Logarithmic Scale Conversion

[Pero2912]

Hello people.

So I'm trying to figure this out:
here is a sensitivity characteristics of my gas sensor, and the both x and y scales are logarithmic.

Now, i'd like to interpolate this data but I guess I can not use simple linear method, like y=(y2-y1)/(x2-x1)*x+y1. What do you think?

Regards,

Pero

 

[BradtheRad]

You must take the log of your data points, then interpolate, then take the antilog of the result.

 

[Pero2912]

Thanks for answer Brad!
But, could you be so nice and provide me some explanation of why is this method legitimate? Or, link some references if it's easier for you.

 

[FvM]

A straight line in log-log scale corresponds to a function Y = X^a. It can be modelled in software.

 

[Pero2912]

Solved it! Thanks for advice.
but if somebody wants to know, I used analytic approximation y = C/sqrt(x),

 

[FvM]

I used analytic approximation y = C/sqrt(x)

Slope of different curves in the above characteristic corresponds to exponents between -0.3 and -0.63, so -0.5 (1/sqrt) is well in the middle. We could try to fit the exponent in an individual calibration, but that's probably beyond reasonable efforts for this sensor.

 

[Pero2912]

Yeah, i also came up with 0.67 for alcohol. But why do you use negative coefficients? I mean, y = 0.67/sqrt(x) works fine for me.

 

[FvM]

sqrt(x) = x^0.5
1/sqrt(x) = x^-0.5
Thus the negative exponent.

 

[Pero2912]

Yeah, you're right. I didnt pay good attention on what you wrote above.