HIGH ORDER STATISTICS VS.

 

CLASSICAL AVERAGING

 

IN BIOELECTRICAL DEVICES

 

 

 

 

Anca Daniela Ionita

 

Fac. Automatica si Calculatoare, Univ. “Politehnica” Bucuresti

Spl. Independentei – 313, 77206 – Bucharest, ROMANIA


NOISE REDUCTION IN MEDICAL APPARATUS

 

·     classical averaging

 

·     high order spectral analysis.

 

 

None of these methods is generally suited.

 

One should choose the former or the latter in terms of the initial signal-to-noise ratio and the signal characteristics.


 

       SYNCHRONOUS AVERAGING

 

 

 

The finite stochastic response of a stimulus:

 

                                             i=1...N                                   

where ti is the time when the stimulus begins and Ti is the time interval of the response.

 

The measured signal:

 

       i=1...N                

where the additive noise ni(t)  tÎ[ti ,ti+T] is a zero mean  process, statistically independent of si(t) and  T is larger or equal to the length of the longest response.


SNR IMPROVEMENT WITH AVERAGING

 

           

Statistically independent responses:

                                                      

 

Totally dependent responses:

 

                      where                                                                 

 


 

HIGH ORDER STATISTICS (HOS)

Supplementary information about the signal in respect to the power spectrum

·      Extract information about the deviations from Gaussianity

·      Recover the phase of a signal

·      Detect and quantify the time serie nonlinearities

 


HOS DEFINITIONS

 

For stationary processes:

 

The third order moment and cumulant sequences for a zero mean process:

 

       

 

The third order spectrum (bispectrum):

 

                                                  ,     ,   

 

 

If {s(k)} is a zero mean Gaussian stationary process, the third order moments and cumulants are equal to zero.

 

NOISE REDUCTION WITH HOS


SIMULATION

 

 

a) Typical EMG signal recorded from the tibia muscle

b) EMG power spectrum

 

Signal-to-noise ratio:

 

 


SIGNAL-TO-NOISE RATIO AFTER AVERAGING  VS THE NUMBER OF REALISATIONS OF SIGNAL PLUS NOISE

 

 

 

 

 

 

Signal-to-noise ratio after noise reduction vs. initial signal-to-noise ratio

SIGNAL-TO-NOISE RATIO AFTER NOISE REDUCTION VS. INITIAL SIGNAL-TO-NOISE RATIO