CWT or DWT , wavelets

[ptc-4374678]

Hello everyone!

I have a problem with the wavelets in Mathcad 14 , I read, that we can use wavelets, CWT or DWT to determine various errors in signal or function

There is a mathematical model defined by a system of two differential equations

T1*y'+y=k1*x

T2*z'+z=k2*y

Where x = sin(t)

At 10 seconds the value of T1(or T2,on my opinion) is changing, and I want to trace this change using wavelet analysis. Read the literature, there should be a characteristic spike in the graph of the wavelet image of the resulting function z(t). But i can't get it:(

I have the installed Wavelet Extension for Mathcad

At the bottom put file with my attempts solving this problem

[ValeryOchkov]

Поменяйте имя файла на английское. А то тут у людей проблемы будут со скачиванием.

Change the file name in English. There are problems with the download.

[PhilipOakley]

Stansilav,

You would be better substituting your formulas into one of the wavelet extension pack's handbook files. It is the best way of getting to see something that matches 'text books'.

I started by simply substituting a picture I had instead of Lena's in the signal processing example (section 5.2) - you should be able to simply insert your function at the right point in that sheet.

It takes a while to get used to appreciating what you see from the results - we are all unused to 'visualising' the 'pyramid' of results.

In your example you only evaluated the wavelets() at zero.

Finally, watch out for the zero point offset. If you use a built in wavelet (unmodified) the system 'knows' its offset (remember mathcad counts from 0...N, while wavelets are typically -N/2...+N/2), but if you use your own wavelet, or modify the mathcad wavelets it forgets the offset (-N/2) and just counts from zero, causing soem confusion.

The folks that wrote the wvelet pack are (mostly) no longer at PTC so PTC doesn't know what it has!

Philip

[ptc-4374678]

Change the name of my file

2 Phlilip:

How can I find the example of Lena' signal processing

I'm newbie here,and dunno where is 5.2 section

[VladimirN]

Stanislav Shpilevoy wrote:

...How can I find the example of Lena' signal processing

I'm newbie here,and dunno where is 5.2 section ...

You need in a main menu, select "Help" -> "E-books" -> "Wavelets Extension Pack" (see attach).

[ptc-4374678]

the question is still open

i did all the things I can, like CWT with this 3D-plane,filtrate original signal with DWT ...

can't receive the characteristic spike

[PhilipOakley]

Stansilav,

I have added your set-up into the example tutorial page for the WAVE function - see attached. I have had to put it as a personal document at http://communities.ptc.com/docs/DOC-2445 because this is labelled as a discussion...

The things I noted was that you had place the transition exactly at the half way boundary, so any of the binary decimation wavelets will never see the step, because it is always exactly between two smooth regions.

The other thing to beware of the way that the solver solution is presented - that is it is an interpolation function between data points, so you you can't get great resolution anyway.

Have a look at Wavelet Galerkin methods for solving the original differential equations directly as wavelets...... e.g. http://math.fullerton.edu/mathews/n2003/GalerkinMod.html

[VladimirN]

Philip Oakley wrote:

... WAVE function - see attached. I have had to put it as a personal document at http://communities.ptc.com/docs/DOC-2445 because this is labelled as a discussion... ...

What does this mean? The same Mathcad document (for Mathcad 14/15 version) normally attached to the message.

[PhilipOakley]

VladimirN. wrote:

Philip Oakley wrote:

... WAVE function - see attached. I have had to put it as a personal document at http://communities.ptc.com/docs/DOC-2445 because this is labelled as a discussion... ...

What does this mean? The same Mathcad document (for Mathcad 14/15 version) normally attached to the message.

I couldn't find the 'attach' button as I prepared the reply (I still can't see it as I type this - I could insert a video or image, or link, but no attachment!).

The poor web interface is one of the reasons I don't read / contribute any more.

[VladimirN]

You need to use the option (in the right corner) "Use advanced editor" (and then you can find "Attach Files" button):

[ptc-4374678]

Thx a lot , Philip!

And one more question: How can I understand, which parameter is changing , T1 or T2?

Can wavelet transformation help me with this problem?