The Measure Test Is A Function Of N And. Essay

The Measure Test Is A Function Of N And. Essay

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The thresholds in (3), is independent of the signal charactersitics
and it is a function of N and .
In this paper, a Gaussianity measure test is formulated
based on the use of HOS (kurtosis estimator) to determine
which IMFs follow a Gaussian distribution, and any IMF
fails in Gaussianity test will be the candidate reference IMF
(IMFR). The EMD modes (IMFs) are shown to follow a
Gaussian distribution when the processed signal is following
a Gaussian distribution, therefore the the Gaussianity measure
test is valid for this work [14]. As a dyadic filter, EMD sifts
the higher frequencies (noise frequencies) of the processed
signal in the first IMFs and the lower frequencies (useful
signal frequencies) in the last IMFs. Consequently, for a
noisy signal, the first IMFs will be occupied by noise (follow
Gaussian distribution) and hence their kurtosis coefficients will
be very small (theoretically equals zero). However, the kurtosis
coefficients (see eq. (2)), reflect the statistical filtering behavior
of EMD, as these coefficients are flipping from negative to
zero then to positive values through the sifting process. The
threshold in (3) is given to provide a confidence interval for
the obtained IMF kurtosis coefficients whereas any coefficient
that fails to exceed the threshold is assumed to follow Gaussian
distribution within %.
Fig. 2, illustrates the proposed method, whereas the reconstructed
signal (filtered signal) is given as,
y(n) =
IMFi(n) + R(n) (4)
In order to demonstrate the performance of the proposed
filter and to compare it to other techniques, we used a synthetic
Electrocardiography (ECG) low pass waveform corrupted with
white Gaussian noise (wGn) is used. In the analysis, Monte-

... middle of paper ...

...s due to the fact that
the input is a low-pass signal and the EMD behaves almost
like a dyadic filter that dissects the spectrum. Lower values of
0.9 and 0.95 will increase the probability of statistical anomaly
(increase probability of outliers) especially for low input SNR
levels (< -10 dB). These anomalies would then cause the S-C
method to improperly select the reference IMF, thus noise is
unnecessarily added to the reconstructed output.
To illustrate the mechanics of the proposed method, the
higher order statistic estimator coefficients are calculated for a
set of IMFs produced for an ECG signal at SNR= -8 dB. The
thresholds and estimator coefficients are shown in Fig. 5 and
tabulated in Table I (kurtosis at top and skewness at bottom). In
Fig. 5a each estimator coefficient changes its sign several times
during the decomposition process. The first IMF index where

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