Deriving input-output relationship

[jayki]

hi frenz

i want to how to derive mathematical relation between dependent(output) and independent(input) variables when i know the relation between them at few samples.
cud someone help me out?
thanks in advance

 

[olgranpappy]

do you know anything about the functional form? even roughly how it should look? if not then there is no way to extrapolate from a few points to every point.

 

[jayki]

do you know anything about the functional form? even roughly how it should look? if not then there is no way to extrapolate from a few points to every point.

as i told , i know the relation between them at few samples. but i want to generalise as a mathematical relation between them

 

[robphy]

as i told , i know the relation between them at few samples. but i want to generalise as a mathematical relation between them

As olgranpappy says, you can't in general... without at least having a guess to the general form. Given a finite number of samples, you can fit it to a polynomial of sufficiently high degree. However, that polynomial is probably not what you are looking for.

http://en.wikipedia.org/wiki/Curve_fitting
In addition, note the diagrams in
http://slack.net/~ant/bl-synth/3.nyquist.html

 

[jayki]

thanks for ur response dear frenz...but let me clear my question again. I have a vector(x) and a vector(y) with the value of x at few points and corresponding value of y. I want to generalize the relation between them with that given samples.