Finding a function to best fit a curve

• Mathematica
• kelly0303
In summary, the speaker is looking for the best function to fit an upside down resonance curve that goes down slowly and then has a fast rise. They are also considering using a log scale for the ordinate and mention a video found through a Google search.

kelly0303

Hello! I want to fit a function to the curve I attached (the first image shows the full curve, while the second one is a zoom-in in the final region). Please ignore the vertical lines, what I care about is the main, central curve. It basically goes down slowly and then it has a fast rise. What is the best function that I can try to use to fit this kind of curve? Thank you!

Attachments

• Screen Shot 2019-11-29 at 04.06.25.png
15.3 KB · Views: 239
• Screen Shot 2019-11-29 at 03.59.27.png
14.2 KB · Views: 231
What is it ?

Looks like an upside down resonance curve like

(from here)

Also: googling 'low-pass filter resonance curve' yields this nice video.

Perhaps you can try a log scale for the ordinate ?

1. What is a function?

A function is a mathematical relationship between two variables, where one variable (the independent variable) is related to the other variable (the dependent variable) through a set of rules or equations.

2. What is curve fitting?

Curve fitting is the process of finding a mathematical function that closely matches a set of data points. The goal is to find a function that can accurately predict the values of the dependent variable based on the values of the independent variable.

3. Why is finding a function to best fit a curve important?

Finding a function to best fit a curve is important because it allows us to understand and make predictions about the relationship between two variables. This can be useful in various fields such as statistics, physics, economics, and engineering.

4. What are some common methods used for curve fitting?

Some common methods used for curve fitting include linear regression, polynomial regression, exponential regression, and logarithmic regression. These methods involve finding the best fitting line or curve that minimizes the distance between the data points and the predicted values.

5. How do you determine the best function to fit a curve?

The best function to fit a curve is determined by comparing the fit of different functions using a measure of goodness of fit, such as the coefficient of determination (R-squared) or the root mean square error (RMSE). The function with the highest goodness of fit is considered the best fit for the curve.

• MATLAB, Maple, Mathematica, LaTeX
Replies
8
Views
2K
• MATLAB, Maple, Mathematica, LaTeX
Replies
14
Views
2K
• MATLAB, Maple, Mathematica, LaTeX
Replies
12
Views
5K
• MATLAB, Maple, Mathematica, LaTeX
Replies
5
Views
2K
• General Math
Replies
9
Views
1K
• Astronomy and Astrophysics
Replies
1
Views
1K
• MATLAB, Maple, Mathematica, LaTeX
Replies
8
Views
1K
• Precalculus Mathematics Homework Help
Replies
7
Views
1K
• General Math
Replies
16
Views
2K
• General Math
Replies
5
Views
287