End Spreading

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End Spreading

• Sifting might spread signal into quiescent region

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Earthquake Elcentro
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Earthquake Elcentro IMF CE(100,3)
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Earthquake Elcentro EIMF (3,0.1,50)
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Orthogonality Indices
IMF OI ij 0.1982 0.0412 0.0336
0.0534 0.2453 0.0557 0.1723 OI
total -0.4986
EIMF OI ij 0.0395 0.0862 0.0570
0.0423 0.0819 0.1682 0.1522
0.0246 0.2225 OI total 0.0606
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End spreading

• This is an annoying problem, for to have some
  thing before the sensors were turned on is
  nonsensical.
• But EMD has the tendency to spread the signal
  through the sifting processes.
• End spreading causes deterioration in the
  resulting IMF components.
• EEMD solved the problem to a large extend.

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Noised Aided Data Analysis II

• Although EEMD alleviates the end spreading
  considerably, there are still cases that signal
  spreading needs to be contained.

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Noise Aided Data Analysis II

• In EEMD, the finite magnitude noise is added once
  in each of the ensemble. The true solution is
  obtained as the limit of having the number in the
  ensemble approaching infinite.
• In NADAII, the infinitesimal magnitude noises is
  added repeatedly for each IMF extraction.

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Delta Function

• Noised Aided Data Analysis II

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Delta Function Data
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The Procedure

• Perform EEMD and select the first EIMF component
  as the 1st component in the RIMF (Recombined IMF)
• Take the residue and adding noise with amplitude
  1/1000 as the data for the first round
  re-processing to produce EIMF1.
• Take the 1st EIMF component from EIMF1 as the
  second component in the RIMF.
• Take the residue and adding noise with amplitude
  1/1000 as the data for the second round
  re-processing EIMF2.
• (repeat the processes) .

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Delta Function EIMF(3,0.1,10)
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Spreading of the signal

• The widths of the IMF signals become increasingly
  wide.
• The spreading increasingly wide into the
  quiescent region as shown in th eprevious figure.
  

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Delta Function IMF1(3,0.1,10)
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Delta Function IMF2(3,0.1,10)
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Delta Function IMF3(3,0.1,10)
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The Re-combined IMF

• So far a manual operation.

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Delta Function RIMF
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Delta Function RIMF(1) EIMF(1)
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Delta Function RIMF(2) EIMF1(1)
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Delta Function RIMF(3) EIMF2(1)
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Delta Function RIMF(4) residue
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Delta Function RIMF(4) residue
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RIMF

• RIMF is a combination of all the individual
  EIMFi, for i1,2,3,
• The spread of each of the component is limited by
  the added noise.
• As a result, the spread is controlled the result
  is more local.