Comparing signal to a function

I have a system of sensors that located along X-axis (i.e. at x = 1,20,40,60,80,100).

The goal is to determine if the received signal in the sensors is a part of a predetermined function.

For example:

Assume that the predetermined function is Y:
x = 1:100; Y = 5*sin(0.5*x);
And the received signal is: I =  [7 22 19 11 22 35]
Note that the signal is at x = 1,20,40,60,80,100

Sometimes, the signal can be a partial of Y but with phase different.

What is the best way to compare the signal to the given function?

Answer 1

[Walter Roberson]

Every signal matches every function that is defined over the same range... to within some error margin.

You need to figure out what you want your error margin to be, and you need to decide whether a longer stretch whose error margin is within the cut-off is to be accepted if there is a sub-sequence over which the error margin is exceeded.