How do you find the trend in some functions?

[clemon!!]

how do you find the trend in some functions??

ok so I'm not sure how to phrase the question, and I'm not sure it will help me anyway but...


if i have say 3 complex functions, and i weight them... can i find the function that follows the trend?


sorry if that's very basic or silly.

basically, i want to weight silence, a traingle wave, a square wave, and a sine wave according to some percceptual quality. i then want to, based on that weighting, calculate the function that best instantiates that quality. of course it won't be perceived like that, but is there a term for the mathematical function of finding the trend of a number of functions according to some weighting?
thank you for any help ha :)

 

[clemon!!]

i guess i would find the function of wieghting by function, then find its highest value.

how do you find that new function though?

 

[chiro]

ok so I'm not sure how to phrase the question, and I'm not sure it will help me anyway but...

if i have say 3 complex functions, and i weight them... can i find the function that follows the trend?

sorry if that's very basic or silly.

basically, i want to weight silence, a traingle wave, a square wave, and a sine wave according to some percceptual quality. i then want to, based on that weighting, calculate the function that best instantiates that quality. of course it won't be perceived like that, but is there a term for the mathematical function of finding the trend of a number of functions according to some weighting?
thank you for any help ha :)

Hey clemon and welcome to the forums.

The first thing you should do is put your function in context.

Some primitives for decomposition and analysis will be preferred towards others because the context of the problem and data favors it.

The other thing to take note of is that usually the minimal representation is the best especially for explanatory purposes because it's going to be a lot easier to analyze, and captures the same characteristics that more complicated models would also show.

But again, if you miss context, you are missing 99%+ of everything.

The context is not easy, but it does have a tendency to become clearer with more effort, time, thought, and discussion with others that are also keen to find the same sorts of things.

In terms of if you wanted to 'fit' a model to a combination of models with weights, the way to do this formally is to first decompose the model into orthogonal parts and then project the data on to each orthogonal part thereby creating the model which you can then back-solve for the coeffecients.

This is done all the time in Fourier analysis and in regression modelling, and I recommend for general functions the integral transform approach.

 

[clemon!!]

i'm sorry but you have completely lost me :)

at this point in time precision doesn't matter that much. i have a test copy of originpro... but i don't know how to do this weighting thing.


sorry for being a berk !

 

[clemon!!]

hmm. maybe i do see what you mean - very very vaguely. this'll take a lot of thinking >_< !

 

[chiro]

hmm. maybe i do see what you mean - very very vaguely. this'll take a lot of thinking >_< !

Finding trends is not a science: it's an art and a science.

If finding trends and making predictions were easy, everyone would be using computers to pick lottery numbers, company stocks, and all kinds of pointless crap.

Even with this in mind, people are able to make predictions all the time without any kind of mathematical analysis and that should tell you something about being able to see trends before they happen.

The easiest thing to start making trends is to get a high level feel for the subject: looking at graphs and charts will make you focus on something a lot more narrow that would make you otherwise miss everything else that is happening.

Once you are able to do this, then the analysis and the mathematics can supplement you once you understand what the techniques actually do and how they do it, but before that you need to understand what it is you are trying to analyze in non-mathematical terms because if you don't, the symbols will just confuse the crap out of you.

 

[clemon!!]

oh right - so there's no computer package that will work out trends like this - even for very simple functions like sine waves?
is there any way to work out what function represents a more complex wave like a recording of human speech?
for some reason i thought there might be because of fft?

 

[chiro]

oh right - so there's no computer package that will work out trends like this - even for very simple functions like sine waves?

is there any way to work out what function represents a more complex wave like a recording of human speech? for some reason i thought there might be because of fft?

You should take a look at signal processing which is a common necessity in telecommunications and related engineering courses.

A more mathematical treatment can be found in integral transforms and things like wavelets, but I would suggest an engineering text first because the stuff is going to be completely applied and put in that context.