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: