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Re: [Tftb-help] Help, why 'morlet' and 'a' expressions are of this form

From: ting xu
Subject: Re: [Tftb-help] Help, why 'morlet' and 'a' expressions are of this form in tfrscalo?
Date: Sat, 12 Mar 2011 22:22:54 +0800

 Prof. Auger, Thank you for your response.
About the wavelet _expression_ in 'tfrscalo', ha  = exp(-(2*log(10)/nha^2)*tha.^2).*exp(i*2*pi*f(ptr)*tha).
I think maybe it is complex Morlet wavelet. Beacause I found it is similar to the definition in 'cmorwavf ' function in MATLAB.
In 'cmorwavf ', PSI(x)=( ( pi*fb) ^ (-0.5) )*exp( 2*i*pi*fc*x)*exp( -x^2/fb),
here fb is the bandwidth parameter and fc is the center frequency.
I can understand here 'nha' in tfrscalo serves as 'fb' in cmorwavf, 'tha' is equivalent to 'x' in cmorwavf. Then I have another question about fc, center frequency. In cmorwavf, fc is a constant, but in tfrscalo, f(ptr) is a vector, the value will be changed according to every loop. Can center frequency change after the wavelet has been chosen? Could you please send me some reference about this? I really appreciate your help!
My second question is about the relationship between scale and the frequency in wavelet analysis.
In Fourier anslysis, we transform the signal from time domain to frequency domain. However, in wavelet analysis, the signal is transformed into time-scale domain instead of time-frequency domain.
I need the frequency information so I want to know how to calculate the frequency from scale. In MATLAB, it can be done by this formula, f=fc*fs/a (see 'scal2frq' function in MATLAB).
Here is my question, the f and a definition as follow in tfrscalo does not seem to fulfil f=fc*fs/a. why?
f = logspace(log10(fmin),log10(fmax),N);
a = logspace(log10(fmax/fmin),log10(1),N);
Thank you again!
Best Regards!
On Fri, Mar 11, 2011 at 4:27 PM, François AUGER <address@hidden> wrote:
Dear Ting Xu,

At 03:45 10/03/2011, ting xu wrote:
Greetings all,
I am trying to use wavelet method to analyze the brain signal. I found the results from 'tfrscalo' and 'cwt' were different. It is difficult for me to understand the following questions:
(1) In tfrscalo, the script showed that the morlet wavelet was generated by ha  = exp(-(2*log(10)/nha^2)*tha.^2).*exp(i*2*pi*f(ptr)*tha). Should the morlet be exp(-x^2/2)*cos(5*x)?

I think that exp(-x^2/2)*cos(5*x) is the Mexican hat wavelet, not the Morlet Wavelet.

(2) the scale 'a' and the frequency 'f' have a relationship f=fc*fs/a, here fc is the center frequency of a wavelet, fs is the sampling frequency. But in tfrscalo, f = logspace(log10(fmin),log10(fmax),N), a = logspace(log10(fmax/fmin),log10(1),N), it does not seem to satisfy f=fc*fs/a. I have confused about it.

The dilation factor is adimensional. If you multiply fc by fs, the result will be in s^{-2}, and can't be equal to the frequency  f.
I am not sure to be able to understand your question.

Best regards,

Can anyone help me please? Much appreciate!

Best regards,
Ting Xu

Neuropsychology and Applied Cognitive Neuroscience (NACN) Lab
Institute of Psychology
Chinese Academy of Sciences
Beijing 100101
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Francois Auger,

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