[Eeglablist] timef wavelet bandwidth

[A. Debebe]

The following papers may shade light on the bandwidth:

Debebe Asefa et al, 	Restoration of fMRI Signal using
Wiener Filters in a Wavelet Domain, submitted for
publication in International Conference on Mathematics
and Engineering Techniques in Medicine and Biological
Society, 2006. 

Debebe Asefa et al, Activation Points Extraction and
Noise Removal of fMRI Signal using Local Cosine and
its Comparison with Gaussian and other filtering
methods, submitted for publication in International
Conference on Mathematics and Engineering Techniques
in Medicine and Biological Society, 2006

The derivation of the consatnat 0.6366 is shown I
believe on the 1st paper.

The papers may not have been published though accepted
due to the fee since I was a student at that time. If
there is a need I will post them.

Debebe Asefa, PhD
--- arno <arno at salk.edu> wrote:

> That's a tough question, that we were just
> discussing with Rey Ramirez 
> in our Lab.
> 
> 1. Another approach consist in using the standard
> deviations of 
> normalized Morlet wavelets in time. Each wavelet is
> composed of a 
> Gaussian window multiplied by a sinus (=Gabor). For
> the time domain, you 
> simply use 2 standard deviation of the Gaussian
> taper (there is 95% of 
> the power within 2 standard deviation in time).
> Using 2 is a random 
> definition though. For the frequency domain, you use
> also 2 standard 
> deviation of the wavelet in frequency domain (just
> FFT the real part of 
> the wavelet). According to Rey, for the type of
> wavelets used in 
> Tallon-Baudry et Bertrand, Biomag, 1996, this is
> always equal to 
> irrespective of the value of the frequency and
> number of cycles.
> 
> 2. Multitaper theory is all about setting a specific
> time and frequency 
> resolution. As you increase the number of tapers,
> you have to sacrifice 
> both time and frequency resolution (but you gain in
> SNR). This is not 
> such a big problem at high frequencies (40Hz) but
> really does not make 
> sense at low frequencies (5Hz).
> 
> 3. However, according to this paper for instance,
> 
>
http://ieeexplore.ieee.org/iel5/6171/16493/00762269.pdf?arnumber=762269
> 
> for any type of Gaussian wavelet, we have according
> the Heisenberg's 
> uncertainty principle
> 
> Df Dt >= 1/(4pi)                (or without the
> special characters 
> delta_f * delta_t >= 1/(4pi))
> 
> They come up with the number 4pi by using a Gaussian
> modulated pulse. I 
> could not access the reference (in 1946) so if
> someone could explain 
> that to us, that would be great.
> 
> 4. Yes, other references state that
> 
> Df Dt >= 1                      (or without the
> special characters 
> delta_f * delta_t >= 1)
> 
> But this seems to be related to the Heisenberg's
> uncertainty principle 
> in quantum mechanics (about the vibration frequency
> of a particle) so I 
> am not sure it applies in our case.
> 
> 5. In timef(),we are still using sinusoidal wavelets
> which are nearly 
> indistinguishable from Morlet from a user
> perspective (the only 
> difference rely in the taper which is not Gaussian
> but a hanning window, 
> the reason being that you do not loose energy of the
> wavelet on the 
> extremities as you do with Gaussian). We will update
> the timef() 
> function to allow Morlet in the next release and
> make it a default.
> 
> If you know the exact formula between delta_f and
> delta_t, then it 
> becomes easy to compute both the time and frequency
> resolution (because 
> we can compute the time used at each single
> frequency). I hope some 
> signal processing savvy participants to the list can
> enlighten us 
> further on this topic.
> 
> Best,
> 
> Arno
> 
> Clemens Brunner wrote:
> > I'm using timef to calculate wavelet-based
> time-frequency maps with  
> > the parameter cycles = [4 0.75]. Now I was
> wondering if I can find  
> > out the bandwidth of the returned values as only
> the center  
> > frequencies are given. Is the bandwidth constant
> over the frequency  
> > range? Or does it change (i.e. grow) with
> frequency?
> >
> > Second, if I would be using the FFT-based method
> (i.e. cycles = 0),  
> > how could I find out the bandwidth of the single
> bands?
> >
> > TIA
> > Clemens
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