[Eeglablist] Heisenberg, .....

[M V Chilukuri]

Dear Asefa,

S-Transform(Stockwell Transform) is a time-frequency technique with better
resolution in time and frequency. In fact, it is very useful for non-stationary
signal analysis, unlike Fourier transform which is applicable to only
stationary signals. Many practical application involves analysis of non
stationary signals, and they are often corrupted with noise. In such a scenario
Generalized S-Transform/Hyperbolic S-Transform/Complex S-Transform are very
useful in extracting information from the signal. However, these techniques use
analytical signal to obtain time-frequency plots and analytical signal is
obtained from Hilbert Transform of real signal. Also, they give better
resolution than STFT(poor resolution)/Wigner-Ville distribution(suffers from
cross terms). There may be many techniques coming out in future.

Sincerely,
M V Chilukuri

"A. Debebe" wrote:

> Dear All,
>
> 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
> previous paragraph.
>
> Regards,
>
> Debebe Asefa, PhD
>
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