Question about fitting periodic data

In summary, the conversation revolved around the speaker's poor experience with data fitting and their need for help. They mentioned that a Fourier series did not work for their data, but a 40-degree polynomial provided a good fit. However, the polynomial did not preserve periodicity and they were seeking advice on finding a better fitting function. Suggestions were made to use a combination of straight lines and include many terms in a Fourier series to get more accurate approximations. The conversation also touched on the idea that fitting with a polynomial of degree larger than 3 is not a good idea.
  • #1
ftft
21
0
My experience with data fitting is poor so I am in real need for help.
The potential in the following is periodic over [0,Pi]
-TvEuURwmnboNeDc1hN8aBhBkWcK4kYbjZhf4lPAZeE6fUeQvsEFcp56MUrHXa2Y9tATurVnxQLgm3EVsdR=w360-h211-no.gif

I need to find a fitting function that I can use to perform further mathematics. Fourier series does not work, but a 40-degree polynomial give the following fit
9iL8mytaLHj6GJp882dVJnCy-Nqr62qTLGS0dNx4JEdCKuJWhwD_DRFy3JoUr6X6kWcId3eSMQshzo9jtIM=w360-h215-no.gif

However, the polynomial does not preserve its periodicity over the cycle. Could someone please advice what I should do to get a good fitting function for my data?
 
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  • #2
Fitting with a polynomial with degree larger than 3 is a really bad idea.

Why don't you try to fit this function with a combination of straight lines?? And why do Fourier series not work?
 
  • #3
A set of straight lines for different ranges should fit best. A Fourier series should give reasonable approximations, but only if you include many terms.
 
  • #4
Looking at the vertical scale: Is your data set really constricted to the value -9.74771?
 

1. How do I determine the period of my periodic data?

The period of a periodic data can be determined by finding the time interval between two consecutive peaks or valleys in the data. This time interval will represent one full cycle and can be used as the period.

2. What is the best method for fitting periodic data?

The best method for fitting periodic data depends on the type of data and the specific patterns present. Some common methods include Fourier analysis, spline fitting, and least squares fitting. It is important to carefully consider the data and the desired outcome in order to choose the most appropriate method.

3. Can periodic data be fitted with a linear regression model?

No, periodic data cannot be accurately fitted with a linear regression model because it assumes a linear relationship between the variables. Periodic data typically follows a sinusoidal pattern, which cannot be captured by a linear model.

4. How can outliers affect the fitting of periodic data?

Outliers can significantly affect the fitting of periodic data by distorting the overall pattern and introducing errors. It is important to identify and remove outliers before attempting to fit the data in order to obtain more accurate results.

5. Is it possible to fit non-periodic data to a periodic function?

Yes, it is possible to fit non-periodic data to a periodic function using techniques such as Fourier analysis or spline fitting. However, the resulting fit may not accurately represent the underlying pattern of the data and should be interpreted with caution.

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