whats-fractal.unemployment.jpg
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above: unemployment rate / nyt 2.6.09 "economy shed 598k jobs in january"
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. ..below.. .
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figures from:
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as. rybakov / wavelet decomposition and fractal analysis for joint measurements of laser signal delay and amplitude
avtomatika i vychislitel'naya tekhnika [automatic control & computer sciences] 2001
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a regression algorithm is considered for balancing out the effects of echo signal amplitude
spread on the error in range measurement to artificial satellites
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noise excursions can be filtered out in
nonstationary sequences of lidar measurements
by means of a procedure
for multiple-scale
wavelet
decomposition
the stationarity indicator
for the multiple-scale components is
provided by the fractal
dimensions
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whats-fractal.lidar-wavelet.jpg

above: reflected-signal amplitude distribution @photocell output in locating a reflector on a satellite
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multiscale processes are associated with fat-tailed distributions
eg the contributions of processes up and down the
fractal scaling hierarchy
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whats-fractal.rybakov-daubechies.jpg

above: multiscale decomposition of a sequence of delays in the daubechies-4 wavelet basis
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whats-fractal.rybakov-haar.jpg

above: decomposition in the haar wavelet basis
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whats-fractal.dim.png

the small scale [high frequency] are very similar no matter what the wavelet basis used
might as well use the simpler haar "lens"
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once we know about the existence
of a chaotic scaling regime
in the data
it is natural to ask if the dynamics are
deterministically chaotic
or not
however if all we know
is the time series
then we will not be able to distinguish further
between noisy chaos and
noise induced chaos
- j gao, y cao, ww tung, j hu / multiscale analysis of complex time series 2007
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. . .

. ..since we're talking satellites.. .

content/china.destroys.satellite.jpg