signals integration

[ivanjoel]

here., i would like to integrate a signal f(x) with another function p(x) . but p(x) is a morlet function (attached function below )whose parameters are not known  .. Is that possible to integrate entire signal with morlet in a specific range ??

[cbutcher]

What do you mean by "integrate entire signal with morlet in a specific range". Or indeed, "integrate a signal f(x) with another function p(x)".

It sounds like what you want to do is find the parameters of the function p(x) that fit p(x) to the measured values f(x) for some set of measurement data. Is that correct?

If so, you can use the "Non-Linear Curve Fit" VI available under the Mathematics palette. This can take either a VI or a "function string" as an input and determines the parameters to fit data to a function. In this case, you would write either a string or a VI that matches your Morlet curve (Morlet Wavelet) and then pass in your f(x) values, and it would produce the relevant parameters.

I confess, the Wikipedia page above seems quite intimidating to try and characterize the signal, but if this is what you want, you should go ahead and try (or at least confirm it is what you mean, and maybe I or others can help you try).

[cbutcher]

MATLAB lists a much simpler formula for the Morlet wavelet: https://uk.mathworks.com/help/wavelet/ref/morlet.html

Psi(x) = e^(-0.5 x^2) * cos(5x).

[ivanjoel]

i mean like .. i have an equation related to wavelet transform i.e.

integral (f(x)*p(x))dx  .. now being a basic-learner iam unable to create the signal p(x) i.e morlet wavelet and also unable to integrate two signals and obtain the output in labview ?? 

[ivanjoel]

if am having a contionous signal generating from simulate signal (express vi) and if iam considering it as the function which is to be made integral operation with another wavelet function .. any clear suggestion will be thankfull

[GerdW]

Hi Ivan,

if iam considering it as the function which is to be made integral operation with another wavelet function .. any clear suggestion will be thankfull

Well, any clear description of the problem will be helpful!

What is an "integral operation"? (What do you understand as "integral"?)

What is "another wavelet function"? (What do you mean with "wavelet function"?)

Can you provide an example VI? Can you provide example data and expected result?

Can you even provide a sketch of your desired algorithm drawn on a sheet of paper?

[ivanjoel]

okay thank you for replying !

here it is attachment ..what i want to implement is this equation (attached as cwt.jpg) where s(t) is any fundamental function i.e. square , sine , ramp etc.,and the other function in the attachment is a morlet function(attached as morlet.png) .i dont know exactly what was the expected output for it .. i want to learn how to implement this continuous integration in lab-view with these funtions !?

[cbutcher]

LabVIEW is capable of carrying out numerical integration. The VIs can be found under the Mathematics palette. However, this is numerical integration - not a symbolic integration.

It carries out integration essentially like breaking the interval into small pieces, and then taking the value of the function in that interval (different methods make different calculations, but for simple explanations, let's just say that it takes the value of the function at the midpoint of the interval) then adding them all up.

In your case, your function becomes the complex conjugate of the Morlet function, multiplied by your real input function. Do you have a functional form for the Morlet function yet? As I pointed out earlier (when I thought you were trying to fit data with the function... oops) the Wikipedia article for Morlet Wavelets has a much more complicated (although not that difficult to code in LabVIEW) definition of the function compared with the MATLAB morlet(..) function.

If your Morlet wavelet definition is real, then the complex conjugate is also real, and the same. As a result, then you just need to multiply your two functions together and you're set. I imagine the integration functions taking a VI reference work in a very similar fashion to the fitting functions. They can also take a function string, which might be easier to get started with, but will run much more slowly.