION FILTER???
Signal Statistics5.23dB attenuation
• Hanning window: 4.19 dB attenuation
About 50% increase in variance!
About 35% increase in variance!
Regression Frequency Response64 point time series for polynomial orders 3 - 7
Frequency Response 264 point time series for polynomial orders 9, 11, 13, 15, 19
Frequency response depends on sequence length and polynomial order
Modified Regression Filtering
1 2 3 4 ….. …N
Standard technique: Take length N sequence, fit a polynomial to it and subtract to remove the low frequency clutter components.
Modified technique: Break the sequence into blocks, lets say 4 for this example:
1 Nl l l
N/4 N/2 3N/4
1. Do 4 regression fits, thus suppressing the ground clutter in each block2. Concatenate the blocks back into one sequence3. Calculate radar variables
block 1 block 2 block 3 block 4
time series
1 N
m points
m points
Length N sequence broken into overlapping blocks. The overlap is m pointsand these regions are shown in green.After filtering, overlapping pairs of points are averaged so that a N pointfiltered sequences is created. This is done to smooth the transition from oneblock to the next.
The Blocks Can Be Overlapped and WeightedThis is to reduce slight discontinuities at end points.
.1 .3 .7 .9
.9 .7 .3 .1
weightsBlock1
Block2
S-Pol Clutter Environmentat Marshall
22 April 20180.5 elevation
Compare Clutter Rejection of the Regression and GMAP like filters (notch width is constant)
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Scatter Plots Regression vs Window and Notch(4 blocks of 16)
KFTG Data. “Bomb Cyclone” 13 March 2019Short PRT data from VCP 212
25 km50 km
225o
Z Vel
Raw Blackman-Nuttall
9 pt notch
KFTG LPRT Data VCP212, 20 deg/sec, 16 points
6th order
KFTG 227 Az. 0.45 elev13 March 2019
Unfiltered data
5th order regression filter Blackman window 7 point notch
A Comparison of Regression versus Window and Notch Clutter Filters
Smearing Effects of Windowing
Raw data (rectangular window) Blackman-Nuttall Window
S-Pol data
Resulting Implications for the Clutter Filter Bandwidth
5 pt notch insufficient!!
Window function spreads the clutterpower so that wider bandwidth is needed
Vmax-Vmax Vmax
Clutter 0.25 m/s
0
Weather 2 m/s
Modeling Efforts Have Begun
28 m/s-28 m/s
64 points30 dB SNR weather30 dB CNR clutterBlackman Window, 9pt notchRegression 7th order
~ 50% increase in STD~ 30% increase in STD
Application to Data Sets Has Begun
Bomb Cyclone Level 2 Data Times Series Processed with Regression Filter
KFTG
Old frequency response
Compensatedfrequency response
Passband Stopband
Frequency
Frequency Compensation
After regression filtering, FFT the resulting timeseries and compensate the frequencies as desired as guided by the frequency response of the regression filter.
An interesting possibility
Conclusions
much better signal statistics can be achieved.
• Windowing the data, while containing “clutter leakage”, spreads the clutter (causes wider clutter bandwidth). This then requires a wider bandwidth notch as compared to regression filtering.
• Thus underlying weather signal is is more effectively recovered with a regression filter