Finding the fundamental and overtones with amplitude and phase amongst samples in a time-signal

I have a time-signal containing a few hundred samples. The saved samples is exactly on period long. I need to find the fundamental (the sine-wave that has exactly one period from the first to the last sample) and optionally the first 16 overtones in the signal. I also need information about the amplitude and phase for the different sine waves). How can I do this and what toolbox is needed?

Earlier I used Excel with a plug-in from NumXL that was capable of doing a DFT and IDFT. When doing a IDFT I was able to chose whitch components to include, e.g. the dc-offset and the fundamental only. It worked fine but of some reasons I need to use Matlab instead.

Below is a picture showing the result when doing this operation in excel (IDFT with the first two components).

Answer 1

[David Ding]

Hi Ejje,

I understand that you have a periodic time sample (of one period) and you would like to perform Fourier Series analysis to find the corresponding tones of the signal. In MATLAB, you may do so via fitting the signal with a curve comprised of the Fourier Series (up to how many tones you would like to include). This requires only the "Curve Fitting Toolbox".

Example below:

https://www.mathworks.com/help/curvefit/fourier.html

More about Curve Fitting Toolbox below:

https://www.mathworks.com/help/curvefit/index.html

Thanks,

David