Fit sinc square to FFT peak

Good evening,

I have an FFT peak to which I need to fit a sinc square function to obtain an improved estimate for the peak location and peak width. However there doesn't seem to be a function to perform this properly. Has someone done this before/knows the correct function? Below is the figure in question. Any help would be much appreciated.

Answer 1

[Matt J]

A more direct method would be to use the Curve Fitting Toolbox to fit a Fourier Series

https://www.mathworks.com/help/curvefit/list-of-library-models-for-curve-and-surface-fitting.html#btbcxno-1

[Tobias Reichold]

So if I limited the range about the peak to e.g. two minima either side would this fourier series fit produce a sinc? In your link there are 8 variants. Each just increases the number of coefficients? Would e.g. two be enough here?

[Matt J]

I meant that you should do all the analysis in the time domain. Fitting sincs in the frequency domain is equivalent to fitting sines and cosines in the time domain, which the Curve Fitting Toolbox already provides methods for.

But now I realize that you said sinc-squared. So you are really trying to fit triangle waves in the time domain?

[Tobias Reichold]

Not quite. Basically I have a sinusoidal fringe pattern I extract from an optical spectrum line. I have recovered the fringe frequency by taking a 1D fft and getting the frequency in cycles as shown previously. But rather than just taking the point of highest magnitude (other than the DC term) I thought fitting a sinc squared would be better as it immediately gives the peak position and width. But I didn't find any function to implement this.

[Matt J]

I don't really understand though why your model is a sinc-squared. A sinc-squared spectrum is the Fourier transform of a triangular time domain pulse.