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From: Abe Lau on 13 Dec 2009 23:02
Dear all,
I am trying to evaluate the wavelet power spectrum by means of the "cwt" command in Matlab but getting a bit confused with the cwt function.

As far as I understand, I am expecting the center frequency of each wavelet coefficient band is halved when the scale is increased by 1. ( as shown in this image http://pagesperso-orange.fr/polyvalens/clemens/wavelets/fig3-3.png )

However, using a Morlet ('morl') mother wavelet, and scal2frq to obtain the corresponding frequencies, it doesn't look like the frequency is halved for each increment of the scale.

scal2frq(1:5, 'morl') gives [0.8125 0.4063 0.2708 0.2031 0.1625]

Am I missing something here? basically I am trying to find the corresponding bandwidth of each wavelet coefficient band, so as to compute the wave power spectrum.

Thanks,
Abe
From: Rune Allnor on 14 Dec 2009 01:36
On 14 Des, 05:02, "Abe Lau" <a...(a)nonexistancegmail.com> wrote:

> Am I missing something here?  basically I am trying to find the corresponding bandwidth of each wavelet coefficient band, so as to compute the wave power spectrum.  

You are using the wrong tool. If you want the power
spectrum, use one of the standard methods to compute
the power spectrum.

Rune
From: Abe Lau on 14 Dec 2009 19:45
Rune Allnor <allnor(a)tele.ntnu.no> wrote in message <d9cb4561-d127-44d1-aba4-1f89512ac7d4(a)b2g2000yqi.googlegroups.com>...
> On 14 Des, 05:02, "Abe Lau" <a...(a)nonexistancegmail.com> wrote:
>
> > Am I missing something here? ?basically I am trying to find the corresponding bandwidth of each wavelet coefficient band, so as to compute the wave power spectrum. ?
>
> You are using the wrong tool. If you want the power
> spectrum, use one of the standard methods to compute
> the power spectrum.
>
> Rune

Rune, thanks for pointing it out. yeah I shouldn't have use the wavelet coefficient for power spectrum analysis.... I've lost track of the big picture.... should have step back :-)

but just for my understanding, is my interpretation of the central frequency and bandwidth of the wavelet coefficient band correct? Am I missing something that lead to the discrepancy between the output of "cwt" and what I am expecting to get?

Thanks,
Abe
From: Frank on 5 Jan 2010 12:36
On Dec 13 2009, 10:02 pm, "Abe Lau" <a...(a)nonexistancegmail.com>
wrote:
> Dear all,
> I am trying to evaluate the wavelet powerspectrumby means of the "cwt" command in Matlab but getting a bit confused with the cwt function.
>
> As far as I understand, I am expecting the centerfrequencyof each wavelet coefficient band is halved when the scale is increased by 1.  ( as shown in this imagehttp://pagesperso-orange.fr/polyvalens/clemens/wavelets/fig3-3.png)

I'm no expert, but I believe the band is halved for each decomposition
level, not each scale.

>
> However, using a Morlet ('morl') mother wavelet, and scal2frq to obtain the corresponding frequencies, it doesn't look like thefrequencyis halved for each increment of the scale.
>
> scal2frq(1:5, 'morl') gives [0.8125    0.4063    0.2708    0.2031    0.1625]
>

To get the halving, you need to use the decomposition levels, which
are power of 2 of scales. Try...

scal2frq(2.^(1:5),'mor') gives [0.406250000 0.203125000 0.101562500
0.050781250 0.025390625]

Hope this helps,
Frank
From: Abe Lau on 5 Jan 2010 18:43
Frank <fbleahy(a)yahoo.com> wrote in message <e1072225-046a-4806-8a7c-b15657124a90(a)u41g2000yqe.googlegroups.com>...
> On Dec 13 2009, 10:02 pm, "Abe Lau" <a...(a)nonexistancegmail.com>
> wrote:
> > Dear all,
> > I am trying to evaluate the wavelet powerspectrumby means of the "cwt" command in Matlab but getting a bit confused with the cwt function.
> >
> > As far as I understand, I am expecting the centerfrequencyof each wavelet coefficient band is halved when the scale is increased by 1.  ( as shown in this imagehttp://pagesperso-orange.fr/polyvalens/clemens/wavelets/fig3-3.png)
>
> I'm no expert, but I believe the band is halved for each decomposition
> level, not each scale.
>
> >
> > However, using a Morlet ('morl') mother wavelet, and scal2frq to obtain the corresponding frequencies, it doesn't look like thefrequencyis halved for each increment of the scale.
> >
> > scal2frq(1:5, 'morl') gives [0.8125    0.4063    0.2708    0.2031    0.1625]
> >
>
> To get the halving, you need to use the decomposition levels, which
> are power of 2 of scales. Try...
>
> scal2frq(2.^(1:5),'mor') gives [0.406250000 0.203125000 0.101562500
> 0.050781250 0.025390625]
>
> Hope this helps,
> Frank

ah, yes it gets halved with unit increment of decomposition level, not scale. Thanks for explaining Frank. :-)
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