[Eeglablist] Heisenberg, .....
debebea at yahoo.com
Tue Oct 3 10:46:10 PDT 2006
There are excellent discussions on this forum, having
listening to all the technical discussions about
Heisenberg uncertainty, etc...., I can not resist
participating. When one discuss about Heisenberg
uncertainty, one should wonder what it means in
relation to event related signal processing, i.e.,
separation of the coherent signal from the noise, and
locating an event.
In signal processing, we are using windows( or certain
resolution)to walk us through the signal during
processing. A window size can not be less a certain
threshold, in general there is a limitation to it.
"Heisenberg uncertainty says, one cannot know the
exact time-frequency representation of a signal, i.e.,
one cannot know what spectral components exist at what
instances of times. What one can know are the time
intervals in which certain band of frequencies exist,
which is a resolution problem( Robi Polikar Tutorial,
and a host of papers on signal processing)".
Each signal processing algorithms, FT,FFT(STFT),
wavelet transform, assume a certain size of the
resolution of the window used for processing, FT
assumes the the size as never ending, thus not good
for time related events, FFT assumes the same size of
resolution through out the life of the signal,but
event related signals are not uniformly distributed(
not in term of statistics), wavelet assumes
variability of the window size or resolution based
upon the size of a band of signals at that location.
Wavelet adapts to the variability of the signal or
event related signal.
There are also continuous and discrete signals,
morlet and FT are good for processing continuous
signal, continuous signal can easily be transformed
to discrete signal though.
Every transformation algorithms are not equal, i.e.,
after transformation the coherent signal may not be
the same as the original signal specially the
location, therefore, one has to take into
consideration a large signal or a periodic signal for
processing to get the original signal minus noise.
Somebody has mentioned s-transformation, my
understanding is s-transformation is periodic Fourier
transformation, it solved the problem mentioned in the
Debebe Asefa, PhD
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